Daily Papers

Large language models (LLMs) are evolving from conversational systems into strong reasoners for tasks such as Olympiad mathematics and competitive programming. While scaling parameters and test-time computation has driven progress, a key bottleneck is the lack of high-quality training problems: human-curated datasets are costly and limited, while existing synthetic corpora are often too easy or narrow. PromptCoT 1.0 showed that injecting rationales into prompt synthesis increases problem difficulty. Building on this, we present PromptCoT 2.0, a scalable framework that replaces hand-crafted heuristics with an expectation-maximization (EM) loop, where rationales are iteratively refined to guide prompt construction. This produces problems that are both harder and more diverse than prior corpora. The synthetic prompts support two post-training regimes: (1) Self-Play, where strong models improve autonomously via verifiable feedback without stronger teachers; and (2) Supervised Fine-Tuning (SFT), where weaker models learn from teacher-distilled traces. Extensive experiments demonstrate the effectiveness of this approach. In self-play, applying PromptCoT 2.0 to Qwen3-30B-A3B-Thinking-2507 sets new state-of-the-art results at the 30B scale, with +4.4, +4.8, and +5.3 on AIME 24/25 and HMMT 25, +6.1 and +5.0 on LiveCodeBench v5/v6, and +35 Elo on Codeforces. In SFT, training Qwen2.5-7B-Instruct solely on synthetic prompts boosts accuracy to 73.1 (AIME 24), 65.6 (AIME 25), and 53.4 (LiveCodeBench v5), surpassing models trained on human or hybrid data. Analyses further confirm that PromptCoT 2.0 yields fundamentally harder and distributionally distinct problems. These results establish prompt synthesis as a new axis for scaling reasoning and position PromptCoT 2.0 as a scalable foundation for future open-source models. The implementation is available at https://github.com/inclusionAI/PromptCoT.

Expectation maximization (EM) algorithm is to find maximum likelihood solution for models having latent variables. A typical example is Gaussian Mixture Model (GMM) which requires Gaussian assumption, however, natural images are highly non-Gaussian so that GMM cannot be applied to perform clustering task on pixel space. To overcome such limitation, we propose a GAN based EM learning framework that can maximize the likelihood of images and estimate the latent variables with only the constraint of L-Lipschitz continuity. We call this model GAN-EM, which is a framework for image clustering, semi-supervised classification and dimensionality reduction. In M-step, we design a novel loss function for discriminator of GAN to perform maximum likelihood estimation (MLE) on data with soft class label assignments. Specifically, a conditional generator captures data distribution for K classes, and a discriminator tells whether a sample is real or fake for each class. Since our model is unsupervised, the class label of real data is regarded as latent variable, which is estimated by an additional network (E-net) in E-step. The proposed GAN-EM achieves state-of-the-art clustering and semi-supervised classification results on MNIST, SVHN and CelebA, as well as comparable quality of generated images to other recently developed generative models.

Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often involves non-convex and high-dimensional objective functions, imposing difficult computational and statistical challenges. The classic expectation-maximization (EM) algorithm is a computationally thrifty iterative method that maximizes a surrogate function minorizing the log-likelihood of observed data in each iteration, which however suffers from bad local maxima even in the special case of the standard Gaussian mixture model with common isotropic covariance matrices. On the other hand, recent studies reveal that the unique global solution of a semidefinite programming (SDP) relaxed K-means achieves the information-theoretically sharp threshold for perfectly recovering the cluster labels under the standard Gaussian mixture model. In this paper, we extend the SDP approach to a general setting by integrating cluster labels as model parameters and propose an iterative likelihood adjusted SDP (iLA-SDP) method that directly maximizes the exact observed likelihood in the presence of data heterogeneity. By lifting the cluster assignment to group-specific membership matrices, iLA-SDP avoids centroids estimation -- a key feature that allows exact recovery under well-separateness of centroids without being trapped by their adversarial configurations. Thus iLA-SDP is less sensitive than EM to initialization and more stable on high-dimensional data. Our numeric experiments demonstrate that iLA-SDP can achieve lower mis-clustering errors over several widely used clustering methods including K-means, SDP and EM algorithms.

While diffusion models can learn complex distributions, sampling requires a computationally expensive iterative process. Existing distillation methods enable efficient sampling, but have notable limitations, such as performance degradation with very few sampling steps, reliance on training data access, or mode-seeking optimization that may fail to capture the full distribution. We propose EM Distillation (EMD), a maximum likelihood-based approach that distills a diffusion model to a one-step generator model with minimal loss of perceptual quality. Our approach is derived through the lens of Expectation-Maximization (EM), where the generator parameters are updated using samples from the joint distribution of the diffusion teacher prior and inferred generator latents. We develop a reparametrized sampling scheme and a noise cancellation technique that together stabilizes the distillation process. We further reveal an interesting connection of our method with existing methods that minimize mode-seeking KL. EMD outperforms existing one-step generative methods in terms of FID scores on ImageNet-64 and ImageNet-128, and compares favorably with prior work on distilling text-to-image diffusion models.

Existing preference optimization methods are mainly designed for directly learning from human feedback with the assumption that paired examples (preferred vs. dis-preferred) are available. In contrast, we propose a method that can leverage unpaired preferred or dis-preferred examples, and works even when only one type of feedback (positive or negative) is available. This flexibility allows us to apply it in scenarios with varying forms of feedback and models, including training generative language models based on human feedback as well as training policies for sequential decision-making problems, where learned (value) functions are available. Our approach builds upon the probabilistic framework introduced in (Dayan and Hinton, 1997), which proposes to use expectation-maximization (EM) to directly optimize the probability of preferred outcomes (as opposed to classic expected reward maximization). To obtain a practical algorithm, we identify and address a key limitation in current EM-based methods: when applied to preference optimization, they solely maximize the likelihood of preferred examples, while neglecting dis-preferred samples. We show how one can extend EM algorithms to explicitly incorporate dis-preferred outcomes, leading to a novel, theoretically grounded, preference optimization algorithm that offers an intuitive and versatile way to learn from both positive and negative feedback.

Diffusion models recently proved to be remarkable priors for Bayesian inverse problems. However, training these models typically requires access to large amounts of clean data, which could prove difficult in some settings. In this work, we present a novel method based on the expectation-maximization algorithm for training diffusion models from incomplete and noisy observations only. Unlike previous works, our method leads to proper diffusion models, which is crucial for downstream tasks. As part of our method, we propose and motivate an improved posterior sampling scheme for unconditional diffusion models. We present empirical evidence supporting the effectiveness of our method.

Latent variable models (LVMs) with discrete compositional latents are an important but challenging setting due to a combinatorially large number of possible configurations of the latents. A key tradeoff in modeling the posteriors over latents is between expressivity and tractable optimization. For algorithms based on expectation-maximization (EM), the E-step is often intractable without restrictive approximations to the posterior. We propose the use of GFlowNets, algorithms for sampling from an unnormalized density by learning a stochastic policy for sequential construction of samples, for this intractable E-step. By training GFlowNets to sample from the posterior over latents, we take advantage of their strengths as amortized variational inference algorithms for complex distributions over discrete structures. Our approach, GFlowNet-EM, enables the training of expressive LVMs with discrete compositional latents, as shown by experiments on non-context-free grammar induction and on images using discrete variational autoencoders (VAEs) without conditional independence enforced in the encoder.

Large language models (LLMs) exhibit hallucinations in long-form question-answering tasks across various domains and wide applications. Current hallucination detection and mitigation datasets are limited in domains and sizes, which struggle to scale due to prohibitive labor costs and insufficient reliability of existing hallucination annotators. To facilitate the scalable oversight of LLM hallucinations, this paper introduces an iterative self-training framework that simultaneously and progressively scales up the hallucination annotation dataset and improves the accuracy of the hallucination annotator. Based on the Expectation Maximization (EM) algorithm, in each iteration, the framework first applies a hallucination annotation pipeline to annotate a scaled dataset and then trains a more accurate hallucination annotator on the dataset. This new hallucination annotator is adopted in the hallucination annotation pipeline used for the next iteration. Extensive experimental results demonstrate that the finally obtained hallucination annotator with only 7B parameters surpasses the performance of GPT-4 and obtains new state-of-the-art hallucination detection results on HaluEval and HalluQA by zero-shot inference. Such an annotator can not only evaluate the hallucination levels of various LLMs on the large-scale dataset but also help to mitigate the hallucination of LLMs generations, with the Natural Language Inference (NLI) metric increasing from 25% to 37% on HaluEval.

Fine-tuning language models~(LMs) on human-generated data remains a prevalent practice. However, the performance of such models is often limited by the quantity and diversity of high-quality human data. In this paper, we explore whether we can go beyond human data on tasks where we have access to scalar feedback, for example, on math problems where one can verify correctness. To do so, we investigate a simple self-training method based on expectation-maximization, which we call ReST^{EM}, where we (1) generate samples from the model and filter them using binary feedback, (2) fine-tune the model on these samples, and (3) repeat this process a few times. Testing on advanced MATH reasoning and APPS coding benchmarks using PaLM-2 models, we find that ReST^{EM} scales favorably with model size and significantly surpasses fine-tuning only on human data. Overall, our findings suggest self-training with feedback can substantially reduce dependence on human-generated data.

Entropy minimization (EM) trains the model to concentrate even more probability mass on its most confident outputs. We show that this simple objective alone, without any labeled data, can substantially improve large language models' (LLMs) performance on challenging math, physics, and coding tasks. We explore three approaches: (1) EM-FT minimizes token-level entropy similarly to instruction finetuning, but on unlabeled outputs drawn from the model; (2) EM-RL: reinforcement learning with negative entropy as the only reward to maximize; (3) EM-INF: inference-time logit adjustment to reduce entropy without any training data or parameter updates. On Qwen-7B, EM-RL, without any labeled data, achieves comparable or better performance than strong RL baselines such as GRPO and RLOO that are trained on 60K labeled examples. Furthermore, EM-INF enables Qwen-32B to match or exceed the performance of proprietary models like GPT-4o, Claude 3 Opus, and Gemini 1.5 Pro on the challenging SciCode benchmark, while being 3x more efficient than self-consistency and sequential refinement. Our findings reveal that many pretrained LLMs possess previously underappreciated reasoning capabilities that can be effectively elicited through entropy minimization alone, without any labeled data or even any parameter updates.

In this paper, we present a cross-entropy optimization method for hyperparameter optimization in stochastic gradient-based approaches to train deep neural networks. The value of a hyperparameter of a learning algorithm often has great impact on the performance of a model such as the convergence speed, the generalization performance metrics, etc. While in some cases the hyperparameters of a learning algorithm can be part of learning parameters, in other scenarios the hyperparameters of a stochastic optimization algorithm such as Adam [5] and its variants are either fixed as a constant or are kept changing in a monotonic way over time. We give an in-depth analysis of the presented method in the framework of expectation maximization (EM). The presented algorithm of cross-entropy optimization for hyperparameter optimization of a learning algorithm (CEHPO) can be equally applicable to other areas of optimization problems in deep learning. We hope that the presented methods can provide different perspectives and offer some insights for optimization problems in different areas of machine learning and beyond.

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The model is instantiated as a mixture of multi-task GPs with common mean processes. A variational EM algorithm is derived for dealing with the optimisation of the hyper-parameters along with the hyper-posteriors' estimation of latent variables and processes. We establish explicit formulas for integrating the mean processes and the latent clustering variables within a predictive distribution, accounting for uncertainty on both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which enhances the performances when dealing with group-structured data. The model handles irregular grid of observations and offers different hypotheses on the covariance structure for sharing additional information across tasks. The performances on both clustering and prediction tasks are assessed through various simulated scenarios and real datasets. The overall algorithm, called MagmaClust, is publicly available as an R package.

We provide a probabilistic interpretation of attention and show that the standard dot-product attention in transformers is a special case of Maximum A Posteriori (MAP) inference. The proposed approach suggests the use of Expectation Maximization algorithms for online adaptation of key and value model parameters. This approach is useful for cases in which external agents, e.g., annotators, provide inference-time information about the correct values of some tokens, e.g, the semantic category of some pixels, and we need for this new information to propagate to other tokens in a principled manner. We illustrate the approach on an interactive semantic segmentation task in which annotators and models collaborate online to improve annotation efficiency. Using standard benchmarks, we observe that key adaptation boosts model performance (sim10% mIoU) in the low feedback regime and value propagation improves model responsiveness in the high feedback regime. A PyTorch layer implementation of our probabilistic attention model will be made publicly available here: https://github.com/apple/ml-probabilistic-attention.

The electrocardiogram (ECG) is an essential non-invasive diagnostic tool for assessing cardiac conditions. Existing automatic interpretation methods suffer from limited generalizability, focusing on a narrow range of cardiac conditions, and typically depend on raw physiological signals, which may not be readily available in resource-limited settings where only printed or digital ECG images are accessible. Recent advancements in multimodal large language models (MLLMs) present promising opportunities for addressing these challenges. However, the application of MLLMs to ECG image interpretation remains challenging due to the lack of instruction tuning datasets and well-established ECG image benchmarks for quantitative evaluation. To address these challenges, we introduce ECGInstruct, a comprehensive ECG image instruction tuning dataset of over one million samples, covering a wide range of ECG-related tasks from diverse data sources. Using ECGInstruct, we develop PULSE, an MLLM tailored for ECG image comprehension. In addition, we curate ECGBench, a new evaluation benchmark covering four key ECG image interpretation tasks across nine different datasets. Our experiments show that PULSE sets a new state-of-the-art, outperforming general MLLMs with an average accuracy improvement of 15% to 30%. This work highlights the potential of PULSE to enhance ECG interpretation in clinical practice.

Large language models (LLMs) solve problems more accurately and interpretably when instructed to work out the answer step by step using a ``chain-of-thought'' (CoT) prompt. One can also improve LLMs' performance on a specific task by supervised fine-tuning, i.e., by using gradient ascent on some tunable parameters to maximize the average log-likelihood of correct answers from a labeled training set. Naively combining CoT with supervised tuning requires supervision not just of the correct answers, but also of detailed rationales that lead to those answers; these rationales are expensive to produce by hand. Instead, we propose a fine-tuning strategy that tries to maximize the marginal log-likelihood of generating a correct answer using CoT prompting, approximately averaging over all possible rationales. The core challenge is sampling from the posterior over rationales conditioned on the correct answer; we address it using a simple Markov-chain Monte Carlo (MCMC) expectation-maximization (EM) algorithm inspired by the self-taught reasoner (STaR), memoized wake-sleep, Markovian score climbing, and persistent contrastive divergence. This algorithm also admits a novel control-variate technique that drives the variance of our gradient estimates to zero as the model improves. Applying our technique to GSM8K and the tasks in BIG-Bench Hard, we find that this MCMC-EM fine-tuning technique typically improves the model's accuracy on held-out examples more than STaR or prompt-tuning with or without CoT.

During the preference optimization of large language models (LLMs), distribution shifts may arise between newly generated model samples and the data used to train the reward model (RM). This shift reduces the efficacy of the RM, which in turn negatively impacts the performance of the policy model (PM). To address this challenge, we propose Mutual-Taught, a self-training method that iteratively improves both the PM and RM without requiring additional human annotation. Our approach mirrors the expectation-maximization (EM) algorithm. In the E-step, the PM is updated using feedback from the current RM, guiding the PM toward a better approximation of the latent optimal preference distribution. In the M-step, we update the RM by constructing training data from the outputs of the PM before and after the E-step update. This process ensures that the RM adapts to the evolving policy distribution. Experimental results demonstrate that this iterative approach leads to consistent improvements in both models. Specifically, our 8B policy model, LLaMA-3-8B-Instruct-MT, achieves a length-controlled win rate of 54.1\% on AlpacaEval-2, while our 8B reward model, FsfairX-LLaMA3-RM-MT, performs on par with GPT-4o-2024-08-06 on RewardBench.

Transductive few-shot learning has recently triggered wide attention in computer vision. Yet, current methods introduce key hyper-parameters, which control the prediction statistics of the test batches, such as the level of class balance, affecting performances significantly. Such hyper-parameters are empirically grid-searched over validation data, and their configurations may vary substantially with the target dataset and pre-training model, making such empirical searches both sub-optimal and computationally intractable. In this work, we advocate and introduce the unrolling paradigm, also referred to as "learning to optimize", in the context of few-shot learning, thereby learning efficiently and effectively a set of optimized hyper-parameters. Specifically, we unroll a generalization of the ubiquitous Expectation-Maximization (EM) optimizer into a neural network architecture, mapping each of its iterates to a layer and learning a set of key hyper-parameters over validation data. Our unrolling approach covers various statistical feature distributions and pre-training paradigms, including recent foundational vision-language models and standard vision-only classifiers. We report comprehensive experiments, which cover a breadth of fine-grained downstream image classification tasks, showing significant gains brought by the proposed unrolled EM algorithm over iterative variants. The achieved improvements reach up to 10% and 7.5% on vision-only and vision-language benchmarks, respectively.

Despite the great advance of Multimodal Large Language Models (MLLMs) in both instruction dataset building and benchmarking, the independence of training and evaluation makes current MLLMs hard to further improve their capability under the guidance of evaluation results with a relatively low human cost. In this paper, we propose MLLM-DataEngine, a novel closed-loop system that bridges data generation, model training, and evaluation. Within each loop iteration, the MLLM-DataEngine first analyze the weakness of the model based on the evaluation results, then generate a proper incremental dataset for the next training iteration and enhance the model capability iteratively. Compared with previous data collection methods which are separate from the benchmarking, the data generated by MLLM-DataEngine shows better targeting, quality, and correctness. For targeting, we propose an Adaptive Bad-case Sampling module, which adjusts the ratio of different types of data within each incremental dataset based on the benchmarking results. For quality, we resort to GPT-4 to generate high-quality data with each given data type. For correctness, prompt design is critical for the data generation results. Rather than previous hand-crafted prompt, we propose an Interactive Prompt Optimization strategy, which optimizes the prompt with the multi-round interaction between human and GPT, and improve the correctness of generated data greatly. Through extensive experiments, we find our MLLM-DataEngine could boost the MLLM capability in a targeted and automatic manner, with only a few human participation. We hope it could be a general solution for the following MLLMs building. The MLLM-DataEngine has been open-sourced and is now available at https://github.com/opendatalab/MLLM-DataEngine.

We study infinite-horizon average-reward Markov decision processes (AMDPs) in the context of general function approximation. Specifically, we propose a novel algorithmic framework named Local-fitted Optimization with OPtimism (LOOP), which incorporates both model-based and value-based incarnations. In particular, LOOP features a novel construction of confidence sets and a low-switching policy updating scheme, which are tailored to the average-reward and function approximation setting. Moreover, for AMDPs, we propose a novel complexity measure -- average-reward generalized eluder coefficient (AGEC) -- which captures the challenge of exploration in AMDPs with general function approximation. Such a complexity measure encompasses almost all previously known tractable AMDP models, such as linear AMDPs and linear mixture AMDPs, and also includes newly identified cases such as kernel AMDPs and AMDPs with Bellman eluder dimensions. Using AGEC, we prove that LOOP achieves a sublinear mathcal{O}(poly(d, sp(V^*)) Tbeta ) regret, where d and beta correspond to AGEC and log-covering number of the hypothesis class respectively, sp(V^*) is the span of the optimal state bias function, T denotes the number of steps, and mathcal{O} (cdot) omits logarithmic factors. When specialized to concrete AMDP models, our regret bounds are comparable to those established by the existing algorithms designed specifically for these special cases. To the best of our knowledge, this paper presents the first comprehensive theoretical framework capable of handling nearly all AMDPs.

Multi-modal Large Language Models (MLLMs) are gaining significant attention for their ability to process multi-modal data, providing enhanced contextual understanding of complex problems. MLLMs have demonstrated exceptional capabilities in tasks such as Visual Question Answering (VQA); however, they often struggle with fundamental engineering problems, and there is a scarcity of specialized datasets for training on topics like digital electronics. To address this gap, we propose a benchmark dataset called ElectroVizQA specifically designed to evaluate MLLMs' performance on digital electronic circuit problems commonly found in undergraduate curricula. This dataset, the first of its kind tailored for the VQA task in digital electronics, comprises approximately 626 visual questions, offering a comprehensive overview of digital electronics topics. This paper rigorously assesses the extent to which MLLMs can understand and solve digital electronic circuit questions, providing insights into their capabilities and limitations within this specialized domain. By introducing this benchmark dataset, we aim to motivate further research and development in the application of MLLMs to engineering education, ultimately bridging the performance gap and enhancing the efficacy of these models in technical fields.

In this paper, we present an algorithm for the sparse signal recovery problem that incorporates damped Gaussian generalized approximate message passing (GGAMP) into Expectation-Maximization (EM)-based sparse Bayesian learning (SBL). In particular, GGAMP is used to implement the E-step in SBL in place of matrix inversion, leveraging the fact that GGAMP is guaranteed to converge with appropriate damping. The resulting GGAMP-SBL algorithm is much more robust to arbitrary measurement matrix A than the standard damped GAMP algorithm while being much lower complexity than the standard SBL algorithm. We then extend the approach from the single measurement vector (SMV) case to the temporally correlated multiple measurement vector (MMV) case, leading to the GGAMP-TSBL algorithm. We verify the robustness and computational advantages of the proposed algorithms through numerical experiments.

We present EMDB, the Electromagnetic Database of Global 3D Human Pose and Shape in the Wild. EMDB is a novel dataset that contains high-quality 3D SMPL pose and shape parameters with global body and camera trajectories for in-the-wild videos. We use body-worn, wireless electromagnetic (EM) sensors and a hand-held iPhone to record a total of 58 minutes of motion data, distributed over 81 indoor and outdoor sequences and 10 participants. Together with accurate body poses and shapes, we also provide global camera poses and body root trajectories. To construct EMDB, we propose a multi-stage optimization procedure, which first fits SMPL to the 6-DoF EM measurements and then refines the poses via image observations. To achieve high-quality results, we leverage a neural implicit avatar model to reconstruct detailed human surface geometry and appearance, which allows for improved alignment and smoothness via a dense pixel-level objective. Our evaluations, conducted with a multi-view volumetric capture system, indicate that EMDB has an expected accuracy of 2.3 cm positional and 10.6 degrees angular error, surpassing the accuracy of previous in-the-wild datasets. We evaluate existing state-of-the-art monocular RGB methods for camera-relative and global pose estimation on EMDB. EMDB is publicly available under https://ait.ethz.ch/emdb

Large language models (LLMs) have shown remarkable capabilities, but still struggle with processing extensive contexts, limiting their ability to maintain coherence and accuracy over long sequences. In contrast, the human brain excels at organising and retrieving episodic experiences across vast temporal scales, spanning a lifetime. In this work, we introduce EM-LLM, a novel approach that integrates key aspects of human episodic memory and event cognition into LLMs, enabling them to effectively handle practically infinite context lengths while maintaining computational efficiency. EM-LLM organises sequences of tokens into coherent episodic events using a combination of Bayesian surprise and graph-theoretic boundary refinement in an on-line fashion. When needed, these events are retrieved through a two-stage memory process, combining similarity-based and temporally contiguous retrieval for efficient and human-like access to relevant information. Experiments on the LongBench dataset demonstrate EM-LLM's superior performance, outperforming the state-of-the-art InfLLM model with an overall relative improvement of 4.3% across various tasks, including a 33% improvement on the PassageRetrieval task. Furthermore, our analysis reveals strong correlations between EM-LLM's event segmentation and human-perceived events, suggesting a bridge between this artificial system and its biological counterpart. This work not only advances LLM capabilities in processing extended contexts but also provides a computational framework for exploring human memory mechanisms, opening new avenues for interdisciplinary research in AI and cognitive science.

While current Multimodal Large Language Models (MLLMs) have demonstrated proficiency in reasoning tasks such as mathematics and logic, their capacity for long-chain reflective reasoning, a prerequisite for solving complex real-world problems, remains largely underexplored. In this work, we first conduct an extensive empirical investigation to evaluate this capability. Leveraging a carefully designed data synthesis engine, we construct MM-HELIX, a multimodal benchmark consisting 1,260 samples of 42 challenging synthetic tasks that require iterative thinking and backtracking. Empirical results on this benchmark reveal that existing MLLMs exhibit significant performance deficits in long-chain reflective reasoning. To address this limitation, we generate post-training data and further explore learning paradigms for exploiting such data. We first develop the Step-Elicited Response Generation pipeline to create MM-HELIX-100K, a large-scale dataset of 100k high-quality, reflective reasoning traces for instruction-tuning stage. Given that standard Reinforcement Learning fails on complex tasks due to sparse reward signals and catastrophic forgetting after Supervised Fine-Tuning, we propose Adaptive Hybrid Policy Optimization (AHPO), a novel training strategy that dynamically unifies offline supervision and online optimization into a single stage. This strategy enables the model to learn from expert data when rewards are sparse and conduct independent exploration once proficient. When applied to the Qwen2.5-VL-7B baseline, our method achieves a +18.6\% accuracy improvement on MM-HELIX benchmark and demonstrates strong generalization with a +5.7\% average performance gain on general mathematic and logic tasks. Our work demonstrate that reflective reasoning in MLLMs can be effectively learned and generalized, paving the way for developing more capable MLLMs.

As synthetic data becomes higher quality and proliferates on the internet, machine learning models are increasingly trained on a mix of human- and machine-generated data. Despite the successful stories of using synthetic data for representation learning, using synthetic data for generative model training creates "self-consuming loops" which may lead to training instability or even collapse, unless certain conditions are met. Our paper aims to stabilize self-consuming generative model training. Our theoretical results demonstrate that by introducing an idealized correction function, which maps a data point to be more likely under the true data distribution, self-consuming loops can be made exponentially more stable. We then propose self-correction functions, which rely on expert knowledge (e.g. the laws of physics programmed in a simulator), and aim to approximate the idealized corrector automatically and at scale. We empirically validate the effectiveness of self-correcting self-consuming loops on the challenging human motion synthesis task, and observe that it successfully avoids model collapse, even when the ratio of synthetic data to real data is as high as 100%.

Appropriately designing the proposal kernel of particle filters is an issue of significant importance, since a bad choice may lead to deterioration of the particle sample and, consequently, waste of computational power. In this paper we introduce a novel algorithm adaptively approximating the so-called optimal proposal kernel by a mixture of integrated curved exponential distributions with logistic weights. This family of distributions, referred to as mixtures of experts, is broad enough to be used in the presence of multi-modality or strongly skewed distributions. The mixtures are fitted, via online-EM methods, to the optimal kernel through minimisation of the Kullback-Leibler divergence between the auxiliary target and instrumental distributions of the particle filter. At each iteration of the particle filter, the algorithm is required to solve only a single optimisation problem for the whole particle sample, yielding an algorithm with only linear complexity. In addition, we illustrate in a simulation study how the method can be successfully applied to optimal filtering in nonlinear state-space models.

Bootstrapping from pre-trained language models has been proven to be an efficient approach for building vision-language models (VLM) for tasks such as image captioning or visual question answering. However, outputs of these models rarely align with user's rationales for specific answers. In order to improve this alignment and reinforce commonsense reasons, we propose a tuning paradigm based on human interactions with machine generated data. Our ILLUME executes the following loop: Given an image-question-answer prompt, the VLM samples multiple candidate rationales, and a human critic provides minimal feedback via preference selection, used for fine-tuning. This loop increases the training data and gradually carves out the VLM's rationalization capabilities that are aligned with human intend. Our exhaustive experiments demonstrate that ILLUME is competitive with standard supervised fine-tuning while using significantly fewer training data and only requiring minimal feedback.

Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model calibration, the rigorous statistical evaluation of model calibration remains less explored. In this work, we develop confidence intervals the ell_2 Expected Calibration Error (ECE). We consider top-1-to-k calibration, which includes both the popular notion of confidence calibration as well as full calibration. For a debiased estimator of the ECE, we show asymptotic normality, but with different convergence rates and asymptotic variances for calibrated and miscalibrated models. We develop methods to construct asymptotically valid confidence intervals for the ECE, accounting for this behavior as well as non-negativity. Our theoretical findings are supported through extensive experiments, showing that our methods produce valid confidence intervals with shorter lengths compared to those obtained by resampling-based methods.

In the realm of multimodal research, numerous studies leverage substantial image-text pairs to conduct modal alignment learning, transforming Large Language Models (LLMs) into Multimodal LLMs and excelling in a variety of visual-language tasks. The prevailing methodologies primarily fall into two categories: self-attention-based and cross-attention-based methods. While self-attention-based methods offer superior data efficiency due to their simple MLP architecture, they often suffer from lower computational efficiency due to concatenating visual and textual tokens as input for LLM. Conversely, cross-attention-based methods, although less data-efficient due to additional learnable parameters, exhibit higher computational efficiency by avoiding long sequence input for LLM. To address these trade-offs, we introduce the Data-Efficient and Compute-Efficient Multimodal Large Language Model (EE-MLLM). Without introducing additional modules or learnable parameters, EE-MLLM achieves both data and compute efficiency. Specifically, we modify the original self-attention mechanism in MLLM to a composite attention mechanism. This mechanism has two key characteristics: 1) Eliminating the computational overhead of self-attention within visual tokens to achieve compute efficiency, and 2) Reusing the weights on each layer of LLM to facilitate effective modality alignment between vision and language for data efficiency. Experimental results demonstrate the effectiveness of EE-MLLM across a range of benchmarks, including general-purpose datasets like MMBench and SeedBench, as well as fine-grained tasks such as TextVQA and DocVQA.

Stochasticity in language model fine-tuning, often caused by the small batch sizes typically used in this regime, can destabilize training by introducing large oscillations in generation quality. A popular approach to mitigating this instability is to take an Exponential moving average (EMA) of weights throughout training. While EMA reduces stochasticity, thereby smoothing training, the introduction of bias from old iterates often creates a lag in optimization relative to vanilla training. In this work, we propose the Bias-Corrected Exponential Moving Average (BEMA), a simple and practical augmentation of EMA that retains variance-reduction benefits while eliminating bias. BEMA is motivated by a simple theoretical model wherein we demonstrate provable acceleration of BEMA over both a standard EMA and vanilla training. Through an extensive suite of experiments on Language Models, we show that BEMA leads to significantly improved convergence rates and final performance over both EMA and vanilla training in a variety of standard LM benchmarks, making BEMA a practical and theoretically motivated intervention for more stable and efficient fine-tuning.

Modern LLMs are trained to "think" primarily via explicit text generation, such as chain-of-thought (CoT), which defers reasoning to post-training and under-leverages pre-training data. We present and open-source Ouro, named after the recursive Ouroboros, a family of pre-trained Looped Language Models (LoopLM) that instead build reasoning into the pre-training phase through (i) iterative computation in latent space, (ii) an entropy-regularized objective for learned depth allocation, and (iii) scaling to 7.7T tokens. Ouro 1.4B and 2.6B models enjoy superior performance that match the results of up to 12B SOTA LLMs across a wide range of benchmarks. Through controlled experiments, we show this advantage stems not from increased knowledge capacity, but from superior knowledge manipulation capabilities. We also show that LoopLM yields reasoning traces more aligned with final outputs than explicit CoT. We hope our results show the potential of LoopLM as a novel scaling direction in the reasoning era. Our model could be found in: http://ouro-llm.github.io.

We present EE-LLM, a framework for large-scale training and inference of early-exit large language models (LLMs). While recent works have shown preliminary evidence for the efficacy of early exiting in accelerating LLM inference, EE-LLM makes a foundational step towards scaling up early-exit LLMs by supporting their training and inference with massive 3D parallelism. Built upon Megatron-LM, EE-LLM implements a variety of algorithmic innovations and performance optimizations tailored to early exiting, including a lightweight method that facilitates backpropagation for the early-exit training objective with pipeline parallelism, techniques of leveraging idle resources in the original pipeline schedule for computation related to early-exit layers, and two approaches of early-exit inference that are compatible with KV caching for autoregressive generation. Our analytical and empirical study shows that EE-LLM achieves great training efficiency with negligible computational overhead compared to standard LLM training, as well as outstanding inference speedup without compromising output quality. To facilitate further research and adoption, we release EE-LLM at https://github.com/pan-x-c/EE-LLM.

Recent studies on large language models (LLMs) and large multimodal models (LMMs) have demonstrated promising skills in various domains including science and mathematics. However, their capability in more challenging and real-world related scenarios like engineering has not been systematically studied. To bridge this gap, we propose EEE-Bench, a multimodal benchmark aimed at assessing LMMs' capabilities in solving practical engineering tasks, using electrical and electronics engineering (EEE) as the testbed. Our benchmark consists of 2860 carefully curated problems spanning 10 essential subdomains such as analog circuits, control systems, etc. Compared to benchmarks in other domains, engineering problems are intrinsically 1) more visually complex and versatile and 2) less deterministic in solutions. Successful solutions to these problems often demand more-than-usual rigorous integration of visual and textual information as models need to understand intricate images like abstract circuits and system diagrams while taking professional instructions, making them excellent candidates for LMM evaluations. Alongside EEE-Bench, we provide extensive quantitative evaluations and fine-grained analysis of 17 widely-used open and closed-sourced LLMs and LMMs. Our results demonstrate notable deficiencies of current foundation models in EEE, with an average performance ranging from 19.48% to 46.78%. Finally, we reveal and explore a critical shortcoming in LMMs which we term laziness: the tendency to take shortcuts by relying on the text while overlooking the visual context when reasoning for technical image problems. In summary, we believe EEE-Bench not only reveals some noteworthy limitations of LMMs but also provides a valuable resource for advancing research on their application in practical engineering tasks, driving future improvements in their capability to handle complex, real-world scenarios.

Since the advent of Multimodal Large Language Models (MLLMs), they have made a significant impact across a wide range of real-world applications, particularly in Autonomous Driving (AD). Their ability to process complex visual data and reason about intricate driving scenarios has paved the way for a new paradigm in end-to-end AD systems. However, the progress of developing end-to-end models for AD has been slow, as existing fine-tuning methods demand substantial resources, including extensive computational power, large-scale datasets, and significant funding. Drawing inspiration from recent advancements in inference computing, we propose OpenEMMA, an open-source end-to-end framework based on MLLMs. By incorporating the Chain-of-Thought reasoning process, OpenEMMA achieves significant improvements compared to the baseline when leveraging a diverse range of MLLMs. Furthermore, OpenEMMA demonstrates effectiveness, generalizability, and robustness across a variety of challenging driving scenarios, offering a more efficient and effective approach to autonomous driving. We release all the codes in https://github.com/taco-group/OpenEMMA.

Seismic advances in generative AI algorithms for imagery, text, and other data types has led to the temptation to use synthetic data to train next-generation models. Repeating this process creates an autophagous (self-consuming) loop whose properties are poorly understood. We conduct a thorough analytical and empirical analysis using state-of-the-art generative image models of three families of autophagous loops that differ in how fixed or fresh real training data is available through the generations of training and in whether the samples from previous generation models have been biased to trade off data quality versus diversity. Our primary conclusion across all scenarios is that without enough fresh real data in each generation of an autophagous loop, future generative models are doomed to have their quality (precision) or diversity (recall) progressively decrease. We term this condition Model Autophagy Disorder (MAD), making analogy to mad cow disease.

While recent multimodal large language models (MLLMs) have advanced automated ECG interpretation, they still face two key limitations: (1) insufficient multimodal synergy between time series signals and visual ECG representations, and (2) limited explainability in linking diagnoses to granular waveform evidence. We introduce GEM, the first MLLM unifying ECG time series, 12-lead ECG images and text for grounded and clinician-aligned ECG interpretation. GEM enables feature-grounded analysis, evidence-driven reasoning, and a clinician-like diagnostic process through three core innovations: a dual-encoder framework extracting complementary time series and image features, cross-modal alignment for effective multimodal understanding, and knowledge-guided instruction generation for generating high-granularity grounding data (ECG-Grounding) linking diagnoses to measurable parameters (e.g., QRS/PR Intervals). Additionally, we propose the Grounded ECG Understanding task, a clinically motivated benchmark designed to comprehensively assess the MLLM's capability in grounded ECG understanding. Experimental results on both existing and our proposed benchmarks show GEM significantly improves predictive performance (CSN 7.4% uparrow), explainability (22.7% uparrow), and grounding (24.8% uparrow), making it more suitable for real-world clinical applications. GitHub repository: https://github.com/lanxiang1017/GEM.git

The recent trend towards Personalized Federated Learning (PFL) has garnered significant attention as it allows for the training of models that are tailored to each client while maintaining data privacy. However, current PFL techniques primarily focus on modeling the conditional distribution heterogeneity (i.e. concept shift), which can result in suboptimal performance when the distribution of input data across clients diverges (i.e. covariate shift). Additionally, these techniques often lack the ability to adapt to unseen data, further limiting their effectiveness in real-world scenarios. To address these limitations, we propose a novel approach, FedGMM, which utilizes Gaussian mixture models (GMM) to effectively fit the input data distributions across diverse clients. The model parameters are estimated by maximum likelihood estimation utilizing a federated Expectation-Maximization algorithm, which is solved in closed form and does not assume gradient similarity. Furthermore, FedGMM possesses an additional advantage of adapting to new clients with minimal overhead, and it also enables uncertainty quantification. Empirical evaluations on synthetic and benchmark datasets demonstrate the superior performance of our method in both PFL classification and novel sample detection.

Current Multimodal Large Language Models (MLLMs) may struggle with understanding long or complex videos due to computational demands at test time, lack of robustness, and limited accuracy, primarily stemming from their feed-forward processing nature. These limitations could be more severe for models with fewer parameters. To address these limitations, we propose a novel framework inspired by cybernetic principles, redesigning video MLLMs as adaptive systems capable of self-monitoring, self-correction, and dynamic resource allocation during inference. Our approach, CyberV, introduces a cybernetic loop consisting of an MLLM Inference System, a Sensor, and a Controller. Specifically, the sensor monitors forward processes of the MLLM and collects intermediate interpretations, such as attention drift, then the controller determines when and how to trigger self-correction and generate feedback to guide the next round. This test-time adaptive scaling framework enhances frozen MLLMs without requiring retraining or additional components. Experiments demonstrate significant improvements: CyberV boosts Qwen2.5-VL-7B by 8.3% and InternVL3-8B by 5.5% on VideoMMMU, surpassing the competitive proprietary model GPT-4o. When applied to Qwen2.5-VL-72B, it yields a 10.0% improvement, achieving performance even comparable to human experts. Furthermore, our method demonstrates consistent gains on general-purpose benchmarks, such as VideoMME and WorldSense, highlighting its effectiveness and generalization capabilities in making MLLMs more robust and accurate for dynamic video understanding. The code is released at https://github.com/marinero4972/CyberV.

Multimodal large language models (MLLMs) have shown promising capabilities but struggle under distribution shifts, where evaluation data differ from instruction tuning distributions. Although previous works have provided empirical evaluations, we argue that establishing a formal framework that can characterize and quantify the risk of MLLMs is necessary to ensure the safe and reliable application of MLLMs in the real world. By taking an information-theoretic perspective, we propose the first theoretical framework that enables the quantification of the maximum risk of MLLMs under distribution shifts. Central to our framework is the introduction of Effective Mutual Information (EMI), a principled metric that quantifies the relevance between input queries and model responses. We derive an upper bound for the EMI difference between in-distribution (ID) and out-of-distribution (OOD) data, connecting it to visual and textual distributional discrepancies. Extensive experiments on real benchmark datasets, spanning 61 shift scenarios empirically validate our theoretical insights.

Automated and semi-automated techniques in biomedical electron microscopy (EM) enable the acquisition of large datasets at a high rate. Segmentation methods are therefore essential to analyze and interpret these large volumes of data, which can no longer completely be labeled manually. In recent years, deep learning algorithms achieved impressive results in both pixel-level labeling (semantic segmentation) and the labeling of separate instances of the same class (instance segmentation). In this review, we examine how these algorithms were adapted to the task of segmenting cellular and sub-cellular structures in EM images. The special challenges posed by such images and the network architectures that overcame some of them are described. Moreover, a thorough overview is also provided on the notable datasets that contributed to the proliferation of deep learning in EM. Finally, an outlook of current trends and future prospects of EM segmentation is given, especially in the area of label-free learning.

We introduce a gradient-free framework for Bayesian Optimal Experimental Design (BOED) in sequential settings, aimed at complex systems where gradient information is unavailable. Our method combines Ensemble Kalman Inversion (EKI) for design optimization with the Affine-Invariant Langevin Dynamics (ALDI) sampler for efficient posterior sampling-both of which are derivative-free and ensemble-based. To address the computational challenges posed by nested expectations in BOED, we propose variational Gaussian and parametrized Laplace approximations that provide tractable upper and lower bounds on the Expected Information Gain (EIG). These approximations enable scalable utility estimation in high-dimensional spaces and PDE-constrained inverse problems. We demonstrate the performance of our framework through numerical experiments ranging from linear Gaussian models to PDE-based inference tasks, highlighting the method's robustness, accuracy, and efficiency in information-driven experimental design.

Continual Instruction Tuning (CIT) is adopted to continually instruct Large Models to follow human intent data by data. It is observed that existing gradient update would heavily destroy the performance on previous datasets during CIT process. Instead, Exponential Moving Average (EMA), owns the ability to trace previous parameters, which can aid in decreasing forgetting. Nonetheless, its stable balance weight fails to deal with the ever-changing datasets, leading to the out-of-balance between plasticity and stability. In this paper, we propose a general continual instruction tuning framework to address the challenge. Starting from the trade-off prerequisite and EMA update, we propose the plasticity and stability ideal condition. Based on Taylor expansion in the loss function, we find the optimal balance weight can be automatically determined by the gradients and learned parameters. Therefore, we propose a stable-plasticity balanced coefficient to avoid knowledge interference. Based on the semantic similarity of the instructions, we can determine whether to retrain or expand the training parameters and allocate the most suitable parameters for the testing instances. Extensive experiments across multiple continual instruction tuning benchmarks demonstrate that our approach not only enhances anti-forgetting capabilities but also significantly improves overall continual tuning performance. Our code is available at https://github.com/JingyangQiao/CoIN.

Electrocardiogram (ECG) is a widely used tool for assessing cardiac function due to its low cost and accessibility. Emergent research shows that ECGs can help make predictions on key outcomes traditionally derived from more complex modalities such as echocardiograms (ECHO), enabling the use of ECGs as a more accessible method to predict broader measurements of cardiac function. ECHO, in particular, are of great importance because they require considerable hospital resources while playing a key role in clinical cardiac assessment. To aid this use case, we introduce EchoingECG, a probabilistic student-teacher model that leverages uncertainty-aware ECG embeddings and ECHO supervision to improve ECG-based cardiac function prediction. Our approach integrates Probabilistic Cross-Modal Embeddings (PCME++), a probabilistic contrastive framework, with ECHO-CLIP, a vision-language pre-trained model trained on ECHO-text pairs, to distill ECHO knowledge into ECG representations. Through experiments and external validation, we showed that EchoingECG outperforms state-of-the-art foundation ECG models in zero-shot, few-shot, and fine-tune settings for ECHO predictions based on ECG. We also highlighted that variance estimation (enabled through our method) enhanced our understanding of model performance by identifying underlying regions of uncertainty within ECGs. The code is available: https://github.com/mcintoshML/EchoingECG.

Bayesian optimization (BO) has established itself as a leading strategy for efficiently optimizing expensive-to-evaluate functions. Existing BO methods mostly rely on Gaussian process (GP) surrogate models and are not applicable to (doubly-stochastic) Gaussian Cox processes, where the observation process is modulated by a latent intensity function modeled as a GP. In this paper, we propose a novel maximum a posteriori inference of Gaussian Cox processes. It leverages the Laplace approximation and change of kernel technique to transform the problem into a new reproducing kernel Hilbert space, where it becomes more tractable computationally. It enables us to obtain both a functional posterior of the latent intensity function and the covariance of the posterior, thus extending existing works that often focus on specific link functions or estimating the posterior mean. Using the result, we propose a BO framework based on the Gaussian Cox process model and further develop a Nystr\"om approximation for efficient computation. Extensive evaluations on various synthetic and real-world datasets demonstrate significant improvement over state-of-the-art inference solutions for Gaussian Cox processes, as well as effective BO with a wide range of acquisition functions designed through the underlying Gaussian Cox process model.

We present an algorithm for learning mixtures of Markov chains and Markov decision processes (MDPs) from short unlabeled trajectories. Specifically, our method handles mixtures of Markov chains with optional control input by going through a multi-step process, involving (1) a subspace estimation step, (2) spectral clustering of trajectories using "pairwise distance estimators," along with refinement using the EM algorithm, (3) a model estimation step, and (4) a classification step for predicting labels of new trajectories. We provide end-to-end performance guarantees, where we only explicitly require the length of trajectories to be linear in the number of states and the number of trajectories to be linear in a mixing time parameter. Experimental results support these guarantees, where we attain 96.6% average accuracy on a mixture of two MDPs in gridworld, outperforming the EM algorithm with random initialization (73.2% average accuracy).

Diffusion models currently dominate the field of data-driven image synthesis with their unparalleled scaling to large datasets. In this paper, we identify and rectify several causes for uneven and ineffective training in the popular ADM diffusion model architecture, without altering its high-level structure. Observing uncontrolled magnitude changes and imbalances in both the network activations and weights over the course of training, we redesign the network layers to preserve activation, weight, and update magnitudes on expectation. We find that systematic application of this philosophy eliminates the observed drifts and imbalances, resulting in considerably better networks at equal computational complexity. Our modifications improve the previous record FID of 2.41 in ImageNet-512 synthesis to 1.81, achieved using fast deterministic sampling. As an independent contribution, we present a method for setting the exponential moving average (EMA) parameters post-hoc, i.e., after completing the training run. This allows precise tuning of EMA length without the cost of performing several training runs, and reveals its surprising interactions with network architecture, training time, and guidance.

This work introduces EE-Tuning, a lightweight and economical solution to training/tuning early-exit large language models (LLMs). In contrast to the common approach of full-parameter pre-training, EE-Tuning augments any pre-trained (and possibly fine-tuned) standard LLM with additional early-exit layers that are tuned in a parameter-efficient manner, which requires significantly less computational resources and training data. Our implementation of EE-Tuning achieves outstanding training efficiency via extensive performance optimizations, as well as scalability due to its full compatibility with 3D parallelism. Results of systematic experiments validate the efficacy of EE-Tuning, confirming that effective early-exit LLM inference can be achieved with a limited training budget. In hope of making early-exit LLMs accessible to the community, we release the source code of our implementation of EE-Tuning at https://github.com/pan-x-c/EE-LLM.

The emergence of multimodal large language models (MLLMs) presents promising opportunities for automation and enhancement in Electronic Design Automation (EDA). However, comprehensively evaluating these models in circuit design remains challenging due to the narrow scope of existing benchmarks. To bridge this gap, we introduce MMCircuitEval, the first multimodal benchmark specifically designed to assess MLLM performance comprehensively across diverse EDA tasks. MMCircuitEval comprises 3614 meticulously curated question-answer (QA) pairs spanning digital and analog circuits across critical EDA stages - ranging from general knowledge and specifications to front-end and back-end design. Derived from textbooks, technical question banks, datasheets, and real-world documentation, each QA pair undergoes rigorous expert review for accuracy and relevance. Our benchmark uniquely categorizes questions by design stage, circuit type, tested abilities (knowledge, comprehension, reasoning, computation), and difficulty level, enabling detailed analysis of model capabilities and limitations. Extensive evaluations reveal significant performance gaps among existing LLMs, particularly in back-end design and complex computations, highlighting the critical need for targeted training datasets and modeling approaches. MMCircuitEval provides a foundational resource for advancing MLLMs in EDA, facilitating their integration into real-world circuit design workflows. Our benchmark is available at https://github.com/cure-lab/MMCircuitEval.

The emergence and growing popularity of multimodal large language models (MLLMs) have significant potential to enhance various aspects of daily life, from improving communication to facilitating learning and problem-solving. Mobile phones, as essential daily companions, represent the most effective and accessible deployment platform for MLLMs, enabling seamless integration into everyday tasks. However, deploying MLLMs on mobile phones presents challenges due to limitations in memory size and computational capability, making it difficult to achieve smooth and real-time processing without extensive optimization. In this paper, we present BlueLM-V-3B, an algorithm and system co-design approach specifically tailored for the efficient deployment of MLLMs on mobile platforms. To be specific, we redesign the dynamic resolution scheme adopted by mainstream MLLMs and implement system optimization for hardware-aware deployment to optimize model inference on mobile phones. BlueLM-V-3B boasts the following key highlights: (1) Small Size: BlueLM-V-3B features a language model with 2.7B parameters and a vision encoder with 400M parameters. (2) Fast Speed: BlueLM-V-3B achieves a generation speed of 24.4 token/s on the MediaTek Dimensity 9300 processor with 4-bit LLM weight quantization. (3) Strong Performance: BlueLM-V-3B has attained the highest average score of 66.1 on the OpenCompass benchmark among models with leq 4B parameters and surpassed a series of models with much larger parameter sizes (e.g., MiniCPM-V-2.6, InternVL2-8B).

Energy-based models (EBMs) are known in the Machine Learning community for decades. Since the seminal works devoted to EBMs dating back to the noughties, there have been a lot of efficient methods which solve the generative modelling problem by means of energy potentials (unnormalized likelihood functions). In contrast, the realm of Optimal Transport (OT) and, in particular, neural OT solvers is much less explored and limited by few recent works (excluding WGAN-based approaches which utilize OT as a loss function and do not model OT maps themselves). In our work, we bridge the gap between EBMs and Entropy-regularized OT. We present a novel methodology which allows utilizing the recent developments and technical improvements of the former in order to enrich the latter. From the theoretical perspective, we prove generalization bounds for our technique. In practice, we validate its applicability in toy 2D and image domains. To showcase the scalability, we empower our method with a pre-trained StyleGAN and apply it to high-res AFHQ 512times 512 unpaired I2I translation. For simplicity, we choose simple short- and long-run EBMs as a backbone of our Energy-guided Entropic OT approach, leaving the application of more sophisticated EBMs for future research. Our code is available at: https://github.com/PetrMokrov/Energy-guided-Entropic-OT

Empirical Risk Minimization (ERM) is fragile in scenarios with insufficient labeled samples. A vanilla extension of ERM to unlabeled samples is Entropy Minimization (EntMin), which employs the soft-labels of unlabeled samples to guide their learning. However, EntMin emphasizes prediction discriminability while neglecting prediction diversity. To alleviate this issue, in this paper, we rethink the guidance information to utilize unlabeled samples. By analyzing the learning objective of ERM, we find that the guidance information for labeled samples in a specific category is the corresponding label encoding. Inspired by this finding, we propose a Label-Encoding Risk Minimization (LERM). It first estimates the label encodings through prediction means of unlabeled samples and then aligns them with their corresponding ground-truth label encodings. As a result, the LERM ensures both prediction discriminability and diversity, and it can be integrated into existing methods as a plugin. Theoretically, we analyze the relationships between LERM and ERM as well as EntMin. Empirically, we verify the superiority of the LERM under several label insufficient scenarios. The codes are available at https://github.com/zhangyl660/LERM.

This paper proposes a new type of generative model that is able to quickly learn a latent representation without an encoder. This is achieved using empirical Bayes to calculate the expectation of the posterior, which is implemented by initialising a latent vector with zeros, then using the gradient of the log-likelihood of the data with respect to this zero vector as new latent points. The approach has similar characteristics to autoencoders, but with a simpler architecture, and is demonstrated in a variational autoencoder equivalent that permits sampling. This also allows implicit representation networks to learn a space of implicit functions without requiring a hypernetwork, retaining their representation advantages across datasets. The experiments show that the proposed method converges faster, with significantly lower reconstruction error than autoencoders, while requiring half the parameters.

The SIML (abbreviation of Separating Information Maximal Likelihood) method, has been introduced by N. Kunitomo and S. Sato and their collaborators to estimate the integrated volatility of high-frequency data that is assumed to be an It\^o process but with so-called microstructure noise. The SIML estimator turned out to share many properties with the estimator introduced by P. Malliavin and M.E. Mancino. The present paper establishes the consistency and the asymptotic normality under a general sampling scheme but without microstructure noise. Specifically, a fast convergence shown for Malliavin--Mancino estimator by E. Clement and A. Gloter is also established for the SIML estimator.

Combined electric power system and High-Altitude Electromagnetic Pulse (HEMP) models are being developed to determine the effect of a HEMP on the US power grid. The work relies primarily on deterministic methods; however, it is computationally untenable to evaluate the E1 HEMP response of large numbers of grid components distributed across a large interconnection. Further, the deterministic assessment of these components' failures are largely unachievable. E1 HEMP laboratory testing of the components is accomplished, but is expensive, leaving few data points to construct failure models of grid components exposed to E1 HEMP. The use of Bayesian priors, developed using the subject matter expertise, combined with the minimal test data in a Bayesian inference process, provides the basis for the development of more robust and cost-effective statistical component failure models. These can be used with minimal computational burden in a simulation environment such as sampling of Cumulative Distribution Functions (CDFs).

Recently, large language models (LLMs) have demonstrated excellent performance in understanding human instructions and generating code, which has inspired researchers to explore the feasibility of generating RTL code with LLMs. However, the existing approaches to fine-tune LLMs on RTL codes typically are conducted on fixed datasets, which do not fully stimulate the capability of LLMs and require large amounts of reference data. To mitigate these issues , we introduce a simple yet effective iterative training paradigm named ITERTL. During each iteration, samples are drawn from the model trained in the previous cycle. Then these new samples are employed for training in this loop. Through this iterative approach, the distribution mismatch between the model and the training samples is reduced. Additionally, the model is thus enabled to explore a broader generative space and receive more comprehensive feedback. Theoretical analyses are conducted to investigate the mechanism of the effectiveness. Experimental results show the model trained through our proposed approach can compete with and even outperform the state-of-the-art (SOTA) open-source model with nearly 37\% reference samples, achieving remarkable 42.9\% and 62.2\% pass@1 rate on two VerilogEval evaluation datasets respectively. While using the same amount of reference samples, our method can achieved a relative improvement of 16.9\% and 12.5\% in pass@1 compared to the non-iterative method. This study facilitates the application of LLMs for generating RTL code in practical scenarios with limited data.

Self-supervised learning excels at learning representations from large amounts of data. At the same time, generative models offer the complementary property of learning information about the underlying data generation process. In this study, we aim at establishing a principled connection between these two paradigms and highlight the benefits of their complementarity. In particular, we perform an analysis of self-supervised learning objectives, elucidating the underlying probabilistic graphical models and presenting a standardized methodology for their derivation from first principles. The analysis suggests a natural means of integrating self-supervised learning with likelihood-based generative models. We instantiate this concept within the realm of cluster-based self-supervised learning and energy models, introducing a lower bound proven to reliably penalize the most important failure modes and unlocking full unification. Our theoretical findings are substantiated through experiments on synthetic and real-world data, including SVHN, CIFAR10, and CIFAR100, demonstrating that our objective function allows to jointly train a backbone network in a discriminative and generative fashion, consequently outperforming existing self-supervised learning strategies in terms of clustering, generation and out-of-distribution detection performance by a wide margin. We also demonstrate that the solution can be integrated into a neuro-symbolic framework to tackle a simple yet non-trivial instantiation of the symbol grounding problem. The code is publicly available at https://github.com/emsansone/GEDI.

Preserving training dynamics across batch sizes is an important tool for practical machine learning as it enables the trade-off between batch size and wall-clock time. This trade-off is typically enabled by a scaling rule, for example, in stochastic gradient descent, one should scale the learning rate linearly with the batch size. Another important tool for practical machine learning is the model Exponential Moving Average (EMA), which is a model copy that does not receive gradient information, but instead follows its target model with some momentum. This model EMA can improve the robustness and generalization properties of supervised learning, stabilize pseudo-labeling, and provide a learning signal for Self-Supervised Learning (SSL). Prior works have treated the model EMA separately from optimization, leading to different training dynamics across batch sizes and lower model performance. In this work, we provide a scaling rule for optimization in the presence of model EMAs and demonstrate its validity across a range of architectures, optimizers, and data modalities. We also show the rule's validity where the model EMA contributes to the optimization of the target model, enabling us to train EMA-based pseudo-labeling and SSL methods at small and large batch sizes. For SSL, we enable training of BYOL up to batch size 24,576 without sacrificing performance, optimally a 6times wall-clock time reduction.

We analyze the layerwise effective dimension (rank of the feature matrix) in fully-connected ReLU networks of finite width. Specifically, for a fixed batch of m inputs and random Gaussian weights, we derive closed-form expressions for the expected rank of the \mtimes n hidden activation matrices. Our main result shows that E[EDim(ell)]=m[1-(1-2/pi)^ell]+O(e^{-c m}) so that the rank deficit decays geometrically with ratio 1-2 / pi approx 0.3634. We also prove a sub-Gaussian concentration bound, and identify the "revival" depths at which the expected rank attains local maxima. In particular, these peaks occur at depths ell_k^*approx(k+1/2)pi/log(1/rho) with height approx (1-e^{-pi/2}) m approx 0.79m. We further show that this oscillatory rank behavior is a finite-width phenomenon: under orthogonal weight initialization or strong negative-slope leaky-ReLU, the rank remains (nearly) full. These results provide a precise characterization of how random ReLU layers alternately collapse and partially revive the subspace of input variations, adding nuance to prior work on expressivity of deep networks.

Multimodal large language models (MLLMs) have demonstrated remarkable capabilities in vision-language answering tasks. Despite their strengths, these models often encounter challenges in achieving complex reasoning tasks such as mathematical problem-solving. Previous works have focused on fine-tuning on specialized mathematical datasets. However, these datasets are typically distilled directly from teacher models, which capture only static reasoning patterns and leaving substantial gaps compared to student models. This reliance on fixed teacher-derived datasets not only restricts the model's ability to adapt to novel or more intricate questions that extend beyond the confines of the training data, but also lacks the iterative depth needed for robust generalization. To overcome these limitations, we propose \method, a Mathematical Self-Evolving framework for MLLMs. In contrast to traditional one-shot fine-tuning paradigms, \method iteratively refines the model through cycles of inference, reflection, and reward-based feedback. Specifically, we leverage iterative fine-tuning by incorporating correct reasoning paths derived from previous-stage inference and integrating reflections from a specialized Outcome Reward Model (ORM). To verify the effectiveness of \method, we evaluate it on a suite of challenging benchmarks, demonstrating significant performance gains over backbone models. Notably, our experimental results on MathVL-test surpass the leading open-source multimodal mathematical reasoning model QVQ. Our code and models are available at https://zheny2751\allowbreak-dotcom.github.io/\allowbreak MathSE.github.io/.

Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between variational inference (VI) and the learning target. While VI's lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, we show that a direct approximation of the marginal likelihood as in Expectation Propagation (EP) is a better learning objective for hyperparameter optimization. We design a hybrid training procedure to bring the best of both worlds: it leverages conjugate-computation VI for inference and uses an EP-like marginal likelihood approximation for hyperparameter learning. We compare VI, EP, Laplace approximation, and our proposed training procedure and empirically demonstrate the effectiveness of our proposal across a wide range of data sets.

Multimodal Large Language Models (MLLMs) have shown significant promise in various applications, leading to broad interest from researchers and practitioners alike. However, a comprehensive evaluation of their long-context capabilities remains underexplored. To address these gaps, we introduce the MultiModal Needle-in-a-haystack (MMNeedle) benchmark, specifically designed to assess the long-context capabilities of MLLMs. Besides multi-image input, we employ image stitching to further increase the input context length, and develop a protocol to automatically generate labels for sub-image level retrieval. Essentially, MMNeedle evaluates MLLMs by stress-testing their capability to locate a target sub-image (needle) within a set of images (haystack) based on textual instructions and descriptions of image contents. This setup necessitates an advanced understanding of extensive visual contexts and effective information retrieval within long-context image inputs. With this benchmark, we evaluate state-of-the-art MLLMs, encompassing both API-based and open-source models. The findings reveal that GPT-4o consistently surpasses other models in long-context scenarios, but suffers from hallucination problems in negative samples, i.e., when needles are not in the haystacks. Our comprehensive long-context evaluation of MLLMs also sheds lights on the considerable performance gap between API-based and open-source models. All the code, data, and instructions required to reproduce the main results are available at https://github.com/Wang-ML-Lab/multimodal-needle-in-a-haystack.

Energy-Based Models (EBMs) have emerged as a powerful framework in the realm of generative modeling, offering a unique perspective that aligns closely with principles of statistical mechanics. This review aims to provide physicists with a comprehensive understanding of EBMs, delineating their connection to other generative models such as Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and Normalizing Flows. We explore the sampling techniques crucial for EBMs, including Markov Chain Monte Carlo (MCMC) methods, and draw parallels between EBM concepts and statistical mechanics, highlighting the significance of energy functions and partition functions. Furthermore, we delve into state-of-the-art training methodologies for EBMs, covering recent advancements and their implications for enhanced model performance and efficiency. This review is designed to clarify the often complex interconnections between these models, which can be challenging due to the diverse communities working on the topic.

The Instruction Following (IF) ability measures how well Multi-modal Large Language Models (MLLMs) understand exactly what users are telling them and whether they are doing it right. Existing multimodal instruction following training data is scarce, the benchmarks are simple with atomic instructions, and the evaluation strategies are imprecise for tasks demanding exact output constraints. To address this, we present MM-IFEngine, an effective pipeline to generate high-quality image-instruction pairs. Our MM-IFEngine pipeline yields large-scale, diverse, and high-quality training data MM-IFInstruct-23k, which is suitable for Supervised Fine-Tuning (SFT) and extended as MM-IFDPO-23k for Direct Preference Optimization (DPO). We further introduce MM-IFEval, a challenging and diverse multi-modal instruction-following benchmark that includes (1) both compose-level constraints for output responses and perception-level constraints tied to the input images, and (2) a comprehensive evaluation pipeline incorporating both rule-based assessment and judge model. We conduct SFT and DPO experiments and demonstrate that fine-tuning MLLMs on MM-IFInstruct-23k and MM-IFDPO-23k achieves notable gains on various IF benchmarks, such as MM-IFEval (+10.2%), MIA (+7.6%), and IFEval (+12.3%). The full data and evaluation code will be released on https://github.com/SYuan03/MM-IFEngine.

Multimodal Large Language Model (MLLM) relies on the powerful LLM to perform multimodal tasks, showing amazing emergent abilities in recent studies, such as writing poems based on an image. However, it is difficult for these case studies to fully reflect the performance of MLLM, lacking a comprehensive evaluation. In this paper, we fill in this blank, presenting the first MLLM Evaluation benchmark MME. It measures both perception and cognition abilities on a total of 14 subtasks. In order to avoid data leakage that may arise from direct use of public datasets for evaluation, the annotations of instruction-answer pairs are all manually designed. The concise instruction design allows us to fairly compare MLLMs, instead of struggling in prompt engineering. Besides, with such an instruction, we can also easily carry out quantitative statistics. A total of 12 advanced MLLMs are comprehensively evaluated on our MME, which not only suggests that existing MLLMs still have a large room for improvement, but also reveals the potential directions for the subsequent model optimization.

An ultra high energy electromagnetic cascade, a purely leptonic process and initiated by either photons or e^pm, can be a source of high energy neutrinos. We present a public python3 code, MUNHECA, to compute the neutrino spectrum by taking into account various QED processes, with the cascade developing either along the propagation in the cosmic microwave background in the high-redshift universe or in a predefined photon background surrounding the astrophysical source. The user can adjust various settings of MUNHECA, including the spectrum of injected high energy photons, the background photon field and the QED processes governing the cascade evolution. We improve the modeling of several processes, provide examples of the execution of MUNHECA and compare it with some earlier and more simplified estimates of the neutrino spectrum from electromagnetic cascades.

Recent advances in multimodal large language models (MLLMs) have shown impressive reasoning capabilities. However, further enhancing existing MLLMs necessitates high-quality vision-language datasets with carefully curated task complexities, which are both costly and challenging to scale. Although recent self-improving models that iteratively refine themselves offer a feasible solution, they still suffer from two core challenges: (i) most existing methods augment visual or textual data separately, resulting in discrepancies in data complexity (e.g., over-simplified diagrams paired with redundant textual descriptions); and (ii) the evolution of data and models is also separated, leading to scenarios where models are exposed to tasks with mismatched difficulty levels. To address these issues, we propose C2-Evo, an automatic, closed-loop self-improving framework that jointly evolves both training data and model capabilities. Specifically, given a base dataset and a base model, C2-Evo enhances them by a cross-modal data evolution loop and a data-model evolution loop. The former loop expands the base dataset by generating complex multimodal problems that combine structured textual sub-problems with iteratively specified geometric diagrams, while the latter loop adaptively selects the generated problems based on the performance of the base model, to conduct supervised fine-tuning and reinforcement learning alternately. Consequently, our method continuously refines its model and training data, and consistently obtains considerable performance gains across multiple mathematical reasoning benchmarks. Our code, models, and datasets will be released.

Learning compact discrete representations of data is a key task on its own or for facilitating subsequent processing of data. In this paper we present a model that produces Discrete InfoMax Codes (DIMCO); we learn a probabilistic encoder that yields k-way d-dimensional codes associated with input data. Our model's learning objective is to maximize the mutual information between codes and labels with a regularization, which enforces entries of a codeword to be as independent as possible. We show that the infomax principle also justifies previous loss functions (e.g., cross-entropy) as its special cases. Our analysis also shows that using shorter codes, as DIMCO does, reduces overfitting in the context of few-shot classification. Through experiments in various domains, we observe this implicit meta-regularization effect of DIMCO. Furthermore, we show that the codes learned by DIMCO are efficient in terms of both memory and retrieval time compared to previous methods.

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

Temporal point processes (TPP) are a natural tool for modeling event-based data. Among all TPP models, Hawkes processes have proven to be the most widely used, mainly due to their adequate modeling for various applications, particularly when considering exponential or non-parametric kernels. Although non-parametric kernels are an option, such models require large datasets. While exponential kernels are more data efficient and relevant for specific applications where events immediately trigger more events, they are ill-suited for applications where latencies need to be estimated, such as in neuroscience. This work aims to offer an efficient solution to TPP inference using general parametric kernels with finite support. The developed solution consists of a fast ell_2 gradient-based solver leveraging a discretized version of the events. After theoretically supporting the use of discretization, the statistical and computational efficiency of the novel approach is demonstrated through various numerical experiments. Finally, the method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG). Given the use of general parametric kernels, results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.

With the rapid advancement of Multimodal Large Language Models (MLLMs), numerous evaluation benchmarks have emerged. However, comprehensive assessments of their performance across diverse industrial applications remain limited. In this paper, we introduce MME-Industry, a novel benchmark designed specifically for evaluating MLLMs in industrial settings.The benchmark encompasses 21 distinct domain, comprising 1050 question-answer pairs with 50 questions per domain. To ensure data integrity and prevent potential leakage from public datasets, all question-answer pairs were manually crafted and validated by domain experts. Besides, the benchmark's complexity is effectively enhanced by incorporating non-OCR questions that can be answered directly, along with tasks requiring specialized domain knowledge. Moreover, we provide both Chinese and English versions of the benchmark, enabling comparative analysis of MLLMs' capabilities across these languages. Our findings contribute valuable insights into MLLMs' practical industrial applications and illuminate promising directions for future model optimization research.

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two observations for M-matrices lauritzen2019maximum,slawski2015estimation and even one observation for diagonally dominant M-matrices truell2021maximum. We propose an adaptive multiple-stage estimation method that refines the estimate by solving a weighted ell_1-regularized problem at each stage. Furthermore, we develop a unified framework based on the gradient projection method to solve the regularized problem, incorporating distinct projections to handle the constraints of M-matrices and diagonally dominant M-matrices. A theoretical analysis of the estimation error is provided. Our method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification, as evidenced by synthetic and financial time-series data sets.

Object hallucination has been an Achilles' heel which hinders the broader applications of large vision-language models (LVLMs). Object hallucination refers to the phenomenon that the LVLMs claim non-existent objects in the image. To mitigate the object hallucinations, instruction tuning and external model-based detection methods have been proposed, which either require large-scare computational resources or depend on the detection result of external models. However, there remains an under-explored field to utilize the LVLM itself to alleviate object hallucinations. In this work, we adopt the intuition that the LVLM tends to respond logically consistently for existent objects but inconsistently for hallucinated objects. Therefore, we propose a Logical Closed Loop-based framework for Object Hallucination Detection and Mitigation, namely LogicCheckGPT. In specific, we devise logical consistency probing to raise questions with logical correlations, inquiring about attributes from objects and vice versa. Whether their responses can form a logical closed loop serves as an indicator of object hallucination. As a plug-and-play method, it can be seamlessly applied to all existing LVLMs. Comprehensive experiments conducted on three benchmarks across four LVLMs have demonstrated significant improvements brought by our method, indicating its effectiveness and generality.

Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo methods can be costly to do so. We propose here a new procedure based on importance sampling and control variates for estimating more efficiently multiple expectations with the same sample. We first show that there exists a family of optimal estimators combining both importance sampling and control variates, which however cannot be used in practice because they require the knowledge of the values of the expectations to estimate. Motivated by the form of these optimal estimators and some interesting properties, we therefore propose an adaptive algorithm. The general idea is to adaptively update the parameters of the estimators for approaching the optimal ones. We suggest then a quantitative stopping criterion that exploits the trade-off between approaching these optimal parameters and having a sufficient budget left. This left budget is then used to draw a new independent sample from the final sampling distribution, allowing to get unbiased estimators of the expectations. We show how to apply our procedure to sensitivity analysis, by estimating Sobol' indices and quantifying the impact of the input distributions. Finally, realistic test cases show the practical interest of the proposed algorithm, and its significant improvement over estimating the expectations separately.

Diffusion models have demonstrated impressive generative capabilities, but their exposure bias problem, described as the input mismatch between training and sampling, lacks in-depth exploration. In this paper, we systematically investigate the exposure bias problem in diffusion models by first analytically modelling the sampling distribution, based on which we then attribute the prediction error at each sampling step as the root cause of the exposure bias issue. Furthermore, we discuss potential solutions to this issue and propose an intuitive metric for it. Along with the elucidation of exposure bias, we propose a simple, yet effective, training-free method called Epsilon Scaling to alleviate the exposure bias. We show that Epsilon Scaling explicitly moves the sampling trajectory closer to the vector field learned in the training phase by scaling down the network output (Epsilon), mitigating the input mismatch between training and sampling. Experiments on various diffusion frameworks (ADM, DDPM/DDIM, EDM, LDM), unconditional and conditional settings, and deterministic vs. stochastic sampling verify the effectiveness of our method. Remarkably, our ADM-ES, as a SOTA stochastic sampler, obtains 2.17 FID on CIFAR-10 under 100-step unconditional generation. The code is available at https://github.com/forever208/ADM-ES and https://github.com/forever208/EDM-ES.

Hallucination, posed as a pervasive challenge of multi-modal large language models (MLLMs), has significantly impeded their real-world usage that demands precise judgment. Existing methods mitigate this issue with either training with specific designed data or inferencing with external knowledge from other sources, incurring inevitable additional costs. In this paper, we present OPERA, a novel MLLM decoding method grounded in an Over-trust Penalty and a Retrospection-Allocation strategy, serving as a nearly free lunch to alleviate the hallucination issue without additional data, knowledge, or training. Our approach begins with an interesting observation that, most hallucinations are closely tied to the knowledge aggregation patterns manifested in the self-attention matrix, i.e., MLLMs tend to generate new tokens by focusing on a few summary tokens, but not all the previous tokens. Such partial over-trust inclination results in the neglecting of image tokens and describes the image content with hallucination. Statistically, we observe an 80%sim95% co-currency rate between hallucination contents and such knowledge aggregation patterns. Based on the observation, OPERA introduces a penalty term on the model logits during the beam-search decoding to mitigate the over-trust issue, along with a rollback strategy that retrospects the presence of summary tokens in the previously generated tokens, and re-allocate the token selection if necessary. With extensive experiments, OPERA shows significant hallucination-mitigating performance on different MLLMs and metrics, proving its effectiveness and generality. Our code is available at: https://github.com/shikiw/OPERA.

Endoscopic procedures are essential for diagnosing and treating internal diseases, and multi-modal large language models (MLLMs) are increasingly applied to assist in endoscopy analysis. However, current benchmarks are limited, as they typically cover specific endoscopic scenarios and a small set of clinical tasks, failing to capture the real-world diversity of endoscopic scenarios and the full range of skills needed in clinical workflows. To address these issues, we introduce EndoBench, the first comprehensive benchmark specifically designed to assess MLLMs across the full spectrum of endoscopic practice with multi-dimensional capacities. EndoBench encompasses 4 distinct endoscopic scenarios, 12 specialized clinical tasks with 12 secondary subtasks, and 5 levels of visual prompting granularities, resulting in 6,832 rigorously validated VQA pairs from 21 diverse datasets. Our multi-dimensional evaluation framework mirrors the clinical workflow--spanning anatomical recognition, lesion analysis, spatial localization, and surgical operations--to holistically gauge the perceptual and diagnostic abilities of MLLMs in realistic scenarios. We benchmark 23 state-of-the-art models, including general-purpose, medical-specialized, and proprietary MLLMs, and establish human clinician performance as a reference standard. Our extensive experiments reveal: (1) proprietary MLLMs outperform open-source and medical-specialized models overall, but still trail human experts; (2) medical-domain supervised fine-tuning substantially boosts task-specific accuracy; and (3) model performance remains sensitive to prompt format and clinical task complexity. EndoBench establishes a new standard for evaluating and advancing MLLMs in endoscopy, highlighting both progress and persistent gaps between current models and expert clinical reasoning. We publicly release our benchmark and code.

Recent advances in generative vision-language models (VLMs) have exciting potential implications for AI in radiology, yet VLMs are also known to produce hallucinations, nonsensical text, and other unwanted behaviors that can waste clinicians' time and cause patient harm. Drawing on recent work on direct preference optimization (DPO), we propose a simple method for modifying the behavior of pretrained VLMs performing radiology report generation by suppressing unwanted types of generations. We apply our method to the prevention of hallucinations of prior exams, addressing a long-established problem behavior in models performing chest X-ray report generation. Across our experiments, we find that DPO fine-tuning achieves a 3.2-4.8x reduction in lines hallucinating prior exams while maintaining model performance on clinical accuracy metrics. Our work is, to the best of our knowledge, the first work to apply DPO to medical VLMs, providing a data- and compute- efficient way to suppress problem behaviors while maintaining overall clinical accuracy.

Vision-language models (VLMs) are highly effective but often underperform on specialized tasks; for example, Llava-1.5 struggles with chart and diagram understanding due to scarce task-specific training data. Existing training data, sourced from general-purpose datasets, fails to capture the nuanced details needed for these tasks. We introduce MM-Gen, a scalable method that generates task-specific, high-quality synthetic text for candidate images by leveraging stronger models. MM-Gen employs a three-stage targeted process: partitioning data into subgroups, generating targeted text based on task descriptions, and filtering out redundant and outlier data. Fine-tuning VLMs with data generated by MM-Gen leads to significant performance gains, including 29% on spatial reasoning and 15% on diagram understanding for Llava-1.5 (7B). Compared to human-curated caption data, MM-Gen achieves up to 1.6x better improvements for the original models, proving its effectiveness in enhancing task-specific VLM performance and bridging the gap between general-purpose datasets and specialized requirements. Code available at https://github.com/sjoshi804/MM-Gen.

Neural language models are probabilistic models of human text. They are predominantly trained using maximum likelihood estimation (MLE), which is equivalent to minimizing the forward cross-entropy between the empirical data distribution and the model distribution. However, various degeneration phenomena are still widely observed when decoding from the distributions learned by such models. We establish that the forward cross-entropy is suboptimal as a distance metric for aligning human and model distribution due to its (1) recall-prioritization (2) negative diversity ignorance and (3) train-test mismatch. In this paper, we propose Earth Mover Distance Optimization (EMO) for auto-regressive language modeling. EMO capitalizes on the inherent properties of earth mover distance to address the aforementioned challenges. Due to the high complexity of direct computation, we further introduce a feasible upper bound for EMO to ease end-to-end training. Upon extensive evaluation of language models trained using EMO and MLE. We find that EMO demonstrates a consistently better language modeling performance than MLE across domains. Moreover, EMO demonstrates noteworthy enhancements in downstream performance with minimal fine-tuning on merely 25,000 sentences. This highlights the tremendous potential of EMO as a lightweight calibration method for enhancing large-scale pre-trained language models.

Autoregressive (AR) models have achieved unified and strong performance across both visual understanding and image generation tasks. However, removing undesired concepts from AR models while maintaining overall generation quality remains an open challenge. In this paper, we propose Erasure Autoregressive Model (EAR), a fine-tuning method for effective and utility-preserving concept erasure in AR models. Specifically, we introduce Windowed Gradient Accumulation (WGA) strategy to align patch-level decoding with erasure objectives, and Thresholded Loss Masking (TLM) strategy to protect content unrelated to the target concept during fine-tuning. Furthermore, we propose a novel benchmark, Erase Concept Generator and Visual Filter (ECGVF), aim at provide a more rigorous and comprehensive foundation for evaluating concept erasure in AR models. Specifically, we first employ structured templates across diverse large language models (LLMs) to pre-generate a large-scale corpus of target-replacement concept prompt pairs. Subsequently, we generate images from these prompts and subject them to rigorous filtering via a visual classifier to ensure concept fidelity and alignment. Extensive experimental results conducted on the ECGVF benchmark with the AR model Janus-Pro demonstrate that EAR achieves marked improvements in both erasure effectiveness and model utility preservation. Code is available at: https://github.com/immc-lab/ear/

The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this work, we give an equivalent definition of the EIM approximation, in which the two variables play symmetric roles. Then, we give a proof for the existence of this approximation, and extend it up to the convergence of the EIM, and for any norm chosen to compute the error in the greedy step. Finally, we introduce a way to compute a separated representation in the case where the number of selected values is different for each variable. In the case of a physical field measured by sensors, this is useful to discard a broken sensor while keeping the information provided by the associated selected field.

A key challenge of modern machine learning systems is to achieve Out-of-Distribution (OOD) generalization -- generalizing to target data whose distribution differs from that of source data. Despite its significant importance, the fundamental question of ``what are the most effective algorithms for OOD generalization'' remains open even under the standard setting of covariate shift. This paper addresses this fundamental question by proving that, surprisingly, classical Maximum Likelihood Estimation (MLE) purely using source data (without any modification) achieves the minimax optimality for covariate shift under the well-specified setting. That is, no algorithm performs better than MLE in this setting (up to a constant factor), justifying MLE is all you need. Our result holds for a very rich class of parametric models, and does not require any boundedness condition on the density ratio. We illustrate the wide applicability of our framework by instantiating it to three concrete examples -- linear regression, logistic regression, and phase retrieval. This paper further complement the study by proving that, under the misspecified setting, MLE is no longer the optimal choice, whereas Maximum Weighted Likelihood Estimator (MWLE) emerges as minimax optimal in certain scenarios.

The remarkable progress of Multi-modal Large Language Models (MLLMs) has attracted significant attention due to their superior performance in visual contexts. However, their capabilities in turning visual figure to executable code, have not been evaluated thoroughly. To address this, we introduce Plot2Code, a comprehensive visual coding benchmark designed for a fair and in-depth assessment of MLLMs. We carefully collect 132 manually selected high-quality matplotlib plots across six plot types from publicly available matplotlib galleries. For each plot, we carefully offer its source code, and an descriptive instruction summarized by GPT-4. This approach enables Plot2Code to extensively evaluate MLLMs' code capabilities across various input modalities. Furthermore, we propose three automatic evaluation metrics, including code pass rate, text-match ratio, and GPT-4V overall rating, for a fine-grained assessment of the output code and rendered images. Instead of simply judging pass or fail, we employ GPT-4V to make an overall judgement between the generated and reference images, which has been shown to be consistent with human evaluation. The evaluation results, which include analyses of 14 MLLMs such as the proprietary GPT-4V, Gemini-Pro, and the open-sourced Mini-Gemini, highlight the substantial challenges presented by Plot2Code. With Plot2Code, we reveal that most existing MLLMs struggle with visual coding for text-dense plots, heavily relying on textual instruction. We hope that the evaluation results from Plot2Code on visual coding will guide the future development of MLLMs. All data involved with Plot2Code are available at https://huggingface.co/datasets/TencentARC/Plot2Code.

Multimodal Large Language Models (MLLMs) are set to transform how machines process and generate human-like responses by integrating diverse modalities such as text, images, and code. Yet, effectively harnessing their capabilities hinges on optimal prompt engineering. We present a comprehensive experimental evaluation of seven prompt engineering methods applied to 13 open-source MLLMs over 24 tasks spanning Reasoning and Compositionality, Multimodal Understanding and Alignment, Complex Code Generation and Execution, and Knowledge Retrieval and Integration. Our approach stratifies models by parameter count into Small (<4B), Medium (4B-10B), and Large (>10B) categories and compares prompting techniques including Zero-Shot, One-Shot, Few-Shot, Chain-of-Thought, Analogical, Generated Knowledge, and Tree-of-Thought. While Large MLLMs excel in structured tasks such as code generation, achieving accuracies up to 96.88% under Few-Shot prompting, all models struggle with complex reasoning and abstract understanding, often yielding accuracies below 60% and high hallucination rates. Structured reasoning prompts frequently increased hallucination up to 75% in small models and led to longer response times (over 20 seconds in Large MLLMs), while simpler prompting methods provided more concise and efficient outputs. No single prompting method uniformly optimises all task types. Instead, adaptive strategies combining example-based guidance with selective structured reasoning are essential to enhance robustness, efficiency, and factual accuracy. Our findings offer practical recommendations for prompt engineering and support more reliable deployment of MLLMs across applications including AI-assisted coding, knowledge retrieval, and multimodal content understanding.

Continuous latent variables (LVs) are a key ingredient of many generative models, as they allow modelling expressive mixtures with an uncountable number of components. In contrast, probabilistic circuits (PCs) are hierarchical discrete mixtures represented as computational graphs composed of input, sum and product units. Unlike continuous LV models, PCs provide tractable inference but are limited to discrete LVs with categorical (i.e. unordered) states. We bridge these model classes by introducing probabilistic integral circuits (PICs), a new language of computational graphs that extends PCs with integral units representing continuous LVs. In the first place, PICs are symbolic computational graphs and are fully tractable in simple cases where analytical integration is possible. In practice, we parameterise PICs with light-weight neural nets delivering an intractable hierarchical continuous mixture that can be approximated arbitrarily well with large PCs using numerical quadrature. On several distribution estimation benchmarks, we show that such PIC-approximating PCs systematically outperform PCs commonly learned via expectation-maximization or SGD.

Speculative decoding is a powerful way to accelerate autoregressive large language models (LLMs), but directly porting it to vision-language models (VLMs) faces unique systems constraints: the prefill stage is dominated by visual tokens whose count scales with image resolution and video length, inflating both compute and memory, especially the key-value (KV) cache. We study speculative decoding for VLMs and introduce SpecVLM, a practical system that (1) establishes a strong EAGLE-2-style baseline, EagleVLM, delivering 1.5--2.3x end-to-end speedups over full autoregressive inference, and (2) further accelerates VLM inference with an elastic visual compressor that adaptively selects among pruning, pooling, convolution, and resampler primitives to balance FLOPs/parameters and accuracy per input. To avoid costly offline distillation corpora, we propose an online-logit distillation protocol that trains the draft model with on-the-fly teacher logits and penultimate features using a combined cross-entropy and Smooth L1 objective, eliminating storage and preprocessing while remaining compute-efficient. This protocol reveals a training-time scaling effect: longer online training monotonically increases the draft model's average accepted length, improving speculative efficiency. Empirically, SpecVLM achieves additional acceleration, culminating in 2.5--2.9x end-to-end speedups within 5 epochs across LLaVA and MMMU, consistently over resolutions and task difficulties, while preserving the target model's output distribution (lossless decoding). Our code is available at https://github.com/haiduo/SpecVLM.

Although vision models such as Contrastive Language-Image Pre-Training (CLIP) show impressive generalization performance, their zero-shot robustness is still limited under Out-of-Distribution (OOD) scenarios without fine-tuning. Instead of undesirably providing human supervision as commonly done, it is possible to take advantage of Multi-modal Large Language Models (MLLMs) that hold powerful visual understanding abilities. However, MLLMs are shown to struggle with vision problems due to the incompatibility of tasks, thus hindering their utilization. In this paper, we propose to effectively leverage MLLMs to conduct Machine Vision Therapy which aims to rectify the noisy predictions from vision models. By fine-tuning with the denoised labels, the learning model performance can be boosted in an unsupervised manner. To solve the incompatibility issue, we propose a novel Denoising In-Context Learning (DICL) strategy to align vision tasks with MLLMs. Concretely, by estimating a transition matrix that captures the probability of one class being confused with another, an instruction containing a correct exemplar and an erroneous one from the most probable noisy class can be constructed. Such an instruction can help any MLLMs with ICL ability to detect and rectify incorrect predictions of vision models. Through extensive experiments on ImageNet, WILDS, DomainBed, and other OOD datasets, we carefully validate the quantitative and qualitative effectiveness of our method. Our code is available at https://github.com/tmllab/Machine_Vision_Therapy.

The remarkable success of the autoregressive paradigm has made significant advancement in Multimodal Large Language Models (MLLMs), with powerful models like Show-o, Transfusion and Emu3 achieving notable progress in unified image understanding and generation. For the first time, we uncover a common phenomenon: the understanding capabilities of MLLMs are typically stronger than their generative capabilities, with a significant gap between the two. Building on this insight, we propose HermesFlow, a simple yet general framework designed to seamlessly bridge the gap between understanding and generation in MLLMs. Specifically, we take the homologous data as input to curate homologous preference data of both understanding and generation. Through Pair-DPO and self-play iterative optimization, HermesFlow effectively aligns multimodal understanding and generation using homologous preference data. Extensive experiments demonstrate the significant superiority of our approach over prior methods, particularly in narrowing the gap between multimodal understanding and generation. These findings highlight the potential of HermesFlow as a general alignment framework for next-generation multimodal foundation models. Code: https://github.com/Gen-Verse/HermesFlow

We propose a novel hierarchical Bayesian model for learning with a large (possibly infinite) number of tasks/episodes, which suits well the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific target generative processes, where these local random variables are governed by a higher-level global random variate. The global variable helps memorize the important information from historic episodes while controlling how much the model needs to be adapted to new episodes in a principled Bayesian manner. Within our model framework, the prediction on a novel episode/task can be seen as a Bayesian inference problem. However, a main obstacle in learning with a large/infinite number of local random variables in online nature, is that one is not allowed to store the posterior distribution of the current local random variable for frequent future updates, typical in conventional variational inference. We need to be able to treat each local variable as a one-time iterate in the optimization. We propose a Normal-Inverse-Wishart model, for which we show that this one-time iterate optimization becomes feasible due to the approximate closed-form solutions for the local posterior distributions. The resulting algorithm is more attractive than the MAML in that it is not required to maintain computational graphs for the whole gradient optimization steps per episode. Our approach is also different from existing Bayesian meta learning methods in that unlike dealing with a single random variable for the whole episodes, our approach has a hierarchical structure that allows one-time episodic optimization, desirable for principled Bayesian learning with many/infinite tasks. The code is available at https://github.com/minyoungkim21/niwmeta.

We introduce a theoretical framework for sampling from unnormalized densities based on a smoothing scheme that uses an isotropic Gaussian kernel with a single fixed noise scale. We prove one can decompose sampling from a density (minimal assumptions made on the density) into a sequence of sampling from log-concave conditional densities via accumulation of noisy measurements with equal noise levels. Our construction is unique in that it keeps track of a history of samples, making it non-Markovian as a whole, but it is lightweight algorithmically as the history only shows up in the form of a running empirical mean of samples. Our sampling algorithm generalizes walk-jump sampling (Saremi & Hyv\"arinen, 2019). The "walk" phase becomes a (non-Markovian) chain of (log-concave) Markov chains. The "jump" from the accumulated measurements is obtained by empirical Bayes. We study our sampling algorithm quantitatively using the 2-Wasserstein metric and compare it with various Langevin MCMC algorithms. We also report a remarkable capacity of our algorithm to "tunnel" between modes of a distribution.

The emergence of large language models (LLMs) has significantly pushed the frontiers of program synthesis. Advancement of LLM-based program synthesis calls for a thorough evaluation of LLM-generated code. Most evaluation frameworks focus on the (functional) correctness of generated code; efficiency, as an important measure of code quality, has been overlooked in existing evaluations. In this work, we develop ENAMEL (EfficeNcy AutoMatic EvaLuator), a rigorous and high-standard benchmark for evaluating the capability of LLMs in generating efficient code. Firstly, we propose a new efficiency metric called eff@k, which generalizes the pass@k metric from correctness to efficiency and appropriately handles right-censored execution time. Furthermore, we derive an unbiased and variance-reduced estimator of eff@k via Rao--Blackwellization; we also provide a numerically stable implementation for the new estimator. Secondly, to set a high-standard for efficiency evaluation, we employ a human expert to design best algorithms and implementations as our reference solutions of efficiency, many of which are much more efficient than existing canonical solutions in HumanEval and HumanEval+. Moreover, to ensure a rigorous evaluation, we employ a human expert to curate strong test case generators to filter out wrong code and differentiate suboptimal algorithms. An extensive study across 30 popular LLMs using our benchmark ENAMEL shows that LLMs still fall short of generating expert-level efficient code. Using two subsets of our problem set, we demonstrate that such deficiency is because current LLMs struggle in designing advanced algorithms and are barely aware of implementation optimization. Our benchmark is publicly available at https://github.com/q-rz/enamel .

Advanced Multimodal Large Language Models (MLLMs) struggle with recent Knowledge-based VQA tasks, such as INFOSEEK and Encyclopedic-VQA, due to their limited and frozen knowledge scope, often leading to ambiguous and inaccurate responses. Thus, multimodal Retrieval-Augmented Generation (mRAG) is naturally introduced to provide MLLMs with comprehensive and up-to-date knowledge, effectively expanding the knowledge scope. However, current mRAG methods have inherent drawbacks, including: 1) Performing retrieval even when external knowledge is not needed. 2) Lacking of identification of evidence that supports the query. 3) Increasing model complexity due to additional information filtering modules or rules. To address these shortcomings, we propose a novel generalized framework called multimodal Retrieval-Reflection-Augmented Generation (mR^2AG), which achieves adaptive retrieval and useful information localization to enable answers through two easy-to-implement reflection operations, preventing high model complexity. In mR^2AG, Retrieval-Reflection is designed to distinguish different user queries and avoids redundant retrieval calls, and Relevance-Reflection is introduced to guide the MLLM in locating beneficial evidence of the retrieved content and generating answers accordingly. In addition, mR^2AG can be integrated into any well-trained MLLM with efficient fine-tuning on the proposed mR^2AG Instruction-Tuning dataset (mR^2AG-IT). mR^2AG significantly outperforms state-of-the-art MLLMs (e.g., GPT-4v/o) and RAG-based MLLMs on INFOSEEK and Encyclopedic-VQA, while maintaining the exceptional capabilities of base MLLMs across a wide range of Visual-dependent tasks.

The whole slide image (WSI) classification is often formulated as a multiple instance learning (MIL) problem. Since the positive tissue is only a small fraction of the gigapixel WSI, existing MIL methods intuitively focus on identifying salient instances via attention mechanisms. However, this leads to a bias towards easy-to-classify instances while neglecting hard-to-classify instances. Some literature has revealed that hard examples are beneficial for modeling a discriminative boundary accurately. By applying such an idea at the instance level, we elaborate a novel MIL framework with masked hard instance mining (MHIM-MIL), which uses a Siamese structure (Teacher-Student) with a consistency constraint to explore the potential hard instances. With several instance masking strategies based on attention scores, MHIM-MIL employs a momentum teacher to implicitly mine hard instances for training the student model, which can be any attention-based MIL model. This counter-intuitive strategy essentially enables the student to learn a better discriminating boundary. Moreover, the student is used to update the teacher with an exponential moving average (EMA), which in turn identifies new hard instances for subsequent training iterations and stabilizes the optimization. Experimental results on the CAMELYON-16 and TCGA Lung Cancer datasets demonstrate that MHIM-MIL outperforms other latest methods in terms of performance and training cost. The code is available at: https://github.com/DearCaat/MHIM-MIL.

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global Optimization), a simple and effective algorithm to solve it. Under certain regularity assumptions, we show that our algorithm enjoys the same cumulative regret bound as that in the unconstrained case and similar cumulative constraint violation upper bounds. For commonly used Matern and Squared Exponential kernels, our bounds are sublinear and allow us to derive a convergence rate to the optimal solution of the original constrained problem. In addition, our method naturally provides a scheme to declare infeasibility when the original black-box optimization problem is infeasible. Numerical experiments on sampled instances from the Gaussian process, artificial numerical problems, and a black-box building controller tuning problem all demonstrate the competitive performance of our algorithm. Compared to the other state-of-the-art methods, our algorithm significantly improves the theoretical guarantees, while achieving competitive empirical performance.

Error Feedback (EF) is a highly popular and immensely effective mechanism for fixing convergence issues which arise in distributed training methods (such as distributed GD or SGD) when these are enhanced with greedy communication compression techniques such as TopK. While EF was proposed almost a decade ago (Seide et al., 2014), and despite concentrated effort by the community to advance the theoretical understanding of this mechanism, there is still a lot to explore. In this work we study a modern form of error feedback called EF21 (Richtarik et al., 2021) which offers the currently best-known theoretical guarantees, under the weakest assumptions, and also works well in practice. In particular, while the theoretical communication complexity of EF21 depends on the quadratic mean of certain smoothness parameters, we improve this dependence to their arithmetic mean, which is always smaller, and can be substantially smaller, especially in heterogeneous data regimes. We take the reader on a journey of our discovery process. Starting with the idea of applying EF21 to an equivalent reformulation of the underlying problem which (unfortunately) requires (often impractical) machine cloning, we continue to the discovery of a new weighted version of EF21 which can (fortunately) be executed without any cloning, and finally circle back to an improved analysis of the original EF21 method. While this development applies to the simplest form of EF21, our approach naturally extends to more elaborate variants involving stochastic gradients and partial participation. Further, our technique improves the best-known theory of EF21 in the rare features regime (Richtarik et al., 2023). Finally, we validate our theoretical findings with suitable experiments.

It is believed that in knowledge distillation (KD), the role of the teacher is to provide an estimate for the unknown Bayes conditional probability distribution (BCPD) to be used in the student training process. Conventionally, this estimate is obtained by training the teacher using maximum log-likelihood (MLL) method. To improve this estimate for KD, in this paper we introduce the concept of conditional mutual information (CMI) into the estimation of BCPD and propose a novel estimator called the maximum CMI (MCMI) method. Specifically, in MCMI estimation, both the log-likelihood and CMI of the teacher are simultaneously maximized when the teacher is trained. Through Eigen-CAM, it is further shown that maximizing the teacher's CMI value allows the teacher to capture more contextual information in an image cluster. Via conducting a thorough set of experiments, we show that by employing a teacher trained via MCMI estimation rather than one trained via MLL estimation in various state-of-the-art KD frameworks, the student's classification accuracy consistently increases, with the gain of up to 3.32\%. This suggests that the teacher's BCPD estimate provided by MCMI method is more accurate than that provided by MLL method. In addition, we show that such improvements in the student's accuracy are more drastic in zero-shot and few-shot settings. Notably, the student's accuracy increases with the gain of up to 5.72\% when 5\% of the training samples are available to the student (few-shot), and increases from 0\% to as high as 84\% for an omitted class (zero-shot). The code is available at https://github.com/iclr2024mcmi/ICLRMCMI.

Scientific Machine Learning (SciML) is concerned with the development of learned emulators of physical systems governed by partial differential equations (PDE). In application domains such as weather forecasting, molecular dynamics, and inverse design, ML-based surrogate models are increasingly used to augment or replace inefficient and often non-differentiable numerical simulation algorithms. While a number of ML-based methods for approximating the solutions of PDEs have been proposed in recent years, they typically do not adapt to the parameters of the PDEs, making it difficult to generalize to PDE parameters not seen during training. We propose a Channel Attention mechanism guided by PDE Parameter Embeddings (CAPE) component for neural surrogate models and a simple yet effective curriculum learning strategy. The CAPE module can be combined with neural PDE solvers allowing them to adapt to unseen PDE parameters. The curriculum learning strategy provides a seamless transition between teacher-forcing and fully auto-regressive training. We compare CAPE in conjunction with the curriculum learning strategy using a popular PDE benchmark and obtain consistent and significant improvements over the baseline models. The experiments also show several advantages of CAPE, such as its increased ability to generalize to unseen PDE parameters without large increases inference time and parameter count.

Most bandit algorithms assume that the reward variances or their upper bounds are known, and that they are the same for all arms. This naturally leads to suboptimal performance and higher regret due to variance overestimation. On the other hand, underestimated reward variances may lead to linear regret due to committing early to a suboptimal arm. This motivated prior works on variance-adaptive frequentist algorithms, which have strong instance-dependent regret bounds but cannot incorporate prior knowledge on reward variances. We lay foundations for the Bayesian setting, which incorporates prior knowledge. This results in lower regret in practice, due to using the prior in the algorithm design, and also improved regret guarantees. Specifically, we study Gaussian bandits with {unknown heterogeneous reward variances}, and develop a Thompson sampling algorithm with prior-dependent Bayes regret bounds. We achieve lower regret with lower reward variances and more informative priors on them, which is precisely why we pay only for what is uncertain. This is the first result of its kind. Finally, we corroborate our theory with extensive experiments, which show the superiority of our variance-adaptive Bayesian algorithm over prior frequentist approaches. We also show that our approach is robust to model misspecification and can be applied with estimated priors.

With the advent of large language models (LLMs) like GPT-3, a natural question is the extent to which these models can be utilized for source code optimization. This paper presents methodologically stringent case studies applied to well-known open source python libraries pillow and numpy. We find that contemporary LLM ChatGPT-4 (state September and October 2023) is surprisingly adept at optimizing energy and compute efficiency. However, this is only the case in interactive use, with a human expert in the loop. Aware of experimenter bias, we document our qualitative approach in detail, and provide transcript and source code. We start by providing a detailed description of our approach in conversing with the LLM to optimize the _getextrema function in the pillow library, and a quantitative evaluation of the performance improvement. To demonstrate qualitative replicability, we report further attempts on another locus in the pillow library, and one code locus in the numpy library, to demonstrate generalization within and beyond a library. In all attempts, the performance improvement is significant (factor up to 38). We have also not omitted reporting of failed attempts (there were none). We conclude that LLMs are a promising tool for code optimization in open source libraries, but that the human expert in the loop is essential for success. Nonetheless, we were surprised by how few iterations were required to achieve substantial performance improvements that were not obvious to the expert in the loop. We would like bring attention to the qualitative nature of this study, more robust quantitative studies would need to introduce a layer of selecting experts in a representative sample -- we invite the community to collaborate.

Quantum error mitigation (QEM) is critical in reducing the impact of noise in the pre-fault-tolerant era, and is expected to complement error correction in fault-tolerant quantum computing (FTQC). In this paper, we propose a novel QEM approach, Q-Cluster, that uses unsupervised learning (clustering) to reshape the measured bit-string distribution. Our approach starts with a simplified bit-flip noise model. It first performs clustering on noisy measurement results, i.e., bit-strings, based on the Hamming distance. The centroid of each cluster is calculated using a qubit-wise majority vote. Next, the noisy distribution is adjusted with the clustering outcomes and the bit-flip error rates using Bayesian inference. Our simulation results show that Q-Cluster can mitigate high noise rates (up to 40% per qubit) with the simple bit-flip noise model. However, real quantum computers do not fit such a simple noise model. To address the problem, we (a) apply Pauli twirling to tailor the complex noise channels to Pauli errors, and (b) employ a machine learning model, ExtraTrees regressor, to estimate an effective bit-flip error rate using a feature vector consisting of machine calibration data (gate & measurement error rates), circuit features (number of qubits, numbers of different types of gates, etc.) and the shape of the noisy distribution (entropy). Our experimental results show that our proposed Q-Cluster scheme improves the fidelity by a factor of 1.46x, on average, compared to the unmitigated output distribution, for a set of low-entropy benchmarks on five different IBM quantum machines. Our approach outperforms the state-of-art QEM approaches M3 [24], Hammer [35], and QBEEP [33] by 1.29x, 1.47x, and 2.65x, respectively.

Generative artificial intelligence (AI) has made unprecedented advances in vision language models over the past two years. During the generative process, new samples (images) are generated from an unknown high-dimensional distribution. Markov Chain Monte Carlo (MCMC) methods are particularly effective in drawing samples from such complex, high-dimensional distributions. This makes MCMC methods an integral component for models like EBMs, ensuring accurate sample generation. Gradient-based optimization is at the core of modern generative models. The update step during the optimization forms a Markov chain where the new update depends only on the current state. This allows exploration of the parameter space in a memoryless manner, thus combining the benefits of gradient-based optimization and MCMC sampling. MCMC methods have shown an equally important role in physically based rendering where complex light paths are otherwise quite challenging to sample from simple importance sampling techniques. A lot of research is dedicated towards bringing physical realism to samples (images) generated from diffusion-based generative models in a data-driven manner, however, a unified framework connecting these techniques is still missing. In this course, we take the first steps toward understanding each of these components and exploring how MCMC could potentially serve as a bridge, linking these closely related areas of research. Our course aims to provide necessary theoretical and practical tools to guide students, researchers and practitioners towards the common goal of generative physically based rendering. All Jupyter notebooks with demonstrations associated to this tutorial can be found on the project webpage: https://sinbag.github.io/mcmc/

This paper introduces Multi-Modal Retrieval-Augmented Generation (M^2RAG), a benchmark designed to evaluate the effectiveness of Multi-modal Large Language Models (MLLMs) in leveraging knowledge from multi-modal retrieval documents. The benchmark comprises four tasks: image captioning, multi-modal question answering, multi-modal fact verification, and image reranking. All tasks are set in an open-domain setting, requiring RAG models to retrieve query-relevant information from a multi-modal document collection and use it as input context for RAG modeling. To enhance the context utilization capabilities of MLLMs, we also introduce Multi-Modal Retrieval-Augmented Instruction Tuning (MM-RAIT), an instruction tuning method that optimizes MLLMs within multi-modal contexts. Our experiments show that MM-RAIT improves the performance of RAG systems by enabling them to effectively learn from multi-modal contexts. All data and code are available at https://github.com/NEUIR/M2RAG.

Inference-time optimization scales computation to derive deliberate reasoning steps for effective performance. While previous search-based strategies address the short-sightedness of auto-regressive generation, the vast search space leads to excessive exploration and insufficient exploitation. To strike an efficient balance to derive the optimal step, we frame the decoding strategy as foresight sampling, leveraging simulated future steps to obtain globally optimal step estimation. Built on it, we propose a novel decoding strategy, named phi-Decoding. To provide a precise and expressive estimation of step value, phi-Decoding approximates two distributions via foresight and clustering. Sampling from the joint distribution, the optimal steps can be selected for exploitation. To support adaptive computation allocation, we propose in-width and in-depth pruning strategies, featuring a light-weight solution to achieve inference efficiency. Extensive experiments across seven benchmarks show phi-Decoding outperforms strong baselines in both performance and efficiency. Additional analysis demonstrates its generalization across various LLMs and scalability across a wide range of computing budgets. The code will be released at https://github.com/xufangzhi/phi-Decoding, and the open-source PyPI package is coming soon.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

Inference-Time Scaling (ITS) improves language models by allocating more computation at generation time. Particle Filtering (PF) has emerged as a strong ITS method for complex mathematical reasoning tasks, but it is vulnerable when guided by process reward models, which often assign overconfident scores early in the reasoning process. This causes PF to suffer from premature exploitation: it myopically commits to locally promising trajectories, prunes potentially correct hypotheses, and converges to suboptimal solutions. This failure mode, known as particle impoverishment, is especially severe under constrained computational budgets. To address this, we analyze the problem and identify two root causes: a lack of diversity in the particle set due to overconfident resampling and consequent inability to assess the potential of a reasoning path. We introduce Entropic Particle Filtering (ePF), an algorithm that integrates two new techniques to solve these issues. The first technique, Entropic Annealing (EA), directly mitigates particle impoverishment by monitoring search diversity via entropy; when diversity drops, it intervenes by dynamically annealing the resampling distribution to preserve exploration. The second, an enhancement called Look-ahead Modulation (LaM), adds a predictive guide to evaluate a state's potential based on its successors. On several challenging math benchmarks, ePF significantly outperforms strong baselines and achieves up to a 50 % relative improvement in task reward. Together, these methods improve PF's resilience by balancing the exploration of diverse solution spaces with the exploitation of high-reward regions, ultimately leading to higher-quality solutions.

In standard autoregressive generation, an LLM predicts the next-token distribution, samples a discrete token, and then discards the distribution, passing only the sampled token as new input. To preserve this distribution's rich information, we propose Mixture of Inputs (MoI), a training-free method for autoregressive generation. After generating a token following the standard paradigm, we construct a new input that blends the generated discrete token with the previously discarded token distribution. Specifically, we employ a Bayesian estimation method that treats the token distribution as the prior, the sampled token as the observation, and replaces the conventional one-hot vector with the continuous posterior expectation as the new model input. MoI allows the model to maintain a richer internal representation throughout the generation process, resulting in improved text quality and reasoning capabilities. On mathematical reasoning, code generation, and PhD-level QA tasks, MoI consistently improves performance across multiple models including QwQ-32B, Nemotron-Super-49B, Gemma-3-27B, and DAPO-Qwen-32B, with no additional training and negligible computational overhead.

We study a family of distributed stochastic optimization algorithms where gradients are sampled by a token traversing a network of agents in random-walk fashion. Typically, these random-walks are chosen to be Markov chains that asymptotically sample from a desired target distribution, and play a critical role in the convergence of the optimization iterates. In this paper, we take a novel approach by replacing the standard linear Markovian token by one which follows a nonlinear Markov chain - namely the Self-Repellent Radom Walk (SRRW). Defined for any given 'base' Markov chain, the SRRW, parameterized by a positive scalar {\alpha}, is less likely to transition to states that were highly visited in the past, thus the name. In the context of MCMC sampling on a graph, a recent breakthrough in Doshi et al. (2023) shows that the SRRW achieves O(1/{\alpha}) decrease in the asymptotic variance for sampling. We propose the use of a 'generalized' version of the SRRW to drive token algorithms for distributed stochastic optimization in the form of stochastic approximation, termed SA-SRRW. We prove that the optimization iterate errors of the resulting SA-SRRW converge to zero almost surely and prove a central limit theorem, deriving the explicit form of the resulting asymptotic covariance matrix corresponding to iterate errors. This asymptotic covariance is always smaller than that of an algorithm driven by the base Markov chain and decreases at rate O(1/{\alpha}^2) - the performance benefit of using SRRW thereby amplified in the stochastic optimization context. Empirical results support our theoretical findings.

Research on large language models (LLMs) has shown remarkable performance in domains such as mathematics, programming, and literary creation. However, most studies have focused on semantic memory-based question answering, neglecting LLMs' potential to handle episodic memory (EM)-related queries. This oversight has led to suboptimal performance in applications requiring EM, including emotional companionship, personal AI assistants, and AI teachers. To address this gap, we introduce Echo, a LLM enhanced with temporal episodic memory. We propose a Multi-Agent Data Generation Framework that guides the model in generating multi-turn, complex scenario episodic memory dialogue data (EM-Train). Temporal information is innovatively incorporated into the LLM training process, and Echo is trained using the EM-Train. Furthermore, We develop an EM-Test benchmark specifically designed to evaluate LLMs' episodic memory capabilities. The EM-Test assesses performance across various time spans and difficulty levels, providing a comprehensive evaluation of multi-turn episodic memory dialogues. Our experiments demonstrate that Echo significantly outperforms state-of-the-art LLMs on EM-Test. Additionally, a qualitative analysis reveals Echo's potential to exhibit human-like episodic memory capabilities. We will open-source all datasets, code, and model weights.

The training and deployment of large language models (LLMs) create a feedback loop with human users: models learn human beliefs from data, reinforce these beliefs with generated content, reabsorb the reinforced beliefs, and feed them back to users again and again. This dynamic resembles an echo chamber. We hypothesize that this feedback loop entrenches the existing values and beliefs of users, leading to a loss of diversity and potentially the lock-in of false beliefs. We formalize this hypothesis and test it empirically with agent-based LLM simulations and real-world GPT usage data. Analysis reveals sudden but sustained drops in diversity after the release of new GPT iterations, consistent with the hypothesized human-AI feedback loop. Code and data available at https://thelockinhypothesis.com

Recently, Multimodal Large Language Models (MLLMs) have gained significant attention across various domains. However, their widespread adoption has also raised serious safety concerns. In this paper, we uncover a new safety risk of MLLMs: the output preference of MLLMs can be arbitrarily manipulated by carefully optimized images. Such attacks often generate contextually relevant yet biased responses that are neither overtly harmful nor unethical, making them difficult to detect. Specifically, we introduce a novel method, Preference Hijacking (Phi), for manipulating the MLLM response preferences using a preference hijacked image. Our method works at inference time and requires no model modifications. Additionally, we introduce a universal hijacking perturbation -- a transferable component that can be embedded into different images to hijack MLLM responses toward any attacker-specified preferences. Experimental results across various tasks demonstrate the effectiveness of our approach. The code for Phi is accessible at https://github.com/Yifan-Lan/Phi.

Multimodal large language models (MLLMs) are broadly empowering various fields. Despite their advancements, the explainability of MLLMs remains less explored, hindering deeper understanding, model credibility, and effective visualization. Unlike conventional vision models (e.g., CNNs, ViTs, CLIP) that produce a single output, MLLMs generate sequences of tokens progressively, where each generated token depends on the previous context. Therefore, earlier context tokens can introduce redundant activations that interfere with the explanation of later tokens beyond their original information. Existing studies often overlook this issue, but our observations reveal that these redundant correlations can significantly hurt the reliability of explanations. To address this, we propose an estimated causal inference method to mitigate the interference of context to achieve high-quality MLLM explanation, with a novel rank Gaussian filter to further reduce activation noises. We term this method Token Activation Map (TAM) to highlight the consideration of interactions between tokens. TAM also indicates that it excels at explaining multiple tokens of MLLM, which is different from the Class Activation Map (CAM) for a single prediction. Our TAM method significantly outperforms existing SoTA methods, showcasing high-quality visualization results that can be utilized for various scenarios, such as object localization, failure case analysis, video visualization, MLLMs visual comparison, and model understanding (e.g., color, shape, action, location, visual reasoning, multi-turn conversation, etc). The code is available atgithub.com/xmed-lab/TAM.

Ensembles of independently trained neural networks are a state-of-the-art approach to estimate predictive uncertainty in Deep Learning, and can be interpreted as an approximation of the posterior distribution via a mixture of delta functions. The training of ensembles relies on non-convexity of the loss landscape and random initialization of their individual members, making the resulting posterior approximation uncontrolled. This paper proposes a novel and principled method to tackle this limitation, minimizing an f-divergence between the true posterior and a kernel density estimator (KDE) in a function space. We analyze this objective from a combinatorial point of view, and show that it is submodular with respect to mixture components for any f. Subsequently, we consider the problem of greedy ensemble construction. From the marginal gain on the negative f-divergence, which quantifies an improvement in posterior approximation yielded by adding a new component into the KDE, we derive a novel diversity term for ensemble methods. The performance of our approach is demonstrated on computer vision out-of-distribution detection benchmarks in a range of architectures trained on multiple datasets. The source code of our method is made publicly available at https://github.com/Oulu-IMEDS/greedy_ensembles_training.

Evolutionary multiobjective optimization (EMO) has made significant strides over the past two decades. However, as problem scales and complexities increase, traditional EMO algorithms face substantial performance limitations due to insufficient parallelism and scalability. While most work has focused on algorithm design to address these challenges, little attention has been given to hardware acceleration, thereby leaving a clear gap between EMO algorithms and advanced computing devices, such as GPUs. To bridge the gap, we propose to parallelize EMO algorithms on GPUs via the tensorization methodology. By employing tensorization, the data structures and operations of EMO algorithms are transformed into concise tensor representations, which seamlessly enables automatic utilization of GPU computing. We demonstrate the effectiveness of our approach by applying it to three representative EMO algorithms: NSGA-III, MOEA/D, and HypE. To comprehensively assess our methodology, we introduce a multiobjective robot control benchmark using a GPU-accelerated physics engine. Our experiments show that the tensorized EMO algorithms achieve speedups of up to 1113x compared to their CPU-based counterparts, while maintaining solution quality and effectively scaling population sizes to hundreds of thousands. Furthermore, the tensorized EMO algorithms efficiently tackle complex multiobjective robot control tasks, producing high-quality solutions with diverse behaviors. Source codes are available at https://github.com/EMI-Group/evomo.

Exponential moving average (EMA) has recently gained significant popularity in training modern deep learning models, especially diffusion-based generative models. However, there have been few theoretical results explaining the effectiveness of EMA. In this paper, to better understand EMA, we establish the risk bound of online SGD with EMA for high-dimensional linear regression, one of the simplest overparameterized learning tasks that shares similarities with neural networks. Our results indicate that (i) the variance error of SGD with EMA is always smaller than that of SGD without averaging, and (ii) unlike SGD with iterate averaging from the beginning, the bias error of SGD with EMA decays exponentially in every eigen-subspace of the data covariance matrix. Additionally, we develop proof techniques applicable to the analysis of a broad class of averaging schemes.

This work studies training instabilities of behavior cloning with deep neural networks. We observe that minibatch SGD updates to the policy network during training result in sharp oscillations in long-horizon rewards, despite negligibly affecting the behavior cloning loss. We empirically disentangle the statistical and computational causes of these oscillations, and find them to stem from the chaotic propagation of minibatch SGD noise through unstable closed-loop dynamics. While SGD noise is benign in the single-step action prediction objective, it results in catastrophic error accumulation over long horizons, an effect we term gradient variance amplification (GVA). We show that many standard mitigation techniques do not alleviate GVA, but find an exponential moving average (EMA) of iterates to be surprisingly effective at doing so. We illustrate the generality of this phenomenon by showing the existence of GVA and its amelioration by EMA in both continuous control and autoregressive language generation. Finally, we provide theoretical vignettes that highlight the benefits of EMA in alleviating GVA and shed light on the extent to which classical convex models can help in understanding the benefits of iterate averaging in deep learning.

Quantitative microstructural characterization is fundamental to materials science, where electron micrograph (EM) provides indispensable high-resolution insights. However, progress in deep learning-based EM characterization has been hampered by the scarcity of large-scale, diverse, and expert-annotated datasets, due to acquisition costs, privacy concerns, and annotation complexity. To address this issue, we introduce UniEM-3M, the first large-scale and multimodal EM dataset for instance-level understanding. It comprises 5,091 high-resolution EMs, about 3 million instance segmentation labels, and image-level attribute-disentangled textual descriptions, a subset of which will be made publicly available. Furthermore, we are also releasing a text-to-image diffusion model trained on the entire collection to serve as both a powerful data augmentation tool and a proxy for the complete data distribution. To establish a rigorous benchmark, we evaluate various representative instance segmentation methods on the complete UniEM-3M and present UniEM-Net as a strong baseline model. Quantitative experiments demonstrate that this flow-based model outperforms other advanced methods on this challenging benchmark. Our multifaceted release of a partial dataset, a generative model, and a comprehensive benchmark -- available at huggingface -- will significantly accelerate progress in automated materials analysis.

We introduce marginalization models (MaMs), a new family of generative models for high-dimensional discrete data. They offer scalable and flexible generative modeling with tractable likelihoods by explicitly modeling all induced marginal distributions. Marginalization models enable fast evaluation of arbitrary marginal probabilities with a single forward pass of the neural network, which overcomes a major limitation of methods with exact marginal inference, such as autoregressive models (ARMs). We propose scalable methods for learning the marginals, grounded in the concept of "marginalization self-consistency". Unlike previous methods, MaMs support scalable training of any-order generative models for high-dimensional problems under the setting of energy-based training, where the goal is to match the learned distribution to a given desired probability (specified by an unnormalized (log) probability function such as energy function or reward function). We demonstrate the effectiveness of the proposed model on a variety of discrete data distributions, including binary images, language, physical systems, and molecules, for maximum likelihood and energy-based training settings. MaMs achieve orders of magnitude speedup in evaluating the marginal probabilities on both settings. For energy-based training tasks, MaMs enable any-order generative modeling of high-dimensional problems beyond the capability of previous methods. Code is at https://github.com/PrincetonLIPS/MaM.

Improving Multi-modal Large Language Models (MLLMs) in the post-training stage typically relies on supervised fine-tuning (SFT) or reinforcement learning (RL). However, these supervised methods require expensive and manually annotated multi-modal data--an ultimately unsustainable resource. While recent efforts have explored unsupervised post-training, their methods are complex and difficult to iterate. In this work, we are the first to investigate the use of GRPO, a stable and scalable online RL algorithm, for enabling continual self-improvement without any external supervision. We propose MM-UPT, a simple yet effective framework for unsupervised post-training of MLLMs. MM-UPT builds upon GRPO, replacing traditional reward signals with a self-rewarding mechanism based on majority voting over multiple sampled responses. Our experiments demonstrate that MM-UPT significantly improves the reasoning ability of Qwen2.5-VL-7B (e.g., 66.3 %rightarrow72.9 % on MathVista, 62.9 %rightarrow68.7 % on We-Math), using standard dataset without ground truth labels. MM-UPT also outperforms prior unsupervised baselines and even approaches the results of supervised GRPO. Furthermore, we show that incorporating synthetic questions, generated solely by MLLM itself, can boost performance as well, highlighting a promising approach for scalable self-improvement. Overall, MM-UPT offers a new paradigm for continual, autonomous enhancement of MLLMs in the absence of external supervision. Our code is available at https://github.com/waltonfuture/MM-UPT.

Large language models are being widely used across industries to generate content that contributes directly to key performance metrics, such as conversion rates. Pretrained models, however, often fall short when it comes to aligning with human preferences or optimizing for business objectives. As a result, fine-tuning with good-quality labeled data is essential to guide models to generate content that achieves better results. Controlled experiments, like A/B tests, can provide such data, but they are often expensive and come with significant engineering and logistical challenges. Meanwhile, companies have access to a vast amount of historical (observational) data that remains underutilized. In this work, we study the challenges and opportunities of fine-tuning LLMs using observational data. We show that while observational outcomes can provide valuable supervision, directly fine-tuning models on such data can lead them to learn spurious correlations. We present empirical evidence of this issue using various real-world datasets and propose DeconfoundLM, a method that explicitly removes the effect of known confounders from reward signals. Using simulation experiments, we demonstrate that DeconfoundLM improves the recovery of causal relationships and mitigates failure modes found in fine-tuning methods that ignore or naively incorporate confounding variables. Our findings highlight that while observational data presents risks, with the right causal corrections, it can be a powerful source of signal for LLM alignment. Please refer to the project page for code and related resources.

The advent of pre-trained code language models (CodeLMs) has lead to significant progress in language-to-code generation. State-of-the-art approaches in this area combine CodeLM decoding with sample pruning and reranking using test cases or heuristics based on the execution results. However, it is challenging to obtain test cases for many real-world language-to-code applications, and heuristics cannot well capture the semantic features of the execution results, such as data type and value range, which often indicates the correctness of the program. In this work, we propose LEVER, a simple approach to improve language-to-code generation by learning to verify the generated programs with their execution results. Specifically, we train verifiers to determine whether a program sampled from the CodeLM is correct or not based on the natural language input, the program itself and its execution results. The sampled programs are reranked by combining the verification score with the CodeLM generation probability, and marginalizing over programs with the same execution results. On four datasets across the domains of table QA, math QA and basic Python programming, LEVER consistently improves over the base CodeLMs (4.6% to 10.9% with code-davinci-002) and achieves new state-of-the-art results on all of them.