Daily Papers

We report the presence of a simple neural mechanism that represents an input-output function as a vector within autoregressive transformer language models (LMs). Using causal mediation analysis on a diverse range of in-context-learning (ICL) tasks, we find that a small number attention heads transport a compact representation of the demonstrated task, which we call a function vector (FV). FVs are robust to changes in context, i.e., they trigger execution of the task on inputs such as zero-shot and natural text settings that do not resemble the ICL contexts from which they are collected. We test FVs across a range of tasks, models, and layers and find strong causal effects across settings in middle layers. We investigate the internal structure of FVs and find while that they often contain information that encodes the output space of the function, this information alone is not sufficient to reconstruct an FV. Finally, we test semantic vector composition in FVs, and find that to some extent they can be summed to create vectors that trigger new complex tasks. Taken together, our findings suggest that LLMs contain internal abstractions of general-purpose functions that can be invoked in a variety of contexts.

Recent work in activation steering has demonstrated the potential to better control the outputs of Large Language Models (LLMs), but it involves finding steering vectors. This is difficult because engineers do not typically know how features are represented in these models. We seek to address this issue by applying the idea of mean-centring to steering vectors. We find that taking the average of activations associated with a target dataset, and then subtracting the mean of all training activations, results in effective steering vectors. We test this method on a variety of models on natural language tasks by steering away from generating toxic text, and steering the completion of a story towards a target genre. We also apply mean-centring to extract function vectors, more effectively triggering the execution of a range of natural language tasks by a significant margin (compared to previous baselines). This suggests that mean-centring can be used to easily improve the effectiveness of activation steering in a wide range of contexts.

Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three levels: 1) The "atomic" small-scale structure contains "crystals" whose faces are parallelograms or trapezoids, generalizing well-known examples such as (man-woman-king-queen). We find that the quality of such parallelograms and associated function vectors improves greatly when projecting out global distractor directions such as word length, which is efficiently done with linear discriminant analysis. 2) The "brain" intermediate-scale structure has significant spatial modularity; for example, math and code features form a "lobe" akin to functional lobes seen in neural fMRI images. We quantify the spatial locality of these lobes with multiple metrics and find that clusters of co-occurring features, at coarse enough scale, also cluster together spatially far more than one would expect if feature geometry were random. 3) The "galaxy" scale large-scale structure of the feature point cloud is not isotropic, but instead has a power law of eigenvalues with steepest slope in middle layers. We also quantify how the clustering entropy depends on the layer.

Steering methods for language models (LMs) have gained traction as lightweight alternatives to fine-tuning, enabling targeted modifications to model activations. However, prior studies primarily report results on a few models, leaving critical gaps in understanding the robustness of these methods. In this work, we systematically examine three prominent steering methods -- DoLa, function vectors, and task vectors. In contrast to the original studies, which evaluated a handful of models, we test up to 36 models belonging to 14 families with sizes ranging from 1.5B to 70B parameters. Our experiments reveal substantial variability in the effectiveness of the steering approaches, with a large number of models showing no improvement and at times degradation in steering performance. Our analysis demonstrate fundamental flaws in the assumptions underlying these methods, challenging their reliability as scalable steering solutions.

The NeuroEvolution of Augmenting Topologies (NEAT) algorithm has received considerable recognition in the field of neuroevolution. Its effectiveness is derived from initiating with simple networks and incrementally evolving both their topologies and weights. Although its capability across various challenges is evident, the algorithm's computational efficiency remains an impediment, limiting its scalability potential. In response, this paper introduces a tensorization method for the NEAT algorithm, enabling the transformation of its diverse network topologies and associated operations into uniformly shaped tensors for computation. This advancement facilitates the execution of the NEAT algorithm in a parallelized manner across the entire population. Furthermore, we develop TensorNEAT, a library that implements the tensorized NEAT algorithm and its variants, such as CPPN and HyperNEAT. Building upon JAX, TensorNEAT promotes efficient parallel computations via automated function vectorization and hardware acceleration. Moreover, the TensorNEAT library supports various benchmark environments including Gym, Brax, and gymnax. Through evaluations across a spectrum of robotics control environments in Brax, TensorNEAT achieves up to 500x speedups compared to the existing implementations such as NEAT-Python. Source codes are available at: https://github.com/EMI-Group/tensorneat.

Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single real-valued function (the one-parameter setting), there is a canonical choice of descriptor for persistent homology: the barcode. The operation mapping a real-valued function to its barcode is differentiable almost everywhere, and the convergence of gradient descent for losses using barcodes is relatively well understood. When optimizing a vector-valued function (the multiparameter setting), there is no unique choice of descriptor for multiparameter persistent homology, and many distinct descriptors have been proposed. This calls for the development of a general framework for differentiability and optimization that applies to a wide range of multiparameter homological descriptors. In this article, we develop such a framework and show that it encompasses well-known descriptors of different flavors, such as signed barcodes and the multiparameter persistence landscape. We complement the theory with numerical experiments supporting the idea that optimizing multiparameter homological descriptors can lead to improved performances compared to optimizing one-parameter descriptors, even when using the simplest and most efficiently computable multiparameter descriptors.

Although BERT and its variants have reshaped the NLP landscape, it still remains unclear how best to derive sentence embeddings from such pre-trained Transformers. In this work, we propose a contrastive learning method that utilizes self-guidance for improving the quality of BERT sentence representations. Our method fine-tunes BERT in a self-supervised fashion, does not rely on data augmentation, and enables the usual [CLS] token embeddings to function as sentence vectors. Moreover, we redesign the contrastive learning objective (NT-Xent) and apply it to sentence representation learning. We demonstrate with extensive experiments that our approach is more effective than competitive baselines on diverse sentence-related tasks. We also show it is efficient at inference and robust to domain shifts.

Multi-vector retrieval models such as ColBERT [Khattab and Zaharia, 2020] allow token-level interactions between queries and documents, and hence achieve state of the art on many information retrieval benchmarks. However, their non-linear scoring function cannot be scaled to millions of documents, necessitating a three-stage process for inference: retrieving initial candidates via token retrieval, accessing all token vectors, and scoring the initial candidate documents. The non-linear scoring function is applied over all token vectors of each candidate document, making the inference process complicated and slow. In this paper, we aim to simplify the multi-vector retrieval by rethinking the role of token retrieval. We present XTR, ConteXtualized Token Retriever, which introduces a simple, yet novel, objective function that encourages the model to retrieve the most important document tokens first. The improvement to token retrieval allows XTR to rank candidates only using the retrieved tokens rather than all tokens in the document, and enables a newly designed scoring stage that is two-to-three orders of magnitude cheaper than that of ColBERT. On the popular BEIR benchmark, XTR advances the state-of-the-art by 2.8 nDCG@10 without any distillation. Detailed analysis confirms our decision to revisit the token retrieval stage, as XTR demonstrates much better recall of the token retrieval stage compared to ColBERT.

The change in data distribution over time, also known as concept drift, poses a significant challenge to the reliability of online learning methods. Existing methods typically require model retraining or drift detection, both of which demand high computational costs and are often unsuitable for real-time applications. To address these limitations, a lightweight, fast and efficient random vector functional-link network termed Lite-RVFL is proposed, capable of adapting to concept drift without drift detection and retraining. Lite-RVFL introduces a novel objective function that assigns weights exponentially increasing to new samples, thereby emphasizing recent data and enabling timely adaptation. Theoretical analysis confirms the feasibility of this objective function for drift adaptation, and an efficient incremental update rule is derived. Experimental results on a real-world safety assessment task validate the efficiency, effectiveness in adapting to drift, and potential to capture temporal patterns of Lite-RVFL. The source code is available at https://github.com/songqiaohu/Lite-RVFL.

Recent advancements in function calling and tool use have significantly enhanced the capabilities of large language models (LLMs) by enabling them to interact with external information sources and execute complex tasks. However, the limited context window of LLMs presents challenges when a large number of tools are available, necessitating efficient methods to manage prompt length and maintain accuracy. Existing approaches, such as fine-tuning LLMs or leveraging their reasoning capabilities, either require frequent retraining or incur significant latency overhead. A more efficient solution involves training smaller models to retrieve the most relevant tools for a given query, although this requires high quality, domain-specific data. To address those challenges, we present a novel framework for generating synthetic data for tool retrieval applications and an efficient data-driven tool retrieval strategy using small encoder models. Empowered by LLMs, we create ToolBank, a new tool retrieval dataset that reflects real human user usages. For tool retrieval methodologies, we propose novel approaches: (1) Tool2Vec: usage-driven tool embedding generation for tool retrieval, (2) ToolRefiner: a staged retrieval method that iteratively improves the quality of retrieved tools, and (3) MLC: framing tool retrieval as a multi-label classification problem. With these new methods, we achieve improvements of up to 27.28 in Recall@K on the ToolBench dataset and 30.5 in Recall@K on ToolBank. Additionally, we present further experimental results to rigorously validate our methods. Our code is available at https://github.com/SqueezeAILab/Tool2Vec

Recent advancements in implicit neural representations have contributed to high-fidelity surface reconstruction and photorealistic novel view synthesis. However, the computational complexity inherent in these methodologies presents a substantial impediment, constraining the attainable frame rates and resolutions in practical applications. In response to this predicament, we propose VQ-NeRF, an effective and efficient pipeline for enhancing implicit neural representations via vector quantization. The essence of our method involves reducing the sampling space of NeRF to a lower resolution and subsequently reinstating it to the original size utilizing a pre-trained VAE decoder, thereby effectively mitigating the sampling time bottleneck encountered during rendering. Although the codebook furnishes representative features, reconstructing fine texture details of the scene remains challenging due to high compression rates. To overcome this constraint, we design an innovative multi-scale NeRF sampling scheme that concurrently optimizes the NeRF model at both compressed and original scales to enhance the network's ability to preserve fine details. Furthermore, we incorporate a semantic loss function to improve the geometric fidelity and semantic coherence of our 3D reconstructions. Extensive experiments demonstrate the effectiveness of our model in achieving the optimal trade-off between rendering quality and efficiency. Evaluation on the DTU, BlendMVS, and H3DS datasets confirms the superior performance of our approach.

Set function learning has emerged as a crucial area in machine learning, addressing the challenge of modeling functions that take sets as inputs. Unlike traditional machine learning that involves fixed-size input vectors where the order of features matters, set function learning demands methods that are invariant to permutations of the input set, presenting a unique and complex problem. This survey provides a comprehensive overview of the current development in set function learning, covering foundational theories, key methodologies, and diverse applications. We categorize and discuss existing approaches, focusing on deep learning approaches, such as DeepSets and Set Transformer based methods, as well as other notable alternative methods beyond deep learning, offering a complete view of current models. We also introduce various applications and relevant datasets, such as point cloud processing and multi-label classification, highlighting the significant progress achieved by set function learning methods in these domains. Finally, we conclude by summarizing the current state of set function learning approaches and identifying promising future research directions, aiming to guide and inspire further advancements in this promising field.

We propose affine concept editing (ACE) as an approach for steering language models' behavior by intervening directly in activations. We begin with an affine decomposition of model activation vectors and show that prior methods for steering model behavior correspond to subsets of terms of this decomposition. We then provide a derivation of ACE and use it to control refusal behavior on ten different models, including Llama 3 70B. ACE combines affine subspace projection and activation addition to reliably control the model's refusal responses across prompt types. We evaluate the results using LLM-based scoring on a collection of harmful and harmless prompts. Our experiments demonstrate that ACE consistently achieves more precise control over model behavior than existing methods and generalizes to models where directional ablation via affine subspace projection alone produces incoherent outputs. Code for reproducing our results is available at https://github.com/EleutherAI/steering-llama3 .

We propose Equiangular Basis Vectors (EBVs) for classification tasks. In deep neural networks, models usually end with a k-way fully connected layer with softmax to handle different classification tasks. The learning objective of these methods can be summarized as mapping the learned feature representations to the samples' label space. While in metric learning approaches, the main objective is to learn a transformation function that maps training data points from the original space to a new space where similar points are closer while dissimilar points become farther apart. Different from previous methods, our EBVs generate normalized vector embeddings as "predefined classifiers" which are required to not only be with the equal status between each other, but also be as orthogonal as possible. By minimizing the spherical distance of the embedding of an input between its categorical EBV in training, the predictions can be obtained by identifying the categorical EBV with the smallest distance during inference. Various experiments on the ImageNet-1K dataset and other downstream tasks demonstrate that our method outperforms the general fully connected classifier while it does not introduce huge additional computation compared with classical metric learning methods. Our EBVs won the first place in the 2022 DIGIX Global AI Challenge, and our code is open-source and available at https://github.com/NJUST-VIPGroup/Equiangular-Basis-Vectors.

Conventional wisdom holds that autoregressive models for image generation are typically accompanied by vector-quantized tokens. We observe that while a discrete-valued space can facilitate representing a categorical distribution, it is not a necessity for autoregressive modeling. In this work, we propose to model the per-token probability distribution using a diffusion procedure, which allows us to apply autoregressive models in a continuous-valued space. Rather than using categorical cross-entropy loss, we define a Diffusion Loss function to model the per-token probability. This approach eliminates the need for discrete-valued tokenizers. We evaluate its effectiveness across a wide range of cases, including standard autoregressive models and generalized masked autoregressive (MAR) variants. By removing vector quantization, our image generator achieves strong results while enjoying the speed advantage of sequence modeling. We hope this work will motivate the use of autoregressive generation in other continuous-valued domains and applications.

Large language models (LLMs) have shown remarkable in-context learning (ICL) capabilities on textual data. We explore whether these capabilities can be extended to continuous vectors from diverse domains, obtained from black-box pretrained encoders. By aligning input data with an LLM's embedding space through lightweight projectors, we observe that LLMs can effectively process and learn from these projected vectors, which we term Vector-ICL. In particular, we find that pretraining projectors with general language modeling objectives enables Vector-ICL, while task-specific finetuning further enhances performance. In our experiments across various tasks and modalities, including text reconstruction, numerical function regression, text classification, summarization, molecule captioning, time-series classification, graph classification, and fMRI decoding, Vector-ICL often surpasses both few-shot ICL and domain-specific model or tuning. We further conduct analyses and case studies, indicating the potential of LLMs to process vector representations beyond traditional token-based paradigms.

We study the sparse recovery problem with an underdetermined linear system characterized by a Kronecker-structured dictionary and a Kronecker-supported sparse vector. We cast this problem into the sparse Bayesian learning (SBL) framework and rely on the expectation-maximization method for a solution. To this end, we model the Kronecker-structured support with a hierarchical Gaussian prior distribution parameterized by a Kronecker-structured hyperparameter, leading to a non-convex optimization problem. The optimization problem is solved using the alternating minimization (AM) method and a singular value decomposition (SVD)-based method, resulting in two algorithms. Further, we analytically guarantee that the AM-based method converges to the stationary point of the SBL cost function. The SVD-based method, though it adopts approximations, is empirically shown to be more efficient and accurate. We then apply our algorithm to estimate the uplink wireless channel in an intelligent reflecting surface-aided MIMO system and extend the AM-based algorithm to address block sparsity in the channel. We also study the SBL cost to show that the minima of the cost function are achieved at sparse solutions and that incorporating the Kronecker structure reduces the number of local minima of the SBL cost function. Our numerical results demonstrate the effectiveness of our algorithms compared to the state-of-the-art.

Convolutional neural networks (CNNs) are similar to "ordinary" neural networks in the sense that they are made up of hidden layers consisting of neurons with "learnable" parameters. These neurons receive inputs, performs a dot product, and then follows it with a non-linearity. The whole network expresses the mapping between raw image pixels and their class scores. Conventionally, the Softmax function is the classifier used at the last layer of this network. However, there have been studies (Alalshekmubarak and Smith, 2013; Agarap, 2017; Tang, 2013) conducted to challenge this norm. The cited studies introduce the usage of linear support vector machine (SVM) in an artificial neural network architecture. This project is yet another take on the subject, and is inspired by (Tang, 2013). Empirical data has shown that the CNN-SVM model was able to achieve a test accuracy of ~99.04% using the MNIST dataset (LeCun, Cortes, and Burges, 2010). On the other hand, the CNN-Softmax was able to achieve a test accuracy of ~99.23% using the same dataset. Both models were also tested on the recently-published Fashion-MNIST dataset (Xiao, Rasul, and Vollgraf, 2017), which is suppose to be a more difficult image classification dataset than MNIST (Zalandoresearch, 2017). This proved to be the case as CNN-SVM reached a test accuracy of ~90.72%, while the CNN-Softmax reached a test accuracy of ~91.86%. The said results may be improved if data preprocessing techniques were employed on the datasets, and if the base CNN model was a relatively more sophisticated than the one used in this study.

Gated Recurrent Unit (GRU) is a recently-developed variation of the long short-term memory (LSTM) unit, both of which are types of recurrent neural network (RNN). Through empirical evidence, both models have been proven to be effective in a wide variety of machine learning tasks such as natural language processing (Wen et al., 2015), speech recognition (Chorowski et al., 2015), and text classification (Yang et al., 2016). Conventionally, like most neural networks, both of the aforementioned RNN variants employ the Softmax function as its final output layer for its prediction, and the cross-entropy function for computing its loss. In this paper, we present an amendment to this norm by introducing linear support vector machine (SVM) as the replacement for Softmax in the final output layer of a GRU model. Furthermore, the cross-entropy function shall be replaced with a margin-based function. While there have been similar studies (Alalshekmubarak & Smith, 2013; Tang, 2013), this proposal is primarily intended for binary classification on intrusion detection using the 2013 network traffic data from the honeypot systems of Kyoto University. Results show that the GRU-SVM model performs relatively higher than the conventional GRU-Softmax model. The proposed model reached a training accuracy of ~81.54% and a testing accuracy of ~84.15%, while the latter was able to reach a training accuracy of ~63.07% and a testing accuracy of ~70.75%. In addition, the juxtaposition of these two final output layers indicate that the SVM would outperform Softmax in prediction time - a theoretical implication which was supported by the actual training and testing time in the study.

We present MELLE, a novel continuous-valued tokens based language modeling approach for text to speech synthesis (TTS). MELLE autoregressively generates continuous mel-spectrogram frames directly from text condition, bypassing the need for vector quantization, which are originally designed for audio compression and sacrifice fidelity compared to mel-spectrograms. Specifically, (i) instead of cross-entropy loss, we apply regression loss with a proposed spectrogram flux loss function to model the probability distribution of the continuous-valued tokens. (ii) we have incorporated variational inference into MELLE to facilitate sampling mechanisms, thereby enhancing the output diversity and model robustness. Experiments demonstrate that, compared to the two-stage codec language models VALL-E and its variants, the single-stage MELLE mitigates robustness issues by avoiding the inherent flaws of sampling discrete codes, achieves superior performance across multiple metrics, and, most importantly, offers a more streamlined paradigm. See https://aka.ms/melle for demos of our work.

Vector quantization (VQ) is a key component in discrete tokenizers for image generation, but its training is often unstable due to straight-through estimation bias, one-step-behind updates, and sparse codebook gradients, which lead to suboptimal reconstruction performance and low codebook usage. In this work, we analyze these fundamental challenges and provide a simple yet effective solution. To maintain high codebook usage in VQ networks (VQN) during learning annealing and codebook size expansion, we propose VQBridge, a robust, scalable, and efficient projector based on the map function method. VQBridge optimizes code vectors through a compress-process-recover pipeline, enabling stable and effective codebook training. By combining VQBridge with learning annealing, our VQN achieves full (100%) codebook usage across diverse codebook configurations, which we refer to as FVQ (FullVQ). Through extensive experiments, we demonstrate that FVQ is effective, scalable, and generalizable: it attains 100% codebook usage even with a 262k-codebook, achieves state-of-the-art reconstruction performance, consistently improves with larger codebooks, higher vector channels, or longer training, and remains effective across different VQ variants. Moreover, when integrated with LlamaGen, FVQ significantly enhances image generation performance, surpassing visual autoregressive models (VAR) by 0.5 and diffusion models (DiT) by 0.2 rFID, highlighting the importance of high-quality tokenizers for strong autoregressive image generation.

Functional data play a pivotal role across science and engineering, yet their infinite-dimensional nature makes representation learning challenging. Conventional statistical models depend on pre-chosen basis expansions or kernels, limiting the flexibility of data-driven discovery, while many deep-learning pipelines treat functions as fixed-grid vectors, ignoring inherent continuity. In this paper, we introduce Functional Attention with a Mixture-of-Experts (FAME), an end-to-end, fully data-driven framework for function-on-function regression. FAME forms continuous attention by coupling a bidirectional neural controlled differential equation with MoE-driven vector fields to capture intra-functional continuity, and further fuses change to inter-functional dependencies via multi-head cross attention. Extensive experiments on synthetic and real-world functional-regression benchmarks show that FAME achieves state-of-the-art accuracy, strong robustness to arbitrarily sampled discrete observations of functions.

Diffusion models are commonly interpreted as learning the score function, i.e., the gradient of the log-density of noisy data. However, this assumption implies that the target of learning is a conservative vector field, which is not enforced by the neural network architectures used in practice. We present numerical evidence that trained diffusion networks violate both integral and differential constraints required of true score functions, demonstrating that the learned vector fields are not conservative. Despite this, the models perform remarkably well as generative mechanisms. To explain this apparent paradox, we advocate a new theoretical perspective: diffusion training is better understood as flow matching to the velocity field of a Wasserstein Gradient Flow (WGF), rather than as score learning for a reverse-time stochastic differential equation. Under this view, the "probability flow" arises naturally from the WGF framework, eliminating the need to invoke reverse-time SDE theory and clarifying why generative sampling remains successful even when the neural vector field is not a true score. We further show that non-conservative errors from neural approximation do not necessarily harm density transport. Our results advocate for adopting the WGF perspective as a principled, elegant, and theoretically grounded framework for understanding diffusion generative models.

Vector similarity search presents significant challenges in terms of scalability for large and high-dimensional datasets, as well as in providing native support for hybrid queries. Serverless computing and cloud functions offer attractive benefits such as elasticity and cost-effectiveness, but are difficult to apply to data-intensive workloads. Jointly addressing these two main challenges, we present SQUASH, the first fully serverless vector search solution with rich support for hybrid queries. It features OSQ, an optimized and highly parallelizable quantization-based approach for vectors and attributes. Its segment-based storage mechanism enables significant compression in resource-constrained settings and offers efficient dimensional extraction operations. SQUASH performs a single distributed pass to guarantee the return of sufficiently many vectors satisfying the filter predicate, achieving high accuracy and avoiding redundant computation for vectors which fail the predicate. A multi-level search workflow is introduced to prune most vectors early to minimize the load on Function-as-a-Service (FaaS) instances. SQUASH is designed to identify and utilize retention of relevant data in re-used runtime containers, which eliminates redundant I/O and reduces costs. Finally, we demonstrate a new tree-based method for rapid FaaS invocation, enabling the bi-directional flow of data via request/response payloads. Experiments comparing SQUASH with state-of-the-art serverless vector search solutions and server-based baselines on vector search benchmarks confirm significant performance improvements at a lower cost.

Vector Symbolic Architectures (VSAs) have emerged as a novel framework for enabling interpretable machine learning algorithms equipped with the ability to reason and explain their decision processes. The basic idea is to represent discrete information through high dimensional random vectors. Complex data structures can be built up with operations over vectors such as the "binding" operation involving element-wise vector multiplication, which associates data together. The reverse task of decomposing the associated elements is a combinatorially hard task, with an exponentially large search space. The main algorithm for performing this search is the resonator network, inspired by Hopfield network-based memory search operations. In this work, we introduce a new variant of the resonator network, based on self-attention based update rules in the iterative search problem. This update rule, based on the Hopfield network with log-sum-exp energy function and norm-bounded states, is shown to substantially improve the performance and rate of convergence. As a result, our algorithm enables a larger capacity for associative memory, enabling applications in many tasks like perception based pattern recognition, scene decomposition, and object reasoning. We substantiate our algorithm with a thorough evaluation and comparisons to baselines.

Given appropriate representations of the semantic relations between carpenter and wood and between mason and stone (for example, vectors in a vector space model), a suitable algorithm should be able to recognize that these relations are highly similar (carpenter is to wood as mason is to stone; the relations are analogous). Likewise, with representations of dog, house, and kennel, an algorithm should be able to recognize that the semantic composition of dog and house, dog house, is highly similar to kennel (dog house and kennel are synonymous). It seems that these two tasks, recognizing relations and compositions, are closely connected. However, up to now, the best models for relations are significantly different from the best models for compositions. In this paper, we introduce a dual-space model that unifies these two tasks. This model matches the performance of the best previous models for relations and compositions. The dual-space model consists of a space for measuring domain similarity and a space for measuring function similarity. Carpenter and wood share the same domain, the domain of carpentry. Mason and stone share the same domain, the domain of masonry. Carpenter and mason share the same function, the function of artisans. Wood and stone share the same function, the function of materials. In the composition dog house, kennel has some domain overlap with both dog and house (the domains of pets and buildings). The function of kennel is similar to the function of house (the function of shelters). By combining domain and function similarities in various ways, we can model relations, compositions, and other aspects of semantics.

In-context learning (ICL) in Large Language Models (LLMs) has emerged as a powerful new learning paradigm. However, its underlying mechanism is still not well understood. In particular, it is challenging to map it to the "standard" machine learning framework, where one uses a training set S to find a best-fitting function f(x) in some hypothesis class. Here we make progress on this problem by showing that the functions learned by ICL often have a very simple structure: they correspond to the transformer LLM whose only inputs are the query x and a single "task vector" calculated from the training set. Thus, ICL can be seen as compressing S into a single task vector theta(S) and then using this task vector to modulate the transformer to produce the output. We support the above claim via comprehensive experiments across a range of models and tasks.

In-context learning (ICL) has revolutionized the capabilities of transformer models in NLP. In our project, we extend the understanding of the mechanisms underpinning ICL by exploring whether transformers can learn from sequential, non-textual function class data distributions. We introduce a novel sliding window sequential function class and employ toy-sized transformers with a GPT-2 architecture to conduct our experiments. Our analysis indicates that these models can indeed leverage ICL when trained on non-textual sequential function classes. Additionally, our experiments with randomized y-label sequences highlights that transformers retain some ICL capabilities even when the label associations are obfuscated. We provide evidence that transformers can reason with and understand sequentiality encoded within function classes, as reflected by the effective learning of our proposed tasks. Our results also show that the performance deteriorated with increasing randomness in the labels, though not to the extent one might expect, implying a potential robustness of learned sequentiality against label noise. Future research may want to look into how previous explanations of transformers, such as induction heads and task vectors, relate to sequentiality in ICL in these toy examples. Our investigation lays the groundwork for further research into how transformers process and perceive sequential data.

Conditional text-to-image generation has seen countless recent improvements in terms of quality, diversity and fidelity. Nevertheless, most state-of-the-art models require numerous inference steps to produce faithful generations, resulting in performance bottlenecks for end-user applications. In this paper we introduce Paella, a novel text-to-image model requiring less than 10 steps to sample high-fidelity images, using a speed-optimized architecture allowing to sample a single image in less than 500 ms, while having 573M parameters. The model operates on a compressed & quantized latent space, it is conditioned on CLIP embeddings and uses an improved sampling function over previous works. Aside from text-conditional image generation, our model is able to do latent space interpolation and image manipulations such as inpainting, outpainting, and structural editing. We release all of our code and pretrained models at https://github.com/dome272/Paella

Text-to-image diffusion models particularly Stable Diffusion, have revolutionized the field of computer vision. However, the synthesis quality often deteriorates when asked to generate images that faithfully represent complex prompts involving multiple attributes and objects. While previous studies suggest that blended text embeddings lead to improper attribute binding, few have explored this in depth. In this work, we critically examine the limitations of the CLIP text encoder in understanding attributes and investigate how this affects diffusion models. We discern a phenomenon of attribute bias in the text space and highlight a contextual issue in padding embeddings that entangle different concepts. We propose Magnet, a novel training-free approach to tackle the attribute binding problem. We introduce positive and negative binding vectors to enhance disentanglement, further with a neighbor strategy to increase accuracy. Extensive experiments show that Magnet significantly improves synthesis quality and binding accuracy with negligible computational cost, enabling the generation of unconventional and unnatural concepts.

Computer-Aided Design (CAD) generative modeling is driving significant innovations across industrial applications. Recent works have shown remarkable progress in creating solid models from various inputs such as point clouds, meshes, and text descriptions. However, these methods fundamentally diverge from traditional industrial workflows that begin with 2D engineering drawings. The automatic generation of parametric CAD models from these 2D vector drawings remains underexplored despite being a critical step in engineering design. To address this gap, our key insight is to reframe CAD generation as a sequence-to-sequence learning problem where vector drawing primitives directly inform the generation of parametric CAD operations, preserving geometric precision and design intent throughout the transformation process. We propose Drawing2CAD, a framework with three key technical components: a network-friendly vector primitive representation that preserves precise geometric information, a dual-decoder transformer architecture that decouples command type and parameter generation while maintaining precise correspondence, and a soft target distribution loss function accommodating inherent flexibility in CAD parameters. To train and evaluate Drawing2CAD, we create CAD-VGDrawing, a dataset of paired engineering drawings and parametric CAD models, and conduct thorough experiments to demonstrate the effectiveness of our method. Code and dataset are available at https://github.com/lllssc/Drawing2CAD.

The choice of activation function plays a critical role in neural networks, yet most architectures still rely on fixed, uniform activation functions across all neurons. We introduce SmartMixed, a two-phase training strategy that allows networks to learn optimal per-neuron activation functions while preserving computational efficiency at inference. In the first phase, neurons adaptively select from a pool of candidate activation functions (ReLU, Sigmoid, Tanh, Leaky ReLU, ELU, SELU) using a differentiable hard-mixture mechanism. In the second phase, each neuron's activation function is fixed according to the learned selection, resulting in a computationally efficient network that supports continued training with optimized vectorized operations. We evaluate SmartMixed on the MNIST dataset using feedforward neural networks of varying depths. The analysis shows that neurons in different layers exhibit distinct preferences for activation functions, providing insights into the functional diversity within neural architectures.

We propose Hyper-Dimensional Function Encoding (HDFE). Given samples of a continuous object (e.g. a function), HDFE produces an explicit vector representation of the given object, invariant to the sample distribution and density. Sample distribution and density invariance enables HDFE to consistently encode continuous objects regardless of their sampling, and therefore allows neural networks to receive continuous objects as inputs for machine learning tasks, such as classification and regression. Besides, HDFE does not require any training and is proved to map the object into an organized embedding space, which facilitates the training of the downstream tasks. In addition, the encoding is decodable, which enables neural networks to regress continuous objects by regressing their encodings. Therefore, HDFE serves as an interface for processing continuous objects. We apply HDFE to function-to-function mapping, where vanilla HDFE achieves competitive performance as the state-of-the-art algorithm. We apply HDFE to point cloud surface normal estimation, where a simple replacement from PointNet to HDFE leads to immediate 12% and 15% error reductions in two benchmarks. In addition, by integrating HDFE into the PointNet-based SOTA network, we improve the SOTA baseline by 2.5% and 1.7% in the same benchmarks.

The maximum element of the vector output by the Softmax function approaches zero as the input vector size increases. Transformer-based language models rely on Softmax to compute attention scores, causing the attention distribution to flatten as the context size grows. This reduces the model's ability to prioritize key information effectively and potentially limits its length generalization. To address this problem, we propose Scalable-Softmax (SSMax), which replaces Softmax in scenarios where the input vector size varies. SSMax can be seamlessly integrated into existing Transformer-based architectures. Experimental results in language modeling show that models using SSMax not only achieve faster loss reduction during pretraining but also significantly improve performance in long contexts and key information retrieval. Furthermore, an analysis of attention scores reveals that SSMax enables the model to focus attention on key information even in long contexts. Additionally, although models that use SSMax from the beginning of pretraining achieve better length generalization, those that have already started pretraining can still gain some of this ability by replacing Softmax in the attention layers with SSMax, either during or after pretraining.

Direct Preference Optimization (DPO), which derives reward signals directly from pairwise preference data, has shown its effectiveness on aligning Large Language Models (LLMs) with human preferences. Despite its widespread use across various tasks, DPO has been criticized for its sensitivity to the SFT's effectiveness and its hindrance to the learning capacity towards human-preferred responses, leading to less satisfactory performance. To overcome those limitations, the theoretical understanding of DPO are indispensable but still lacking. To this end, we take a step towards theoretically analyzing and understanding the limitations of DPO. Specifically, we provide an analytical framework using the field theory to analyze the optimization process of DPO. By analyzing the gradient vector field of the DPO loss function, we find that the DPO loss function decreases the probability of producing human dispreferred data at a faster rate than it increases the probability of producing preferred data. This provides theoretical insights for understanding the limitations of DPO discovered in the related research experiments, thereby setting the foundation for its improvement.

Over the past decade, there has been a steady advancement in enhancing face recognition algorithms leveraging advanced machine learning methods. The role of the loss function is pivotal in addressing face verification problems and playing a game-changing role. These loss functions have mainly explored variations among intra-class or inter-class separation. This research examines the natural phenomenon of facial symmetry in the face verification problem. The symmetry between the left and right hemi faces has been widely used in many research areas in recent decades. This paper adopts this simple approach judiciously by splitting the face image vertically into two halves. With the assumption that the natural phenomena of facial symmetry can enhance face verification methodology, we hypothesize that the two output embedding vectors of split faces must project close to each other in the output embedding space. Inspired by this concept, we penalize the network based on the disparity of embedding of the symmetrical pair of split faces. Symmetrical loss has the potential to minimize minor asymmetric features due to facial expression and lightning conditions, hence significantly increasing the inter-class variance among the classes and leading to more reliable face embedding. This loss function propels any network to outperform its baseline performance across all existing network architectures and configurations, enabling us to achieve SoTA results.

Convolutional neural network training can suffer from diverse issues like exploding or vanishing gradients, scaling-based weight space symmetry and covariant-shift. In order to address these issues, researchers develop weight regularization methods and activation normalization methods. In this work we propose a weight soft-regularization method based on the Oblique manifold. The proposed method uses a loss function which pushes each weight vector to have a norm close to one, i.e. the weight matrix is smoothly steered toward the so-called Oblique manifold. We evaluate our method on the very popular CIFAR-10, CIFAR-100 and ImageNet 2012 datasets using two state-of-the-art architectures, namely the ResNet and wide-ResNet. Our method introduces negligible computational overhead and the results show that it is competitive to the state-of-the-art and in some cases superior to it. Additionally, the results are less sensitive to hyperparameter settings such as batch size and regularization factor.

We propose SketchINR, to advance the representation of vector sketches with implicit neural models. A variable length vector sketch is compressed into a latent space of fixed dimension that implicitly encodes the underlying shape as a function of time and strokes. The learned function predicts the xy point coordinates in a sketch at each time and stroke. Despite its simplicity, SketchINR outperforms existing representations at multiple tasks: (i) Encoding an entire sketch dataset into a fixed size latent vector, SketchINR gives 60times and 10times data compression over raster and vector sketches, respectively. (ii) SketchINR's auto-decoder provides a much higher-fidelity representation than other learned vector sketch representations, and is uniquely able to scale to complex vector sketches such as FS-COCO. (iii) SketchINR supports parallelisation that can decode/render sim100times faster than other learned vector representations such as SketchRNN. (iv) SketchINR, for the first time, emulates the human ability to reproduce a sketch with varying abstraction in terms of number and complexity of strokes. As a first look at implicit sketches, SketchINR's compact high-fidelity representation will support future work in modelling long and complex sketches.

Neural networks are famously nonlinear. However, linearity is defined relative to a pair of vector spaces, f:XtoY. Is it possible to identify a pair of non-standard vector spaces for which a conventionally nonlinear function is, in fact, linear? This paper introduces a method that makes such vector spaces explicit by construction. We find that if we sandwich a linear operator A between two invertible neural networks, f(x)=g_y^{-1}(A g_x(x)), then the corresponding vector spaces X and Y are induced by newly defined addition and scaling actions derived from g_x and g_y. We term this kind of architecture a Linearizer. This framework makes the entire arsenal of linear algebra, including SVD, pseudo-inverse, orthogonal projection and more, applicable to nonlinear mappings. Furthermore, we show that the composition of two Linearizers that share a neural network is also a Linearizer. We leverage this property and demonstrate that training diffusion models using our architecture makes the hundreds of sampling steps collapse into a single step. We further utilize our framework to enforce idempotency (i.e. f(f(x))=f(x)) on networks leading to a globally projective generative model and to demonstrate modular style transfer.

Public service systems in many African regions suffer from delayed emergency response and spatial inequity, causing avoidable suffering. This paper introduces OPTIC-ER, a reinforcement learning (RL) framework for real-time, adaptive, and equitable emergency response. OPTIC-ER uses an attention-guided actor-critic architecture to manage the complexity of dispatch environments. Its key innovations are a Context-Rich State Vector, encoding action sub-optimality, and a Precision Reward Function, which penalizes inefficiency. Training occurs in a high-fidelity simulation using real data from Rivers State, Nigeria, accelerated by a precomputed Travel Time Atlas. The system is built on the TALS framework (Thin computing, Adaptability, Low-cost, Scalability) for deployment in low-resource settings. In evaluations on 500 unseen incidents, OPTIC-ER achieved a 100.00% optimality rate with negligible inefficiency, confirming its robustness and generalization. Beyond dispatch, the system generates Infrastructure Deficiency Maps and Equity Monitoring Dashboards to guide proactive governance and data-informed development. This work presents a validated blueprint for AI-augmented public services, showing how context-aware RL can bridge the gap between algorithmic decision-making and measurable human impact.

Transformer based language models exhibit intelligent behaviors such as understanding natural language, recognizing patterns, acquiring knowledge, reasoning, planning, reflecting and using tools. This paper explores how their underlying mechanics give rise to intelligent behaviors. Towards that end, we propose framing Transformer dynamics as movement through embedding space. Examining Transformers through this perspective reveals key insights, establishing a Theory of Transformers: 1) Intelligent behaviours map to paths in Embedding Space which, the Transformer random-walks through during inferencing. 2) LM training learns a probability distribution over all possible paths. `Intelligence' is learnt by assigning higher probabilities to paths representing intelligent behaviors. No learning can take place in-context; context only narrows the subset of paths sampled during decoding. 5) The Transformer is a self-mapping composition function, folding a context sequence into a context-vector such that it's proximity to a token-vector reflects its co-occurrence and conditioned probability. Thus, the physical arrangement of vectors in Embedding Space determines path probabilities. 6) Context vectors are composed by aggregating features of the sequence's tokens via a process we call the encoding walk. Attention contributes a - potentially redundant - association-bias to this process. 7) This process is comprised of two principal operation types: filtering (data independent) and aggregation (data dependent). This generalization unifies Transformers with other sequence models. Building upon this foundation, we formalize a popular semantic interpretation of embeddings into a ``concept-space theory'' and find some evidence of it's validity.

We consider the linear contextual multi-class multi-period packing problem (LMMP) where the goal is to pack items such that the total vector of consumption is below a given budget vector and the total value is as large as possible. We consider the setting where the reward and the consumption vector associated with each action is a class-dependent linear function of the context, and the decision-maker receives bandit feedback. LMMP includes linear contextual bandits with knapsacks and online revenue management as special cases. We establish a new estimator which guarantees a faster convergence rate, and consequently, a lower regret in such problems. We propose a bandit policy that is a closed-form function of said estimated parameters. When the contexts are non-degenerate, the regret of the proposed policy is sublinear in the context dimension, the number of classes, and the time horizon T when the budget grows at least as T. We also resolve an open problem posed by Agrawal & Devanur (2016) and extend the result to a multi-class setting. Our numerical experiments clearly demonstrate that the performance of our policy is superior to other benchmarks in the literature.

Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory. We consider here the classic regression setup, where a real valued square integrable r.v. Y is to be predicted upon observing a (possibly high dimensional) random vector X by means of a predictive function f(X) as accurately as possible in the mean-squared sense and study a nearest-neighbour-based pointwise estimate of the gradient of the optimal predictive function, the regression function m(x)=E[Ymid X=x]. Under classic smoothness conditions combined with the assumption that the tails of Y-m(X) are sub-Gaussian, we prove nonasymptotic bounds improving upon those obtained for alternative estimation methods. Beyond the novel theoretical results established, several illustrative numerical experiments have been carried out. The latter provide strong empirical evidence that the estimation method proposed works very well for various statistical problems involving gradient estimation, namely dimensionality reduction, stochastic gradient descent optimization and quantifying disentanglement.

This paper presents a novel and uniform algorithm for edge detection based on SVM (support vector machine) with Three-dimensional Gaussian radial basis function with kernel. Because of disadvantages in traditional edge detection such as inaccurate edge location, rough edge and careless on detect soft edge. The experimental results indicate how the SVM can detect edge in efficient way. The performance of the proposed algorithm is compared with existing methods, including Sobel and canny detectors. The results show that this method is better than classical algorithm such as canny and Sobel detector.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

The ability to describe images with natural language sentences is the hallmark for image and language understanding. Such a system has wide ranging applications such as annotating images and using natural sentences to search for images.In this project we focus on the task of bidirectional image retrieval: such asystem is capable of retrieving an image based on a sentence (image search) andretrieve sentence based on an image query (image annotation). We present asystem based on a global ranking objective function which uses a combinationof convolutional neural networks (CNN) and multi layer perceptrons (MLP).It takes a pair of image and sentence and processes them in different channels,finally embedding it into a common multimodal vector space. These embeddingsencode abstract semantic information about the two inputs and can be comparedusing traditional information retrieval approaches. For each such pair, the modelreturns a score which is interpretted as a similarity metric. If this score is high,the image and sentence are likely to convey similar meaning, and if the score is low then they are likely not to. The visual input is modeled via deep convolutional neural network. On theother hand we explore three models for the textual module. The first one isbag of words with an MLP. The second one uses n-grams (bigram, trigrams,and a combination of trigram & skip-grams) with an MLP. The third is morespecialized deep network specific for modeling variable length sequences (SSE).We report comparable performance to recent work in the field, even though ouroverall model is simpler. We also show that the training time choice of how wecan generate our negative samples has a significant impact on performance, and can be used to specialize the bi-directional system in one particular task.

Coecke, Sadrzadeh, and Clark (arXiv:1003.4394v1 [cs.CL]) developed a compositional model of meaning for distributional semantics, in which each word in a sentence has a meaning vector and the distributional meaning of the sentence is a function of the tensor products of the word vectors. Abstractly speaking, this function is the morphism corresponding to the grammatical structure of the sentence in the category of finite dimensional vector spaces. In this paper, we provide a concrete method for implementing this linear meaning map, by constructing a corpus-based vector space for the type of sentence. Our construction method is based on structured vector spaces whereby meaning vectors of all sentences, regardless of their grammatical structure, live in the same vector space. Our proposed sentence space is the tensor product of two noun spaces, in which the basis vectors are pairs of words each augmented with a grammatical role. This enables us to compare meanings of sentences by simply taking the inner product of their vectors.

Existing text simplification or paraphrase datasets mainly focus on sentence-level text generation in a general domain. These datasets are typically developed without using domain knowledge. In this paper, we release a novel dataset, VTechAGP, which is the first academic-to-general-audience text paraphrase dataset consisting of 4,938 document-level these and dissertation academic and general-audience abstract pairs from 8 colleges authored over 25 years. We also propose a novel dynamic soft prompt generative language model, DSPT5. For training, we leverage a contrastive-generative loss function to learn the keyword vectors in the dynamic prompt. For inference, we adopt a crowd-sampling decoding strategy at both semantic and structural levels to further select the best output candidate. We evaluate DSPT5 and various state-of-the-art large language models (LLMs) from multiple perspectives. Results demonstrate that the SOTA LLMs does not provide satisfactory outcomes, while the lightweight DSPT5 can achieve competitive results. To the best of our knowledge, we are the first to build a benchmark dataset and solutions for academic-to-general-audience text paraphrase dataset.

Image registration is an essential step in many medical image analysis tasks. Traditional methods for image registration are primarily optimization-driven, finding the optimal deformations that maximize the similarity between two images. Recent learning-based methods, trained to directly predict transformations between two images, run much faster, but suffer from performance deficiencies due to model generalization and the inefficiency in handling individual image specific deformations. Here we present a new neural net based image registration framework, called NIR (Neural Image Registration), which is based on optimization but utilizes deep neural nets to model deformations between image pairs. NIR represents the transformation between two images with a continuous function implemented via neural fields, receiving a 3D coordinate as input and outputting the corresponding deformation vector. NIR provides two ways of generating deformation field: directly output a displacement vector field for general deformable registration, or output a velocity vector field and integrate the velocity field to derive the deformation field for diffeomorphic image registration. The optimal registration is discovered by updating the parameters of the neural field via stochastic gradient descent. We describe several design choices that facilitate model optimization, including coordinate encoding, sinusoidal activation, coordinate sampling, and intensity sampling. Experiments on two 3D MR brain scan datasets demonstrate that NIR yields state-of-the-art performance in terms of both registration accuracy and regularity, while running significantly faster than traditional optimization-based methods.

Recent years have witnessed a surge in the number of large language models (LLMs), yet efficiently managing and utilizing these vast resources remains a significant challenge. In this work, we explore how to learn compact representations of LLM abilities that can facilitate downstream tasks, such as model routing and performance prediction on new benchmarks. We frame this problem as estimating the probability that a given model will correctly answer a specific query. Inspired by the item response theory (IRT) in psychometrics, we model this probability as a function of three key factors: (i) the model's multi-skill ability vector, (2) the query's discrimination vector that separates models of differing skills, and (3) the query's difficulty scalar. To learn these parameters jointly, we introduce a Mixture-of-Experts (MoE) network that couples model- and query-level embeddings. Extensive experiments demonstrate that our approach leads to state-of-the-art performance in both model routing and benchmark accuracy prediction. Moreover, analysis validates that the learned parameters encode meaningful, interpretable information about model capabilities and query characteristics.

Diffusion models may be formulated as a time-indexed sequence of energy-based models, where the score corresponds to the negative gradient of an energy function. As opposed to learning the score directly, an energy parameterization is attractive as the energy itself can be used to control generation via Monte Carlo samplers. Architectural constraints and training instability in energy parameterized models have so far yielded inferior performance compared to directly approximating the score or denoiser. We address these deficiencies by introducing a novel training regime for the energy function through distillation of pre-trained diffusion models, resembling a Helmholtz decomposition of the score vector field. We further showcase the synergies between energy and score by casting the diffusion sampling procedure as a Feynman Kac model where sampling is controlled using potentials from the learnt energy functions. The Feynman Kac model formalism enables composition and low temperature sampling through sequential Monte Carlo.

Few neural architectures lend themselves to provable learning with gradient based methods. One popular model is the single-index model, in which labels are produced by composing an unknown linear projection with a possibly unknown scalar link function. Learning this model with SGD is relatively well-understood, whereby the so-called information exponent of the link function governs a polynomial sample complexity rate. However, extending this analysis to deeper or more complicated architectures remains challenging. In this work, we consider single index learning in the setting of symmetric neural networks. Under analytic assumptions on the activation and maximum degree assumptions on the link function, we prove that gradient flow recovers the hidden planted direction, represented as a finitely supported vector in the feature space of power sum polynomials. We characterize a notion of information exponent adapted to our setting that controls the efficiency of learning.

Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations both scale well with increasing resolution, are continuous, and can be many-times differentiable. However, given a dataset of signals that we would like to represent, having to optimize a separate neural field for each signal is inefficient, and cannot capitalize on shared information or structures among signals. Existing generalization methods view this as a meta-learning problem and employ gradient-based meta-learning to learn an initialization which is then fine-tuned with test-time optimization, or learn hypernetworks to produce the weights of a neural field. We instead propose a new paradigm that views the large-scale training of neural representations as a part of a partially-observed neural process framework, and leverage neural process algorithms to solve this task. We demonstrate that this approach outperforms both state-of-the-art gradient-based meta-learning approaches and hypernetwork approaches.

A coreset is a tiny weighted subset of an input set, that closely resembles the loss function, with respect to a certain set of queries. Coresets became prevalent in machine learning as they have shown to be advantageous for many applications. While coreset research is an active research area, unfortunately, coresets are constructed in a problem-dependent manner, where for each problem, a new coreset construction algorithm is usually suggested, a process that may take time or may be hard for new researchers in the field. Even the generic frameworks require additional (problem-dependent) computations or proofs to be done by the user. Besides, many problems do not have (provable) small coresets, limiting their applicability. To this end, we suggest an automatic practical framework for constructing coresets, which requires (only) the input data and the desired cost function from the user, without the need for any other task-related computation to be done by the user. To do so, we reduce the problem of approximating a loss function to an instance of vector summation approximation, where the vectors we aim to sum are loss vectors of a specific subset of the queries, such that we aim to approximate the image of the function on this subset. We show that while this set is limited, the coreset is quite general. An extensive experimental study on various machine learning applications is also conducted. Finally, we provide a ``plug and play" style implementation, proposing a user-friendly system that can be easily used to apply coresets for many problems. Full open source code can be found at https://github.com/alaamaalouf/AutoCoreset{https://github.com/alaamaalouf/AutoCoreset}. We believe that these contributions enable future research and easier use and applications of coresets.

Merging multiple expert models offers a promising approach for performing multi-task learning without accessing their original data. Existing methods attempt to alleviate task conflicts by sparsifying task vectors or promoting orthogonality among them. However, they overlook the fundamental target of model merging: the merged model performs as closely as possible to task-specific models on respective tasks. We find these methods inevitably discard task-specific information that, while causing conflicts, is crucial for performance. Based on our findings, we frame model merging as a constrained optimization problem (i.e., minimizing the gap between the merged model and individual models, subject to the constraint of retaining shared knowledge) and solve it via adaptive projective gradient descent. Specifically, we align the merged model with individual models by decomposing and reconstituting the loss function, alleviating conflicts through data-free optimization of task vectors. To retain shared knowledge, we optimize this objective by projecting gradients within a shared subspace spanning all tasks. Moreover, we view merging coefficients as adaptive learning rates and propose a task-aware, training-free strategy. Experiments show that our plug-and-play approach consistently outperforms previous methods, achieving state-of-the-art results across diverse architectures and tasks in both vision and NLP domains.

Token-based video representation has emerged as a promising approach for enabling large language models (LLMs) to interpret video content. However, existing token reduction techniques, such as pruning and merging, often disrupt essential positional embeddings and rely on continuous visual tokens sampled from nearby pixels with similar spatial-temporal locations. By removing only a small fraction of tokens, these methods still produce relatively lengthy continuous sequences, which falls short of the extreme compression required to balance computational efficiency and token count in video LLMs. In this paper, we introduce the novel task of Extreme Short Token Reduction, which aims to represent entire videos using a minimal set of discrete tokens. We propose VQToken, a neural discrete token representation framework that (i) applies adaptive vector quantization to continuous ViT embeddings to learn a compact codebook and (ii) preserves spatial-temporal positions via a token hash function by assigning each grid-level token to its nearest codebook entry. On the Extreme Short Token Reduction task, our VQToken compresses sequences to just 0.07 percent of their original length while incurring only a 0.66 percent drop in accuracy on the NextQA-MC benchmark. It also achieves comparable performance on ActNet-QA, Long Video Bench, and VideoMME. We further introduce the Token Information Density (TokDense) metric and formalize fixed-length and adaptive-length subtasks, achieving state-of-the-art results in both settings. Our approach dramatically lowers theoretical complexity, increases information density, drastically reduces token counts, and enables efficient video LLMs in resource-constrained environments.

The emergence of new nanoscale technologies has imposed significant challenges to designing reliable electronic systems in radiation environments. A few types of radiation like Total Ionizing Dose (TID) effects often cause permanent damages on such nanoscale electronic devices, and current state-of-the-art technologies to tackle TID make use of expensive radiation-hardened devices. This paper focuses on a novel and different approach: using machine learning algorithms on consumer electronic level Field Programmable Gate Arrays (FPGAs) to tackle TID effects and monitor them to replace before they stop working. This condition has a research challenge to anticipate when the board results in a total failure due to TID effects. We observed internal measurements of the FPGA boards under gamma radiation and used three different anomaly detection machine learning (ML) algorithms to detect anomalies in the sensor measurements in a gamma-radiated environment. The statistical results show a highly significant relationship between the gamma radiation exposure levels and the board measurements. Moreover, our anomaly detection results have shown that a One-Class Support Vector Machine with Radial Basis Function Kernel has an average Recall score of 0.95. Also, all anomalies can be detected before the boards stop working.

Feature representation in the form of spatio-spectral decomposition is one of the robust techniques adopted in automatic handwritten character recognition systems. In this regard, we propose a new image representation approach for unconstrained handwritten alphanumeric characters using sparse concept coded Tetrolets. Tetrolets, which does not use fixed dyadic square blocks for spectral decomposition like conventional wavelets, preserve the localized variations in handwritings by adopting tetrominoes those capture the shape geometry. The sparse concept coding of low entropy Tetrolet representation is found to extract the important hidden information (concept) for superior pattern discrimination. Large scale experimentation using ten databases in six different scripts (Bangla, Devanagari, Odia, English, Arabic and Telugu) has been performed. The proposed feature representation along with standard classifiers such as random forest, support vector machine (SVM), nearest neighbor and modified quadratic discriminant function (MQDF) is found to achieve state-of-the-art recognition performance in all the databases, viz. 99.40% (MNIST); 98.72% and 93.24% (IITBBS); 99.38% and 99.22% (ISI Kolkata). The proposed OCR system is shown to perform better than other sparse based techniques such as PCA, SparsePCA and SparseLDA, as well as better than existing transforms (Wavelet, Slantlet and Stockwell).

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.

Neural graphics primitives are faster and achieve higher quality when their neural networks are augmented by spatial data structures that hold trainable features arranged in a grid. However, existing feature grids either come with a large memory footprint (dense or factorized grids, trees, and hash tables) or slow performance (index learning and vector quantization). In this paper, we show that a hash table with learned probes has neither disadvantage, resulting in a favorable combination of size and speed. Inference is faster than unprobed hash tables at equal quality while training is only 1.2-2.6x slower, significantly outperforming prior index learning approaches. We arrive at this formulation by casting all feature grids into a common framework: they each correspond to a lookup function that indexes into a table of feature vectors. In this framework, the lookup functions of existing data structures can be combined by simple arithmetic combinations of their indices, resulting in Pareto optimal compression and speed.

Causal representation learning has showed a variety of settings in which we can disentangle latent variables with identifiability guarantees (up to some reasonable equivalence class). Common to all of these approaches is the assumption that (1) the latent variables are represented as d-dimensional vectors, and (2) that the observations are the output of some injective generative function of these latent variables. While these assumptions appear benign, we show that when the observations are of multiple objects, the generative function is no longer injective and disentanglement fails in practice. We can address this failure by combining recent developments in object-centric learning and causal representation learning. By modifying the Slot Attention architecture arXiv:2006.15055, we develop an object-centric architecture that leverages weak supervision from sparse perturbations to disentangle each object's properties. This approach is more data-efficient in the sense that it requires significantly fewer perturbations than a comparable approach that encodes to a Euclidean space and we show that this approach successfully disentangles the properties of a set of objects in a series of simple image-based disentanglement experiments.

We introduce the Block-Recurrent Transformer, which applies a transformer layer in a recurrent fashion along a sequence, and has linear complexity with respect to sequence length. Our recurrent cell operates on blocks of tokens rather than single tokens during training, and leverages parallel computation within a block in order to make efficient use of accelerator hardware. The cell itself is strikingly simple. It is merely a transformer layer: it uses self-attention and cross-attention to efficiently compute a recurrent function over a large set of state vectors and tokens. Our design was inspired in part by LSTM cells, and it uses LSTM-style gates, but it scales the typical LSTM cell up by several orders of magnitude. Our implementation of recurrence has the same cost in both computation time and parameter count as a conventional transformer layer, but offers dramatically improved perplexity in language modeling tasks over very long sequences. Our model out-performs a long-range Transformer XL baseline by a wide margin, while running twice as fast. We demonstrate its effectiveness on PG19 (books), arXiv papers, and GitHub source code. Our code has been released as open source.

Multi-objective reinforcement learning (MORL) approaches have emerged to tackle many real-world problems with multiple conflicting objectives by maximizing a joint objective function weighted by a preference vector. These approaches find fixed customized policies corresponding to preference vectors specified during training. However, the design constraints and objectives typically change dynamically in real-life scenarios. Furthermore, storing a policy for each potential preference is not scalable. Hence, obtaining a set of Pareto front solutions for the entire preference space in a given domain with a single training is critical. To this end, we propose a novel MORL algorithm that trains a single universal network to cover the entire preference space scalable to continuous robotic tasks. The proposed approach, Preference-Driven MORL (PD-MORL), utilizes the preferences as guidance to update the network parameters. It also employs a novel parallelization approach to increase sample efficiency. We show that PD-MORL achieves up to 25% larger hypervolume for challenging continuous control tasks and uses an order of magnitude fewer trainable parameters compared to prior approaches.

The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where (a) the number of unknowns may potentially be larger than the number of observations and (b) f* admits a sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

Electroencephalography (EEG) captures neural activity across multiple temporal and spectral scales, yielding signals that are rich but complex for representation learning. Recently, EEG foundation models trained to predict masked signal-tokens have shown promise for learning generalizable representations. However, their performance is hindered by their signal tokenization modules. Existing neural tokenizers fail to preserve high-frequency dynamics, limiting their ability to reconstruct EEG signals with high fidelity. We introduce NeuroRVQ, a scalable Large Brainwave Model (LBM) centered on a codebook-based tokenizer. Our tokenizer integrates: (i) multi-scale feature extraction modules that capture the full frequency neural spectrum; (ii) hierarchical residual vector quantization (RVQ) codebooks for high-resolution encoding; and, (iii) an EEG signal phase- and amplitude-aware loss function for efficient training. This design enables efficient EEG compression while supporting accurate reconstruction across all frequency bands, leading to robust generative masked modeling. Our empirical results demonstrate that NeuroRVQ achieves lower reconstruction error and outperforms existing LBMs on a variety of downstream tasks. More broadly, NeuroRVQ tokenizer establishes a strong prior for codebook-based general-purpose brainwave models, enabling advances in neural decoding, generative modeling and multimodal biosignal integration.

Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each data sample. However, these algorithms rely on independent data and noise samples, and do not exploit underlying structure in the data distribution for constructing probability paths. We propose Multisample Flow Matching, a more general framework that uses non-trivial couplings between data and noise samples while satisfying the correct marginal constraints. At very small overhead costs, this generalization allows us to (i) reduce gradient variance during training, (ii) obtain straighter flows for the learned vector field, which allows us to generate high-quality samples using fewer function evaluations, and (iii) obtain transport maps with lower cost in high dimensions, which has applications beyond generative modeling. Importantly, we do so in a completely simulation-free manner with a simple minimization objective. We show that our proposed methods improve sample consistency on downsampled ImageNet data sets, and lead to better low-cost sample generation.

Feature attribution methods identify which features of an input most influence a model's output. Most widely-used feature attribution methods (such as SHAP, LIME, and Grad-CAM) are "class-dependent" methods in that they generate a feature attribution vector as a function of class. In this work, we demonstrate that class-dependent methods can "leak" information about the selected class, making that class appear more likely than it is. Thus, an end user runs the risk of drawing false conclusions when interpreting an explanation generated by a class-dependent method. In contrast, we introduce "distribution-aware" methods, which favor explanations that keep the label's distribution close to its distribution given all features of the input. We introduce SHAP-KL and FastSHAP-KL, two baseline distribution-aware methods that compute Shapley values. Finally, we perform a comprehensive evaluation of seven class-dependent and three distribution-aware methods on three clinical datasets of different high-dimensional data types: images, biosignals, and text.

At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit, thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: during gradient descent on the parameters of an ANN, the network function f_theta (which maps input vectors to output vectors) follows the kernel gradient of the functional cost (which is convex, in contrast to the parameter cost) w.r.t. a new kernel: the Neural Tangent Kernel (NTK). This kernel is central to describe the generalization features of ANNs. While the NTK is random at initialization and varies during training, in the infinite-width limit it converges to an explicit limiting kernel and it stays constant during training. This makes it possible to study the training of ANNs in function space instead of parameter space. Convergence of the training can then be related to the positive-definiteness of the limiting NTK. We prove the positive-definiteness of the limiting NTK when the data is supported on the sphere and the non-linearity is non-polynomial. We then focus on the setting of least-squares regression and show that in the infinite-width limit, the network function f_theta follows a linear differential equation during training. The convergence is fastest along the largest kernel principal components of the input data with respect to the NTK, hence suggesting a theoretical motivation for early stopping. Finally we study the NTK numerically, observe its behavior for wide networks, and compare it to the infinite-width limit.

Text retrieval is a long-standing research topic on information seeking, where a system is required to return relevant information resources to user's queries in natural language. From classic retrieval methods to learning-based ranking functions, the underlying retrieval models have been continually evolved with the ever-lasting technical innovation. To design effective retrieval models, a key point lies in how to learn the text representation and model the relevance matching. The recent success of pretrained language models (PLMs) sheds light on developing more capable text retrieval approaches by leveraging the excellent modeling capacity of PLMs. With powerful PLMs, we can effectively learn the representations of queries and texts in the latent representation space, and further construct the semantic matching function between the dense vectors for relevance modeling. Such a retrieval approach is referred to as dense retrieval, since it employs dense vectors (a.k.a., embeddings) to represent the texts. Considering the rapid progress on dense retrieval, in this survey, we systematically review the recent advances on PLM-based dense retrieval. Different from previous surveys on dense retrieval, we take a new perspective to organize the related work by four major aspects, including architecture, training, indexing and integration, and summarize the mainstream techniques for each aspect. We thoroughly survey the literature, and include 300+ related reference papers on dense retrieval. To support our survey, we create a website for providing useful resources, and release a code repertory and toolkit for implementing dense retrieval models. This survey aims to provide a comprehensive, practical reference focused on the major progress for dense text retrieval.

A recurrent neural network (RNN) is a widely used deep-learning network for dealing with sequential data. Imitating a dynamical system, an infinite-width RNN can approximate any open dynamical system in a compact domain. In general, deep networks with bounded widths are more effective than wide networks in practice; however, the universal approximation theorem for deep narrow structures has yet to be extensively studied. In this study, we prove the universality of deep narrow RNNs and show that the upper bound of the minimum width for universality can be independent of the length of the data. Specifically, we show that a deep RNN with ReLU activation can approximate any continuous function or L^p function with the widths d_x+d_y+2 and max{d_x+1,d_y}, respectively, where the target function maps a finite sequence of vectors in R^{d_x} to a finite sequence of vectors in R^{d_y}. We also compute the additional width required if the activation function is tanh or more. In addition, we prove the universality of other recurrent networks, such as bidirectional RNNs. Bridging a multi-layer perceptron and an RNN, our theory and proof technique can be an initial step toward further research on deep RNNs.

Electronic health record (EHR) systems are used extensively throughout the healthcare domain. However, data interchangeability between EHR systems is limited due to the use of different coding standards across systems. Existing methods of mapping coding standards based on manual human experts mapping, dictionary mapping, symbolic NLP and classification are unscalable and cannot accommodate large scale EHR datasets. In this work, we present Text2Node, a cross-domain mapping system capable of mapping medical phrases to concepts in a large taxonomy (such as SNOMED CT). The system is designed to generalize from a limited set of training samples and map phrases to elements of the taxonomy that are not covered by training data. As a result, our system is scalable, robust to wording variants between coding systems and can output highly relevant concepts when no exact concept exists in the target taxonomy. Text2Node operates in three main stages: first, the lexicon is mapped to word embeddings; second, the taxonomy is vectorized using node embeddings; and finally, the mapping function is trained to connect the two embedding spaces. We compared multiple algorithms and architectures for each stage of the training, including GloVe and FastText word embeddings, CNN and Bi-LSTM mapping functions, and node2vec for node embeddings. We confirmed the robustness and generalisation properties of Text2Node by mapping ICD-9-CM Diagnosis phrases to SNOMED CT and by zero-shot training at comparable accuracy. This system is a novel methodological contribution to the task of normalizing and linking phrases to a taxonomy, advancing data interchangeability in healthcare. When applied, the system can use electronic health records to generate an embedding that incorporates taxonomical medical knowledge to improve clinical predictive models.

We consider the Similarity Sketching problem: Given a universe [u] = {0,ldots, u-1} we want a random function S mapping subsets Asubseteq [u] into vectors S(A) of size t, such that the Jaccard similarity J(A,B) = |Acap B|/|Acup B| between sets A and B is preserved. More precisely, define X_i = [S(A)[i] = S(B)[i]] and X = sum_{iin [t]} X_i. We want E[X_i]=J(A,B), and we want X to be strongly concentrated around E[X] = t cdot J(A,B) (i.e. Chernoff-style bounds). This is a fundamental problem which has found numerous applications in data mining, large-scale classification, computer vision, similarity search, etc. via the classic MinHash algorithm. The vectors S(A) are also called sketches. Strong concentration is critical, for often we want to sketch many sets B_1,ldots,B_n so that we later, for a query set A, can find (one of) the most similar B_i. It is then critical that no B_i looks much more similar to A due to errors in the sketch. The seminal ttimesMinHash algorithm uses t random hash functions h_1,ldots, h_t, and stores left ( min_{ain A} h_1(A),ldots, min_{ain A} h_t(A) right ) as the sketch of A. The main drawback of MinHash is, however, its O(tcdot |A|) running time, and finding a sketch with similar properties and faster running time has been the subject of several papers. (continued...)

We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an Ntimes N matrix M, an N-dimensional vector emph{b}, and an initial vector emph{x}(0), obtain a target vector emph{x}(t) as a function of time t according to the constraint demph{x}(t)/dt=Memph{x}(t)+emph{b}. We show that our algorithm exhibits an exponential speedup over its classical counterpart in certain circumstances. In addition, we demonstrate our quantum algorithm for a 4times4 linear differential equation using a 4-qubit nuclear magnetic resonance quantum information processor. Our algorithm provides a key technique for solving many important problems which rely on the solutions to linear differential equations.

Vectors are universal mathematical objects that can represent text, images, speech, or a mix of these data modalities. That happens regardless of whether data is represented by hand-crafted features or learnt embeddings. Collect a large enough quantity of such vectors and the question of retrieval becomes urgently relevant: Finding vectors that are more similar to a query vector. This monograph is concerned with the question above and covers fundamental concepts along with advanced data structures and algorithms for vector retrieval. In doing so, it recaps this fascinating topic and lowers barriers of entry into this rich area of research.

We extend JAX with the capability to automatically differentiate higher-order functions (functionals and operators). By representing functions as a generalization of arrays, we seamlessly use JAX's existing primitive system to implement higher-order functions. We present a set of primitive operators that serve as foundational building blocks for constructing several key types of functionals. For every introduced primitive operator, we derive and implement both linearization and transposition rules, aligning with JAX's internal protocols for forward and reverse mode automatic differentiation. This enhancement allows for functional differentiation in the same syntax traditionally use for functions. The resulting functional gradients are themselves functions ready to be invoked in python. We showcase this tool's efficacy and simplicity through applications where functional derivatives are indispensable. The source code of this work is released at https://github.com/sail-sg/autofd .

This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and return a matrix inverse or factorization, derivatives of ODE solutions, and even stochastic derivatives of random functions. It emphasizes practical computational applications, such as large-scale optimization and machine learning, where derivatives must be re-imagined in order to be propagated through complicated calculations. The class also discusses efficiency concerns leading to "adjoint" or "reverse-mode" differentiation (a.k.a. "backpropagation"), and gives a gentle introduction to modern automatic differentiation (AD) techniques.

While multitask representation learning has become a popular approach in reinforcement learning (RL) to boost the sample efficiency, the theoretical understanding of why and how it works is still limited. Most previous analytical works could only assume that the representation function is already known to the agent or from linear function class, since analyzing general function class representation encounters non-trivial technical obstacles such as generalization guarantee, formulation of confidence bound in abstract function space, etc. However, linear-case analysis heavily relies on the particularity of linear function class, while real-world practice usually adopts general non-linear representation functions like neural networks. This significantly reduces its applicability. In this work, we extend the analysis to general function class representations. Specifically, we consider an agent playing M contextual bandits (or MDPs) concurrently and extracting a shared representation function phi from a specific function class Phi using our proposed Generalized Functional Upper Confidence Bound algorithm (GFUCB). We theoretically validate the benefit of multitask representation learning within general function class for bandits and linear MDP for the first time. Lastly, we conduct experiments to demonstrate the effectiveness of our algorithm with neural net representation.

Innovations like protein diffusion have enabled significant progress in de novo protein design, which is a vital topic in life science. These methods typically depend on protein structure encoders to model residue backbone frames, where atoms do not exist. Most prior encoders rely on atom-wise features, such as angles and distances between atoms, which are not available in this context. Thus far, only several simple encoders, such as IPA, have been proposed for this scenario, exposing the frame modeling as a bottleneck. In this work, we proffer the Vector Field Network (VFN), which enables network layers to perform learnable vector computations between coordinates of frame-anchored virtual atoms, thus achieving a higher capability for modeling frames. The vector computation operates in a manner similar to a linear layer, with each input channel receiving 3D virtual atom coordinates instead of scalar values. The multiple feature vectors output by the vector computation are then used to update the residue representations and virtual atom coordinates via attention aggregation. Remarkably, VFN also excels in modeling both frames and atoms, as the real atoms can be treated as the virtual atoms for modeling, positioning VFN as a potential universal encoder. In protein diffusion (frame modeling), VFN exhibits an impressive performance advantage over IPA, excelling in terms of both designability (67.04% vs. 53.58%) and diversity (66.54% vs. 51.98%). In inverse folding (frame and atom modeling), VFN outperforms the previous SoTA model, PiFold (54.7% vs. 51.66%), on sequence recovery rate. We also propose a method of equipping VFN with the ESM model, which significantly surpasses the previous ESM-based SoTA (62.67% vs. 55.65%), LM-Design, by a substantial margin.

Control variates are variance reduction tools for Monte Carlo estimators. They can provide significant variance reduction, but usually require a large number of samples, which can be prohibitive when sampling or evaluating the integrand is computationally expensive. Furthermore, there are many scenarios where we need to compute multiple related integrals simultaneously or sequentially, which can further exacerbate computational costs. In this paper, we propose vector-valued control variates, an extension of control variates which can be used to reduce the variance of multiple Monte Carlo estimators jointly. This allows for the transfer of information across integration tasks, and hence reduces the need for a large number of samples. We focus on control variates based on kernel interpolants and our novel construction is obtained through a generalised Stein identity and the development of novel matrix-valued Stein reproducing kernels. We demonstrate our methodology on a range of problems including multifidelity modelling, Bayesian inference for dynamical systems, and model evidence computation through thermodynamic integration.

We study the problem of designing models for machine learning tasks defined on sets. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics poczos13aistats, to anomaly detection in piezometer data of embankment dams Jung15Exploration, to cosmology Ntampaka16Dynamical,Ravanbakhsh16ICML1. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate dimension reduction, typically achieved via basis expansions. Currently, these bases are chosen a priori without the information for the task at hand and thus may not be effective for the designated task. We instead propose to adaptively learn these bases in an end-to-end fashion. We introduce neural networks that employ a new Basis Layer whose hidden units are each basis functions themselves implemented as a micro neural network. Our architecture learns to apply parsimonious dimension reduction to functional inputs that focuses only on information relevant to the target rather than irrelevant variation in the input function. Across numerous classification/regression tasks with functional data, our method empirically outperforms other types of neural networks, and we prove that our approach is statistically consistent with low generalization error. Code is available at: https://github.com/jwyyy/AdaFNN.

Motivated by the problem of fast processing of attention matrices, we study fast algorithms for computing matrix-vector products for asymmetric Gaussian Kernel matrices Kin R^{ntimes n}. K's columns are indexed by a set of n keys k_1,k_2ldots, k_nin R^d, rows by a set of n queries q_1,q_2,ldots,q_nin R^d , and its i,j entry is K_{ij} = e^{-|q_i-k_j|_2^2/2sigma^2} for some bandwidth parameter sigma>0. Given a vector xin R^n and error parameter epsilon>0, our task is to output a yin R^n such that |Kx-y|_2leq epsilon |x|_2 in time subquadratic in n and linear in d. Our algorithms rely on the following modelling assumption about the matrices K: the sum of the entries of K scales linearly in n, as opposed to worst case quadratic growth. We validate this assumption experimentally, for Gaussian kernel matrices encountered in various settings such as fast attention computation in LLMs. We obtain the first subquadratic-time algorithm that works under this assumption, for unrestricted vectors.

Generative models for structure-based drug design are often limited to a specific modality, restricting their broader applicability. To address this challenge, we introduce FuncBind, a framework based on computer vision to generate target-conditioned, all-atom molecules across atomic systems. FuncBind uses neural fields to represent molecules as continuous atomic densities and employs score-based generative models with modern architectures adapted from the computer vision literature. This modality-agnostic representation allows a single unified model to be trained on diverse atomic systems, from small to large molecules, and handle variable atom/residue counts, including non-canonical amino acids. FuncBind achieves competitive in silico performance in generating small molecules, macrocyclic peptides, and antibody complementarity-determining region loops, conditioned on target structures. FuncBind also generated in vitro novel antibody binders via de novo redesign of the complementarity-determining region H3 loop of two chosen co-crystal structures. As a final contribution, we introduce a new dataset and benchmark for structure-conditioned macrocyclic peptide generation. The code is available at https://github.com/prescient-design/funcbind.

Kolmogorov-Arnold Networks (KANs) have inspired numerous works exploring their applications across a wide range of scientific problems, with the potential to replace Multilayer Perceptrons (MLPs). While many KANs are designed using basis and polynomial functions, such as B-splines, ReLU-KAN utilizes a combination of ReLU functions to mimic the structure of B-splines and take advantage of ReLU's speed. However, ReLU-KAN is not built for multiple inputs, and its limitations stem from ReLU's handling of negative values, which can restrict feature extraction. To address these issues, we introduce Activation Function-Based Kolmogorov-Arnold Networks (AF-KAN), expanding ReLU-KAN with various activations and their function combinations. This novel KAN also incorporates parameter reduction methods, primarily attention mechanisms and data normalization, to enhance performance on image classification datasets. We explore different activation functions, function combinations, grid sizes, and spline orders to validate the effectiveness of AF-KAN and determine its optimal configuration. In the experiments, AF-KAN significantly outperforms MLP, ReLU-KAN, and other KANs with the same parameter count. It also remains competitive even when using fewer than 6 to 10 times the parameters while maintaining the same network structure. However, AF-KAN requires a longer training time and consumes more FLOPs. The repository for this work is available at https://github.com/hoangthangta/All-KAN.

A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically infinite-dimensional, deep learning has predominantly advanced through applications in computer vision and natural language processing that focus on mappings between finite-dimensional spaces. Such fundamental disparities in the nature of the data have limited neural networks from achieving a comparable level of success in scientific applications as seen in other fields. Neural operators are a principled way to generalize neural networks to mappings between function spaces, offering a pathway to replicate deep learning's transformative impact on scientific problems. For instance, neural operators can learn solution operators for entire classes of PDEs, e.g., physical systems with different boundary conditions, coefficient functions, and geometries. A key factor in deep learning's success has been the careful engineering of neural architectures through extensive empirical testing. Translating these neural architectures into neural operators allows operator learning to enjoy these same empirical optimizations. However, prior neural operator architectures have often been introduced as standalone models, not directly derived as extensions of existing neural network architectures. In this paper, we identify and distill the key principles for constructing practical implementations of mappings between infinite-dimensional function spaces. Using these principles, we propose a recipe for converting several popular neural architectures into neural operators with minimal modifications. This paper aims to guide practitioners through this process and details the steps to make neural operators work in practice. Our code can be found at https://github.com/neuraloperator/NNs-to-NOs

Function calling is a core capability of large language models, essential for AI agents. Existing benchmarks such as the Berkeley Function Calling Leaderboard (BFCL), tau^2-Bench (arXiv:2506.07982), and ACEBench (arXiv:2501.12851) evaluate argument correctness but do not test adherence to format instructions embedded in parameter descriptions, such as enclosing values in double quotes or using ISO date formats. We introduce IFEval-FC, a benchmark inspired by IFEval (arXiv:2311.07911) that assesses precise instruction following in function calling. IFEval-FC encodes verifiable formats directly within JSON schema descriptions, for example specifying that a value must not contain punctuation. It includes 750 test cases, each consisting of a function with an embedded format for one of its input parameters and a corresponding user query. Evaluation is fully algorithmic, ensuring objectivity, reproducibility, and scalability. Our results show that even state-of-the-art proprietary models, including GPT-5 and Claude 4.1 Opus, frequently fail to follow basic formatting rules, highlighting a practical limitation for real-world agent systems. The complete codebase and data are publicly available at https://github.com/Skripkon/IFEval-FC.

CONTEXT The R programming language has a huge and active community, especially in the area of statistical computing. Its interpreted nature allows for several interesting constructs, like the manipulation of functions at run-time, that hinder the static analysis of R programs. At the same time, there is a lack of existing research regarding how these features, or even the R language as a whole are used in practice. OBJECTIVE In this paper, we conduct a large-scale, static analysis of more than 50 million lines of real-world R programs and packages to identify their characteristics and the features that are actually used. Moreover, we compare the similarities and differences between the scripts of R users and the implementations of package authors. We provide insights for static analysis tools like the lintr package as well as potential interpreter optimizations and uncover areas for future research. METHOD We analyze 4230 R scripts submitted alongside publications and the sources of 19450 CRAN packages for over 350000 R files, collecting and summarizing quantitative information for features of interest. RESULTS We find a high frequency of name-based indexing operations, assignments, and loops, but a low frequency for most of R's reflective functions. Furthermore, we find neither testing functions nor many calls to R's foreign function interface (FFI) in the publication submissions. CONCLUSION R scripts and package sources differ, for example, in their size, the way they include other packages, and their usage of R's reflective capabilities. We provide features that are used frequently and should be prioritized by static analysis tools, like operator assignments, function calls, and certain reflective functions like load.

Modern deep learning models have the ability to generate high-dimensional vectors whose similarity reflects semantic resemblance. Thus, similarity search, i.e., the operation of retrieving those vectors in a large collection that are similar to a given query, has become a critical component of a wide range of applications that demand highly accurate and timely answers. In this setting, the high vector dimensionality puts similarity search systems under compute and memory pressure, leading to subpar performance. Additionally, cross-modal retrieval tasks have become increasingly common, e.g., where a user inputs a text query to find the most relevant images for that query. However, these queries often have different distributions than the database embeddings, making it challenging to achieve high accuracy. In this work, we present LeanVec, a framework that combines linear dimensionality reduction with vector quantization to accelerate similarity search on high-dimensional vectors while maintaining accuracy. We present LeanVec variants for in-distribution (ID) and out-of-distribution (OOD) queries. LeanVec-ID yields accuracies on par with those from recently introduced deep learning alternatives whose computational overhead precludes their usage in practice. LeanVec-OOD uses a novel technique for dimensionality reduction that considers the query and database distributions to simultaneously boost the accuracy and the performance of the framework even further (even presenting competitive results when the query and database distributions match). All in all, our extensive and varied experimental results show that LeanVec produces state-of-the-art results, with up to 3.7x improvement in search throughput and up to 4.9x faster index build time over the state of the art.

The training process of neural networks usually optimize weights and bias parameters of linear transformations, while nonlinear activation functions are pre-specified and fixed. This work develops a systematic approach to constructing matrix activation functions whose entries are generalized from ReLU. The activation is based on matrix-vector multiplications using only scalar multiplications and comparisons. The proposed activation functions depend on parameters that are trained along with the weights and bias vectors. Neural networks based on this approach are simple and efficient and are shown to be robust in numerical experiments.

We provide a construction for categorical representation learning and introduce the foundations of "categorifier". The central theme in representation learning is the idea of everything to vector. Every object in a dataset S can be represented as a vector in R^n by an encoding map E: Obj(S)toR^n. More importantly, every morphism can be represented as a matrix E: Hom(S)toR^{n}_{n}. The encoding map E is generally modeled by a deep neural network. The goal of representation learning is to design appropriate tasks on the dataset to train the encoding map (assuming that an encoding is optimal if it universally optimizes the performance on various tasks). However, the latter is still a set-theoretic approach. The goal of the current article is to promote the representation learning to a new level via a category-theoretic approach. As a proof of concept, we provide an example of a text translator equipped with our technology, showing that our categorical learning model outperforms the current deep learning models by 17 times. The content of the current article is part of the recent US patent proposal (patent application number: 63110906).

Can we pre-train a generalist agent from a large amount of unlabeled offline trajectories such that it can be immediately adapted to any new downstream tasks in a zero-shot manner? In this work, we present a functional reward encoding (FRE) as a general, scalable solution to this zero-shot RL problem. Our main idea is to learn functional representations of any arbitrary tasks by encoding their state-reward samples using a transformer-based variational auto-encoder. This functional encoding not only enables the pre-training of an agent from a wide diversity of general unsupervised reward functions, but also provides a way to solve any new downstream tasks in a zero-shot manner, given a small number of reward-annotated samples. We empirically show that FRE agents trained on diverse random unsupervised reward functions can generalize to solve novel tasks in a range of simulated robotic benchmarks, often outperforming previous zero-shot RL and offline RL methods. Code for this project is provided at: https://github.com/kvfrans/fre

We study the problem of learning hierarchical polynomials over the standard Gaussian distribution with three-layer neural networks. We specifically consider target functions of the form h = g circ p where p : R^d rightarrow R is a degree k polynomial and g: R rightarrow R is a degree q polynomial. This function class generalizes the single-index model, which corresponds to k=1, and is a natural class of functions possessing an underlying hierarchical structure. Our main result shows that for a large subclass of degree k polynomials p, a three-layer neural network trained via layerwise gradient descent on the square loss learns the target h up to vanishing test error in mathcal{O}(d^k) samples and polynomial time. This is a strict improvement over kernel methods, which require widetilde Theta(d^{kq}) samples, as well as existing guarantees for two-layer networks, which require the target function to be low-rank. Our result also generalizes prior works on three-layer neural networks, which were restricted to the case of p being a quadratic. When p is indeed a quadratic, we achieve the information-theoretically optimal sample complexity mathcal{O}(d^2), which is an improvement over prior work~nichani2023provable requiring a sample size of widetildeTheta(d^4). Our proof proceeds by showing that during the initial stage of training the network performs feature learning to recover the feature p with mathcal{O}(d^k) samples. This work demonstrates the ability of three-layer neural networks to learn complex features and as a result, learn a broad class of hierarchical functions.

Given a matrix Ain R^{ntimes d} and a vector bin R^n, we consider the regression problem with ell_infty guarantees: finding a vector x'in R^d such that |x'-x^*|_infty leq epsilon{d}cdot |Ax^*-b|_2cdot |A^dagger| where x^*=argmin_{xin R^d}|Ax-b|_2. One popular approach for solving such ell_2 regression problem is via sketching: picking a structured random matrix Sin R^{mtimes n} with mll n and SA can be quickly computed, solve the ``sketched'' regression problem argmin_{xin R^d} |SAx-Sb|_2. In this paper, we show that in order to obtain such ell_infty guarantee for ell_2 regression, one has to use sketching matrices that are dense. To the best of our knowledge, this is the first user case in which dense sketching matrices are necessary. On the algorithmic side, we prove that there exists a distribution of dense sketching matrices with m=epsilon^{-2}dlog^3(n/delta) such that solving the sketched regression problem gives the ell_infty guarantee, with probability at least 1-delta. Moreover, the matrix SA can be computed in time O(ndlog n). Our row count is nearly-optimal up to logarithmic factors, and significantly improves the result in [Price, Song and Woodruff, ICALP'17], in which a super-linear in d rows, m=Omega(epsilon^{-2}d^{1+gamma}) for gamma=Theta(frac{loglog n{log d}}) is required. We also develop a novel analytical framework for ell_infty guarantee regression that utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in [Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for tensor product of vectors.

Neural networks have proven to be a highly effective tool for solving complex problems in many areas of life. Recently, their importance and practical usability have further been reinforced with the advent of deep learning. One of the important conditions for the success of neural networks is the choice of an appropriate activation function introducing non-linearity into the model. Many types of these functions have been proposed in the literature in the past, but there is no single comprehensive source containing their exhaustive overview. The absence of this overview, even in our experience, leads to redundancy and the unintentional rediscovery of already existing activation functions. To bridge this gap, our paper presents an extensive survey involving 400 activation functions, which is several times larger in scale than previous surveys. Our comprehensive compilation also references these surveys; however, its main goal is to provide the most comprehensive overview and systematization of previously published activation functions with links to their original sources. The secondary aim is to update the current understanding of this family of functions.

Dense retrieval models use bi-encoder network architectures for learning query and document representations. These representations are often in the form of a vector representation and their similarities are often computed using the dot product function. In this paper, we propose a new representation learning framework for dense retrieval. Instead of learning a vector for each query and document, our framework learns a multivariate distribution and uses negative multivariate KL divergence to compute the similarity between distributions. For simplicity and efficiency reasons, we assume that the distributions are multivariate normals and then train large language models to produce mean and variance vectors for these distributions. We provide a theoretical foundation for the proposed framework and show that it can be seamlessly integrated into the existing approximate nearest neighbor algorithms to perform retrieval efficiently. We conduct an extensive suite of experiments on a wide range of datasets, and demonstrate significant improvements compared to competitive dense retrieval models.

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be seen as an extension of classical diffusion models to an infinite-dimensional domain. Functional diffusion is very versatile as images, videos, audio, 3D shapes, deformations, \etc, can be handled by the same framework with minimal changes. In addition, functional diffusion is especially suited for irregular data or data defined in non-standard domains. In our work, we derive the necessary foundations for functional diffusion and propose a first implementation based on the transformer architecture. We show generative results on complicated signed distance functions and deformation functions defined on 3D surfaces.

Recent progress in Graph Neural Networks has resulted in wide adoption by many applications, including recommendation systems. The reason for Graph Neural Networks' superiority over other approaches is that many problems in recommendation systems can be naturally modeled as graphs, where nodes can be either users or items and edges represent preference relationships. In current Graph Neural Network approaches, nodes are represented with a static vector learned at training time. This static vector might only be suitable to capture some of the nuances of users or items they define. To overcome this limitation, we propose using a recently proposed model inspired by category theory: Sheaf Neural Networks. Sheaf Neural Networks, and its connected Laplacian, can address the previous problem by associating every node (and edge) with a vector space instead than a single vector. The vector space representation is richer and allows picking the proper representation at inference time. This approach can be generalized for different related tasks on graphs and achieves state-of-the-art performance in terms of F1-Score@N in collaborative filtering and Hits@20 in link prediction. For collaborative filtering, the approach is evaluated on the MovieLens 100K with a 5.1% improvement, on MovieLens 1M with a 5.4% improvement and on Book-Crossing with a 2.8% improvement, while for link prediction on the ogbl-ddi dataset with a 1.6% refinement with respect to the respective baselines.

This paper proposes a method for the automatic creation of variables (in the case of regression) that complement the information contained in the initial input vector. The method works as a pre-processing step in which the continuous values of the variable to be regressed are discretized into a set of intervals which are then used to define value thresholds. Then classifiers are trained to predict whether the value to be regressed is less than or equal to each of these thresholds. The different outputs of the classifiers are then concatenated in the form of an additional vector of variables that enriches the initial vector of the regression problem. The implemented system can thus be considered as a generic pre-processing tool. We tested the proposed enrichment method with 5 types of regressors and evaluated it in 33 regression datasets. Our experimental results confirm the interest of the approach.

We build upon vec2vec, a procedure designed to align text embedding spaces without parallel data. vec2vec finds a near-perfect alignment, but it is expensive and unstable. We present mini-vec2vec, a simple and efficient alternative that requires substantially lower computational cost and is highly robust. Moreover, the learned mapping is a linear transformation. Our method consists of three main stages: a tentative matching of pseudo-parallel embedding vectors, transformation fitting, and iterative refinement. Our linear alternative exceeds the original instantiation of vec2vec by orders of magnitude in efficiency, while matching or exceeding their results. The method's stability and interpretable algorithmic steps facilitate scaling and unlock new opportunities for adoption in new domains and fields.

We have developed a novel activation function, named the Cauchy Activation Function. This function is derived from the Cauchy Integral Theorem in complex analysis and is specifically tailored for problems requiring high precision. This innovation has led to the creation of a new class of neural networks, which we call (Comple)XNet, or simply XNet. We will demonstrate that XNet is particularly effective for high-dimensional challenges such as image classification and solving Partial Differential Equations (PDEs). Our evaluations show that XNet significantly outperforms established benchmarks like MNIST and CIFAR-10 in computer vision, and offers substantial advantages over Physics-Informed Neural Networks (PINNs) in both low-dimensional and high-dimensional PDE scenarios.

Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related concept that captures, in a nontrivial way, much of the underlying geometry of the original metric space. Recent work has demonstrated that when the metric space is Euclidean, the weighting vector serves as an effective tool for boundary detection. We recast this result and show the weighting vector may be viewed as a solution to a kernelized SVM. As one consequence, we apply this new insight to the task of outlier detection, and we demonstrate performance that is competitive or exceeds performance of state-of-the-art techniques on benchmark data sets. Under mild assumptions, we show the weighting vector, which has computational cost of matrix inversion, can be efficiently approximated in linear time. We show how nearest neighbor methods can approximate solutions to the minimization problems defined by SVMs.

Activation functions are fundamental in deep neural networks and directly impact gradient flow, optimization stability, and generalization. Although ReLU remains standard because of its simplicity, it suffers from vanishing gradients and lacks adaptability. Alternatives like Swish and GELU introduce smooth transitions, but fail to dynamically adjust to input statistics. We propose VeLU, a Variance-enhanced Learning Unit as an activation function that dynamically scales based on input variance by integrating ArcTan-Sin transformations and Wasserstein-2 regularization, effectively mitigating covariate shifts and stabilizing optimization. Extensive experiments on ViT_B16, VGG19, ResNet50, DenseNet121, MobileNetV2, and EfficientNetB3 confirm VeLU's superiority over ReLU, ReLU6, Swish, and GELU on six vision benchmarks. The codes of VeLU are publicly available on GitHub.

The field of Automatic Machine Learning (AutoML) has recently attained impressive results, including the discovery of state-of-the-art machine learning solutions, such as neural image classifiers. This is often done by applying an evolutionary search method, which samples multiple candidate solutions from a large space and evaluates the quality of each candidate through a long training process. As a result, the search tends to be slow. In this paper, we show that large efficiency gains can be obtained by employing a fast unified functional hash, especially through the functional equivalence caching technique, which we also present. The central idea is to detect by hashing when the search method produces equivalent candidates, which occurs very frequently, and this way avoid their costly re-evaluation. Our hash is "functional" in that it identifies equivalent candidates even if they were represented or coded differently, and it is "unified" in that the same algorithm can hash arbitrary representations; e.g. compute graphs, imperative code, or lambda functions. As evidence, we show dramatic improvements on multiple AutoML domains, including neural architecture search and algorithm discovery. Finally, we consider the effect of hash collisions, evaluation noise, and search distribution through empirical analysis. Altogether, we hope this paper may serve as a guide to hashing techniques in AutoML.

In this paper, we describe Function Assistant, a lightweight Python-based toolkit for querying and exploring source code repositories using natural language. The toolkit is designed to help end-users of a target API quickly find information about functions through high-level natural language queries and descriptions. For a given text query and background API, the tool finds candidate functions by performing a translation from the text to known representations in the API using the semantic parsing approach of Richardson and Kuhn (2017). Translations are automatically learned from example text-code pairs in example APIs. The toolkit includes features for building translation pipelines and query engines for arbitrary source code projects. To explore this last feature, we perform new experiments on 27 well-known Python projects hosted on Github.

We present time vectors, a simple tool to customize language models to new time periods. Time vectors are created by finetuning a language model on data from a single time (e.g., a year or month), and then subtracting the weights of the original pretrained model. This vector specifies a direction in weight space that, as our experiments show, improves performance on text from that time period. Time vectors specialized to adjacent time periods appear to be positioned closer together in a manifold. Using this structure, we interpolate between time vectors to induce new models that perform better on intervening and future time periods, without any additional training. We demonstrate the consistency of our findings across different tasks, domains, model sizes, and time scales. Our results suggest that time is encoded in the weight space of finetuned models.

In this work, we introduce Boolformer, the first Transformer architecture trained to perform end-to-end symbolic regression of Boolean functions. First, we show that it can predict compact formulas for complex functions which were not seen during training, when provided a clean truth table. Then, we demonstrate its ability to find approximate expressions when provided incomplete and noisy observations. We evaluate the Boolformer on a broad set of real-world binary classification datasets, demonstrating its potential as an interpretable alternative to classic machine learning methods. Finally, we apply it to the widespread task of modelling the dynamics of gene regulatory networks. Using a recent benchmark, we show that Boolformer is competitive with state-of-the art genetic algorithms with a speedup of several orders of magnitude. Our code and models are available publicly.

Metric space magnitude, an active subject of research in algebraic topology, originally arose in the context of biology, where it was used to represent the effective number of distinct species in an environment. In a more general setting, the magnitude of a metric space is a real number that aims to quantify the effective number of distinct points in the space. The contribution of each point to a metric space's global magnitude, which is encoded by the {\em weighting vector}, captures much of the underlying geometry of the original metric space. Surprisingly, when the metric space is Euclidean, the weighting vector also serves as an effective tool for boundary detection. This allows the weighting vector to serve as the foundation of novel algorithms for classic machine learning tasks such as classification, outlier detection and active learning. We demonstrate, using experiments and comparisons on classic benchmark datasets, the promise of the proposed magnitude and weighting vector-based approaches.

Deep functional maps have recently emerged as a powerful tool for solving non-rigid shape correspondence tasks. Methods that use this approach combine the power and flexibility of the functional map framework, with data-driven learning for improved accuracy and generality. However, most existing methods in this area restrict the learning aspect only to the feature functions and still rely on axiomatic modeling for formulating the training loss or for functional map regularization inside the networks. This limits both the accuracy and the applicability of the resulting approaches only to scenarios where assumptions of the axiomatic models hold. In this work, we show, for the first time, that both in-network regularization and functional map training can be replaced with data-driven methods. For this, we first train a generative model of functional maps in the spectral domain using score-based generative modeling, built from a large collection of high-quality maps. We then exploit the resulting model to promote the structural properties of ground truth functional maps on new shape collections. Remarkably, we demonstrate that the learned models are category-agnostic, and can fully replace commonly used strategies such as enforcing Laplacian commutativity or orthogonality of functional maps. Our key technical contribution is a novel distillation strategy from diffusion models in the spectral domain. Experiments demonstrate that our learned regularization leads to better results than axiomatic approaches for zero-shot non-rigid shape matching. Our code is available at: https://github.com/daidedou/diffumatch/

Normalization layers and activation functions are fundamental components in deep networks and typically co-locate with each other. Here we propose to design them using an automated approach. Instead of designing them separately, we unify them into a single tensor-to-tensor computation graph, and evolve its structure starting from basic mathematical functions. Examples of such mathematical functions are addition, multiplication and statistical moments. The use of low-level mathematical functions, in contrast to the use of high-level modules in mainstream NAS, leads to a highly sparse and large search space which can be challenging for search methods. To address the challenge, we develop efficient rejection protocols to quickly filter out candidate layers that do not work well. We also use multi-objective evolution to optimize each layer's performance across many architectures to prevent overfitting. Our method leads to the discovery of EvoNorms, a set of new normalization-activation layers with novel, and sometimes surprising structures that go beyond existing design patterns. For example, some EvoNorms do not assume that normalization and activation functions must be applied sequentially, nor need to center the feature maps, nor require explicit activation functions. Our experiments show that EvoNorms work well on image classification models including ResNets, MobileNets and EfficientNets but also transfer well to Mask R-CNN with FPN/SpineNet for instance segmentation and to BigGAN for image synthesis, outperforming BatchNorm and GroupNorm based layers in many cases.

Auxiliary function is a helpful component to improve language model's code generation ability. However, a systematic exploration of how they affect has yet to be done. In this work, we comprehensively evaluate the ability to utilize auxiliary functions encoded in recent code-pretrained language models. First, we construct a human-crafted evaluation set, called HumanExtension, which contains examples of two functions where one function assists the other. With HumanExtension, we design several experiments to examine their ability in a multifaceted way. Our evaluation processes enable a comprehensive understanding of including auxiliary functions in the prompt in terms of effectiveness and robustness. An additional implementation style analysis captures the models' various implementation patterns when they access the auxiliary function. Through this analysis, we discover the models' promising ability to utilize auxiliary functions including their self-improving behavior by implementing the two functions step-by-step. However, our analysis also reveals the model's underutilized behavior to call the auxiliary function, suggesting the future direction to enhance their implementation by eliciting the auxiliary function call ability encoded in the models. We release our code and dataset to facilitate this research direction.

Changing how pre-trained models behave -- e.g., improving their performance on a downstream task or mitigating biases learned during pre-training -- is a common practice when developing machine learning systems. In this work, we propose a new paradigm for steering the behavior of neural networks, centered around task vectors. A task vector specifies a direction in the weight space of a pre-trained model, such that movement in that direction improves performance on the task. We build task vectors by subtracting the weights of a pre-trained model from the weights of the same model after fine-tuning on a task. We show that these task vectors can be modified and combined together through arithmetic operations such as negation and addition, and the behavior of the resulting model is steered accordingly. Negating a task vector decreases performance on the target task, with little change in model behavior on control tasks. Moreover, adding task vectors together can improve performance on multiple tasks at once. Finally, when tasks are linked by an analogy relationship of the form ``A is to B as C is to D", combining task vectors from three of the tasks can improve performance on the fourth, even when no data from the fourth task is used for training. Overall, our experiments with several models, modalities and tasks show that task arithmetic is a simple, efficient and effective way of editing models.

Despite recent progress made by large language models in code generation, they still struggle with programs that meet complex requirements. Recent work utilizes plan-and-solve decomposition to decrease the complexity and leverage self-tests to refine the generated program. Yet, planning deep-inside requirements in advance can be challenging, and the tests need to be accurate to accomplish self-improvement. To this end, we propose FunCoder, a code generation framework incorporating the divide-and-conquer strategy with functional consensus. Specifically, FunCoder recursively branches off sub-functions as smaller goals during code generation, represented by a tree hierarchy. These sub-functions are then composited to attain more complex objectives. Additionally, we designate functions via a consensus formed by identifying similarities in program behavior, mitigating error propagation. FunCoder outperforms state-of-the-art methods by +9.8% on average in HumanEval, MBPP, xCodeEval and MATH with GPT-3.5 and GPT-4. Moreover, our method demonstrates superiority on smaller models: With FunCoder, StableCode-3b surpasses GPT-3.5 by +18.6% and achieves 97.7% of GPT-4's performance on HumanEval. Further analysis reveals that our proposed dynamic function decomposition is capable of handling complex requirements, and the functional consensus prevails over self-testing in correctness evaluation.

Vector Symbolic Architectures (VSAs) give a way to represent a complex object as a single fixed-length vector, so that similar objects have similar vector representations. These vector representations then become easy to use for machine learning or nearest-neighbor search. We review a previously proposed VSA method, MBAT (Matrix Binding of Additive Terms), which uses multiplication by random matrices for binding related terms. However, multiplying by such matrices introduces instabilities which can harm performance. Making the random matrices be orthogonal matrices provably fixes this problem. With respect to larger scale applications, we see how to apply MBAT vector representations for any data expressed in JSON. JSON is used in numerous programming languages to express complex data, but its native format appears highly unsuited for machine learning. Expressing JSON as a fixed-length vector makes it readily usable for machine learning and nearest-neighbor search. Creating such JSON vectors also shows that a VSA needs to employ binding operations that are non-commutative. VSAs are now ready to try with full-scale practical applications, including healthcare, pharmaceuticals, and genomics. Keywords: MBAT (Matrix Binding of Additive Terms), VSA (Vector Symbolic Architecture), HDC (Hyperdimensional Computing), Distributed Representations, Binding, Orthogonal Matrices, Recurrent Connections, Machine Learning, Search, JSON, VSA Applications

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there are finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, real-world data is often not naturally posed in this setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions. Then, we convert each GP into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications. We release the code of FunBaT at https://github.com/xuangu-fang/Functional-Bayesian-Tucker-Decomposition.

A supervised learning algorithm searches over a set of functions A to B parametrised by a space P to find the best approximation to some ideal function fcolon A to B. It does this by taking examples (a,f(a)) in Atimes B, and updating the parameter according to some rule. We define a category where these update rules may be composed, and show that gradient descent---with respect to a fixed step size and an error function satisfying a certain property---defines a monoidal functor from a category of parametrised functions to this category of update rules. This provides a structural perspective on backpropagation, as well as a broad generalisation of neural networks.

Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a promising milestone toward mapping functions directly. Despite impressive results they still face challenges with respect to the domain geometry and typically rely on some form of discretization. In order to alleviate such limitations, we present CORAL, a new method that leverages coordinate-based networks for solving PDEs on general geometries. CORAL is designed to remove constraints on the input mesh, making it applicable to any spatial sampling and geometry. Its ability extends to diverse problem domains, including PDE solving, spatio-temporal forecasting, and inverse problems like geometric design. CORAL demonstrates robust performance across multiple resolutions and performs well in both convex and non-convex domains, surpassing or performing on par with state-of-the-art models.

In this paper, we introduce BSRBF-KAN, a Kolmogorov Arnold Network (KAN) that combines B-splines and radial basis functions (RBFs) to fit input vectors during data training. We perform experiments with BSRBF-KAN, multi-layer perception (MLP), and other popular KANs, including EfficientKAN, FastKAN, FasterKAN, and GottliebKAN over the MNIST and Fashion-MNIST datasets. BSRBF-KAN shows stability in 5 training runs with a competitive average accuracy of 97.55% on MNIST and 89.33% on Fashion-MNIST and obtains convergence better than other networks. We expect BSRBF-KAN to open many combinations of mathematical functions to design KANs. Our repo is publicly available at: https://github.com/hoangthangta/BSRBF_KAN.

Nowadays, data is represented by vectors. Retrieving those vectors, among millions and billions, that are similar to a given query is a ubiquitous problem, known as similarity search, of relevance for a wide range of applications. Graph-based indices are currently the best performing techniques for billion-scale similarity search. However, their random-access memory pattern presents challenges to realize their full potential. In this work, we present new techniques and systems for creating faster and smaller graph-based indices. To this end, we introduce a novel vector compression method, Locally-adaptive Vector Quantization (LVQ), that uses per-vector scaling and scalar quantization to improve search performance with fast similarity computations and a reduced effective bandwidth, while decreasing memory footprint and barely impacting accuracy. LVQ, when combined with a new high-performance computing system for graph-based similarity search, establishes the new state of the art in terms of performance and memory footprint. For billions of vectors, LVQ outcompetes the second-best alternatives: (1) in the low-memory regime, by up to 20.7x in throughput with up to a 3x memory footprint reduction, and (2) in the high-throughput regime by 5.8x with 1.4x less memory.

The choice of activation functions in deep networks has a significant effect on the training dynamics and task performance. Currently, the most successful and widely-used activation function is the Rectified Linear Unit (ReLU). Although various hand-designed alternatives to ReLU have been proposed, none have managed to replace it due to inconsistent gains. In this work, we propose to leverage automatic search techniques to discover new activation functions. Using a combination of exhaustive and reinforcement learning-based search, we discover multiple novel activation functions. We verify the effectiveness of the searches by conducting an empirical evaluation with the best discovered activation function. Our experiments show that the best discovered activation function, f(x) = x cdot sigmoid(beta x), which we name Swish, tends to work better than ReLU on deeper models across a number of challenging datasets. For example, simply replacing ReLUs with Swish units improves top-1 classification accuracy on ImageNet by 0.9\% for Mobile NASNet-A and 0.6\% for Inception-ResNet-v2. The simplicity of Swish and its similarity to ReLU make it easy for practitioners to replace ReLUs with Swish units in any neural network.

Vector databases manage large collections of embedding vectors. As AI applications are growing rapidly, so are the number of embeddings that need to be stored and indexed. The Faiss library is dedicated to vector similarity search, a core functionality of vector databases. Faiss is a toolkit of indexing methods and related primitives used to search, cluster, compress and transform vectors. This paper first describes the tradeoff space of vector search, then the design principles of Faiss in terms of structure, approach to optimization and interfacing. We benchmark key features of the library and discuss a few selected applications to highlight its broad applicability.