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Applications · Chemistry, Physics, and Earth Sciences

Wenyin Zhou, Christopher I Sprague, Vsevolod Viliuga, Matteo Tadiello, Arne Elofsson, Hossein Azizpour

Molecular structure generation is a fundamental problem that involves determining the 3D positions of molecules' constituents. It has crucial biological applications, such as molecular docking, protein folding, and molecular design.Recent advances in generative modeling, such as diffusion models and flow matching, have made great progress on these tasks by modeling molecular conformations as a distribution.In this work, we focus on flow matching and adopt an energy-based perspective to improve training and inference of structure generation models. Our view results in a mapping function, represented by a deep network, that is directly learned to \textit{iteratively} map random configurations, i.e. samples from the source distribution, to target structures, i.e. points in the data manifold. This yields a conceptually simple and empirically effective flow matching setup that is theoretically justified and has interesting connections to fundamental properties such as idempotency and stability, as well as the empirically useful techniques such as structure refinement in AlphaFold. Experiments on protein docking as well as protein backbone generation consistently demonstrate the method's effectiveness, where it outperforms recent baselines of task-associated flow matching and diffusion models, using a similar computational budget.

Probabilistic Methods · Bayesian Models and Methods

Michael Munn, Susan Wei

Recent advances in artificial intelligence have been fueled by the development of foundation models such as BERT, GPT, T5, and VisionTransformers. These models are first pretrained on vast and diverse datasets and then adapted to specific downstream tasks, often with significantly less data. However, the mechanisms behind the success of this ubiquitous pretrain-then-adapt paradigm remain underexplored, particularly the characteristics of pretraining checkpoints that enhance downstream adaptation. We introduce a Bayesian model selection criterion, called the downstream free energy, which quantifies a checkpoint’s adaptability by measuring the concentration of nearby favorable parameters for a downstream task. We demonstrate that this Bayesian model selection criterion can be effectively implemented without access to the downstream data or prior knowledge of the downstream task. Furthermore, we provide empirical evidence that the criterion reliably correlates with improved fine-tuning performance, offering a principled approach to predicting model adaptability.

Deep Learning · Generative Models and Autoencoders

Chenze Shao, Fandong Meng, Jie Zhou

Conventional wisdom suggests that autoregressive models are used to process discrete data. When applied to continuous modalities such as visual data, Visual AutoRegressive modeling (VAR) typically resorts to quantization-based approaches to cast the data into a discrete space, which can introduce significant information loss. To tackle this issue, we introduce a Continuous VAR framework that enables direct visual autoregressive generation without vector quantization. The underlying theoretical foundation is strictly proper scoring rules, which provide powerful statistical tools capable of evaluating how well a generative model approximates the true distribution. Within this framework, all we need is to select a strictly proper score and set it as the training objective to optimize. We primarily explore a class of training objectives based on the energy score, which is likelihood-free and thus overcomes the difficulty of making probabilistic predictions in the continuous space. Previous efforts on continuous autoregressive generation, such as GIVT and diffusion loss, can also be derived from our framework using other strictly proper scores. Source code: \url{https://github.com/shaochenze/EAR}.

Theory · Deep Learning

Duc Anh Nguyen, Ernesto Araya, Adalbert Fono, Gitta Kutyniok

Recent years have seen significant progress in developing spiking neural networks (SNNs) as a potential solution to the energy challenges posed by conventional artificial neural networks (ANNs). However, our theoretical understanding of SNNs remains relatively limited compared to the ever-growing body of literature on ANNs. In this paper, we study a discrete-time model of SNNs based on leaky integrate-and-fire (LIF) neurons, referred to as discrete-time LIF-SNNs, a widely used framework that still lacks solid theoretical foundations. We demonstrate that discrete-time LIF-SNNs realize piecewise constant functions defined on polyhedral regions, and more importantly, we quantify the network size required to approximate continuous functions. Moreover, we investigate the impact of latency (number of time steps) and depth (number of layers) on the complexity of the input space partitioning induced by discrete-time LIF-SNNs. Our analysis highlights the importance of latency and contrasts these networks with ANNs that use piecewise linear activation functions. Finally, we present numerical experiments to support our theoretical findings.

Applications · Neuroscience, Cognitive Science

Zecheng Hao, Qichao Ma, Kang Chen, Yi Zhang, Zhaofei Yu, Tiejun Huang

Spiking Neural Network (SNN), as a brain-inspired and energy-efficient network, is currently facing the pivotal challenge of exploring a suitable and efficient learning framework. The predominant training methodologies, namely Spatial-Temporal Back-propagation (STBP) and ANN-SNN Conversion, are encumbered by substantial training overhead or pronounced inference latency, which impedes the advancement of SNNs in scaling to larger networks and navigating intricate application domains. In this work, we propose a novel parallel conversion learning framework, which establishes a mathematical mapping relationship between each time-step of the parallel spiking neurons and the cumulative spike firing rate. We theoretically validate the lossless and sorting properties of the conversion process, as well as pointing out the optimal shifting distance for each step. Furthermore, by integrating the above framework with the distribution-aware error calibration technique, we can achieve efficient conversion towards more general activation functions or training-free circumstance. Extensive experiments have confirmed the significant performance advantages of our method for various conversion cases under ultra-low time latency. To our best knowledge, this is the first work which jointly utilizes parallel spiking calculation and ANN-SNN Conversion, providing a highly promising approach for SNN supervised training. Code is available at https://github.com/hzc1208/Parallel_Conversion.

General Machine Learning · Evaluation

Zeyu Yang, Wesley Armour

Deep learning has achieved significant success but poses increasing concerns about energy consumption and sustainability. Despite these concerns, there is a lack of understanding of their energy efficiency during inference. In this study, we conduct a comprehensive analysis of the inference energy consumption of 1,200 ImageNet classification models—the largest evaluation of its kind to date. Our findings reveal a steep decline in accuracy gains relative to the increase in energy usage, highlighting sustainability concerns in the pursuit of marginal improvements. We identify key factors contributing to energy consumption and demonstrate methods to improve energy efficiency. To promote more sustainable AI practices, we introduce an energy efficiency scoring system and develop an interactive web application that allows users to compare models based on accuracy and energy consumption. By providing extensive empirical data and practical tools, we aim to facilitate informed decision-making and encourage collaborative efforts in the development of energy-efficient AI technologies.

Applications · Chemistry, Physics, and Earth Sciences

Henrik Schopmans, Pascal Friederich

Efficient sampling of unnormalized probability densities such as theBoltzmann distribution of molecular systems is a longstanding challenge.Next to conventional approaches like molecular dynamics or Markov chainMonte Carlo, variational approaches, such as training normalizing flows withthe reverse Kullback-Leibler divergence, have been introduced. However, suchmethods are prone to mode collapse and often do not learn to sample the fullconfigurational space. Here, we present temperature-annealed Boltzmanngenerators (TA-BG) to address this challenge. First, we demonstrate thattraining a normalizing flow with the reverse Kullback-Leibler divergence athigh temperatures is possible without mode collapse. Furthermore, weintroduce a reweighting-based training objective to anneal the distribution to lower target temperatures.We apply this methodology to three molecular systems of increasing complexity and, compared to the baseline, achieve better results in almost all metrics while requiring up to three times fewer target energy evaluations. For the largest system, our approach is the only method that accurately resolves the metastable states of the system.

Deep Learning

Yanbo Wang, Justin Dauwels, Yilun Du

Generative models have demonstrated remarkable abilities in generating high-fidelity visual content. In this work, we explore how generative models can further be used not only to synthesize visual content but also to understand the properties of a scene given a natural image. We formulate scene understanding as an inverse generative modeling problem, where we seek to find conditional parameters of a visual generative model to best fit a given natural image. To enable this procedure to infer scene structure from images substantially different than those seen during training, we further propose to build this visual generative model compositionally from smaller models over pieces of a scene. We illustrate how this procedure enables us to infer the set of objects in a scene, enabling robust generalization to new test scenes with an increased number of objects of new shapes. We further illustrate how this enables us to infer global scene factors, likewise enabling robust generalization to new scenes. Finally, we illustrate how this approach can be directly applied to existing pretrained text-to-image generative models for zero-shot multi-object perception. Code and visualizations are at https://energy-based-model.github.io/compositional-inference.

Applications · Neuroscience, Cognitive Science

chang liu, Jiangrong Shen, Xuming Ran, Mingkun Xu, Qi Xu, Yi Xu, Gang Pan

Artificial neural networks (ANNs) have demonstrated outstanding performance in numerous tasks, but deployment in resource-constrained environments remains a challenge due to their high computational and memory requirements. Spiking neural networks (SNNs) operate through discrete spike events and offer superior energy efficiency, providing a bio-inspired alternative. However, current ANN-to-SNN conversion often results in significant accuracy loss and increased inference time due to conversion errors such as clipping, quantization, and uneven activation. This paper proposes a novel ANN-to-SNN conversion framework based on error compensation learning. We introduce a learnable threshold clipping function, dual-threshold neurons, and an optimized membrane potential initialization strategy to mitigate the conversion error. Together, these techniques address the clipping error through adaptive thresholds, dynamically reduce the quantization error through dual-threshold neurons, and minimize the non-uniformity error by effectively managing the membrane potential. Experimental results on CIFAR-10, CIFAR-100, ImageNet datasets show that our method achieves high-precision and ultra-low latency among existing conversion methods. Using only two time steps, our method significantly reduces the inference time while maintains competitive accuracy of 94.75% on CIFAR-10 dataset under ResNet-18 structure. This research promotes the practical application of SNNs on low-power hardware, making efficient real-time processing possible.

Applications · Time Series

Chenrui Wu, Haishuai Wang, Xiang Zhang, Chengqi Zhang, Jiajun Bu

Time series analysis is crucial across various fields like energy, environment, transportation, finance and health. Deep learning has significantly advanced this field, particularly, the Time Series Foundation Model (TSFM) excels in multiple domains due to extensive pre-training. In this work, we focus on TSFM's challenges in medical practice: limited computing resources and medical data privacy. TSFM variants include fine-tuned models and those pre-trained for rapid deployment on diverse data. There may not be enough computing resources to train physiological signals locally in hospitals, and generalized TSFM is still inferior to task-specific methods on private, imbalanced local data. To address this, we propose PhysioPFM, a framework for efficiently personalizing TSFM. Our approach involves low-rank pre-training on public datasets, generator training by trained LoRA weights, and efficient weight generation via local data. Experimental results demonstrate that integrating generated models with TSFM enhances performance, and transferability, and reduces the need for additional sensitive data training.

Applications · Chemistry, Physics, and Earth Sciences

Tao Zhang, Zhenhai Liu, Feipeng Qi, Yongjun Jiao, Tailin Wu

Multiphysics simulation, which models the interactions between multiple physical processes, and multi-component simulation of complex structures are critical in fields like nuclear and aerospace engineering. Previous studies use numerical solvers or ML-based surrogate models for these simulations. However, multiphysics simulations typically require integrating multiple specialized solvers-each for a specific physical process-into a coupled program, which introduces significant development challenges. Furthermore, existing numerical algorithms struggle with highly complex large-scale structures in multi-component simulations. Here we propose compositional Multiphysics and Multi-component PDE Simulation with Diffusion models (M2PDE) to overcome these challenges. During diffusion-based training, M2PDE learns energy functions modeling the conditional probability of one physical process/component conditioned on other processes/components. In inference, M2PDE generates coupled multiphysics and multi-component solutions by sampling from the joint probability distribution. We evaluate M2PDE on two multiphysics tasks-reaction-diffusion and nuclear thermal coupling--where it achieves more accurate predictions than surrogate models in challenging scenarios. We then apply it to a multi-component prismatic fuel element problem, demonstrating that M2PDE scales from single-component training to a 64-component structure and outperforms existing domain-decomposition and graph-based approaches. The code is available at github.com/AI4Science-WestlakeU/M2PDE.

Deep Learning · Generative Models and Autoencoders

Ruiqi Feng, Chenglei Yu, Wenhao Deng, Peiyan Hu, Tailin Wu

Flow matching has shown state-of-the-art performance in various generative tasks, ranging from image generation to decision-making, where generation under energy guidance (abbreviated as guidance in the following) is pivotal. However, the guidance of flow matching is more general than and thus substantially different from that of its predecessor, diffusion models. Therefore, the challenge in guidance for general flow matching remains largely underexplored. In this paper, we propose the first framework of general guidance for flow matching. From this framework, we derive a family of guidance techniques that can be applied to general flow matching. These include a new training-free asymptotically exact guidance, novel training losses for training-based guidance, and two classes of approximate guidance that cover classical gradient guidance methods as special cases. We theoretically investigate these different methods to give a practical guideline for choosing suitable methods in different scenarios. Experiments on synthetic datasets, image inverse problems, and offline reinforcement learning demonstrate the effectiveness of our proposed guidance methods and verify the correctness of our flow matching guidance framework. Code to reproduce the experiments can be found at https://github.com/AI4Science-WestlakeU/flow_guidance.

Applications · Computer Vision

Bonan Li, Yinhan Hu, Songhua Liu, Xinchao Wang

Layout-to-Image generation aims to create complex scenes with precise control over the placement and arrangement of subjects. Existing works have demonstrated that pre-trained Text-to-Image diffusion models can achieve this goal without training on any specific data; however, they often face challenges with imprecise localization and unrealistic artifacts. Focusing on these drawbacks, we propose a novel training-free method, WinWinLay. At its core, WinWinLay presents two key strategies—Non-local Attention Energy Function and Adaptive Update—that collaboratively enhance control precision and realism. On one hand, we theoretically demonstrate that the commonly used attention energy function introduces inherent spatial distribution biases, hindering objects from being uniformly aligned with layout instructions. To overcome this issue, non-local attention prior is explored to redistribute attention scores, facilitating objects to better conform to the specified spatial conditions. On the other hand, we identify that the vanilla backpropagation update rule can cause deviations from the pre-trained domain, leading to out-of-distribution artifacts. We accordingly introduce a Langevin dynamics-based adaptive update scheme as a remedy that promotes in-domain updating while respecting layout constraints. Extensive experiments demonstrate that WinWinLay excels in controlling element placement and achieving photorealistic visual fidelity, outperforming the current state-of-the-art methods.

Deep Learning · Theory

Divyat Mahajan, Mohammad Pezeshki, Charles Arnal, Ioannis Mitliagkas, Kartik Ahuja, Pascal Vincent

Compositional generalization is a crucial step towards developing data-efficient intelligent machines that generalize in human-like ways. In this work, we tackle a challenging form of distribution shift, termed compositional shift, where some attribute combinations are completely absent at training but present in the test distribution. This shift tests the model's ability to generalize compositionally to novel attribute combinations in discriminative tasks. We model the data with flexible additive energy distributions, where each energy term represents an attribute, and derive a simple alternative to empirical risk minimization termed compositional risk minimization (CRM). We first train an additive energy classifier to predict the multiple attributes and then adjust this classifier to tackle compositional shifts. We provide an extensive theoretical analysis of CRM, where we show that our proposal extrapolates to special affine hulls of seen attribute combinations. Empirical evaluations on benchmark datasets confirms the improved robustness of CRM compared to other methods from the literature designed to tackle various forms of subpopulation shifts.

Deep Learning · Everything Else

Chengting Yu, Xiaochen Zhao, Lei Liu, Shu Yang, Gaoang Wang, Erping Li, Aili Wang

Spiking Neural Networks (SNNs) are emerging as a brain-inspired alternative to traditional Artificial Neural Networks (ANNs), prized for their potential energy efficiency on neuromorphic hardware. Despite this, SNNs often suffer from accuracy degradation compared to ANNs and face deployment challenges due to fixed inference timesteps, which require retraining for adjustments, limiting operational flexibility. To address these issues, our work considers the spatio-temporal property inherent in SNNs, and proposes a novel distillation framework for deep SNNs that optimizes performance across full-range timesteps without specific retraining, enhancing both efficacy and deployment adaptability. We provide both theoretical analysis and empirical validations to illustrate that training guarantees the convergence of all implicit models across full-range timesteps. Experimental results on CIFAR-10, CIFAR-100, CIFAR10-DVS, and ImageNet demonstrate state-of-the-art performance among distillation-based SNNs training methods. Our code is available at https://github.com/Intelli-Chip-Lab/snn_temporal_decoupling_distillation.

Deep Learning · Algorithms

Le-Trung Nguyen, Aël Quélennec, Van-Tam Nguyen, Enzo Tartaglione

On-device learning has emerged as a promising direction for AI development, particularly because of its potential to reduce latency issues and mitigate privacy risks associated with device-server communication, while improving energy efficiency. Despite these advantages, significant memory and computational constraints still represent major challenges for its deployment. Drawing on previous studies on low-rank decomposition methods that address activation memory bottlenecks in backpropagation, we propose a novel shortcut approach as an alternative. Our analysis and experiments demonstrate that our method can reduce activation memory usage, even up to $120.09\times$ compared to vanilla training, while also reducing overall training FLOPs up to $1.86\times$ when evaluated on traditional benchmarks.

Deep Learning · Large Language Models

Wonsuk Jang, Thierry Tambe

The rapidly increasing size of large language models (LLMs) presents significant challenges in memory usage and computational costs. Quantizing both weights and activations can address these issues, with hardware-supported fine-grained scaling emerging as a promising solution to mitigate outliers. However, existing methods struggle to capture nuanced block data distributions. We propose BlockDialect, a block-wise fine-grained mixed format technique that assigns a per-block optimal number format from a formatbook for better data representation. Additionally, we introduce DialectFP4, a formatbook of FP4 variants (akin to dialects) that adapt to diverse data distributions. To leverage this efficiently, we propose a two-stage approach for online DialectFP4 activation quantization. Importantly, DialectFP4 ensures energy efficiency by selecting representable values as scaled integers compatible with low-precision integer arithmetic. BlockDialect achieves 10.78% (7.48%) accuracy gain on the LLaMA3-8B (LLaMA2-7B) model compared to MXFP4 format with lower bit usage per data, while being only 5.45% (2.69%) below full precision even when quantizing full-path matrix multiplication. Focusing on how to represent over how to scale, our work presents a promising path for energy-efficient LLM inference.

General Machine Learning · Unsupervised and Semi-supervised Learning

Giovanni Catania, Aurélien Decelle, Cyril Furtlehner, Beatriz Seoane

We investigate the impact of limited data on training pairwise energy-based models for inverse problems aimed at identifying interaction networks. Utilizing the Gaussian model as testbed, we dissect training trajectories across the eigenbasis of the coupling matrix, exploiting the independent evolution of eigenmodes and revealing that the learning timescales are tied to the spectral decomposition of the empirical covariance matrix. We see that optimal points for early stopping arise from the interplay between these timescales and the initial conditions of training. Moreover, we show that finite data corrections can be accurately modeled through asymptotic random matrix theory calculations and provide the counterpart of generalized cross-validation in the energy based model context. Our analytical framework extends to binary-variable maximum-entropy pairwise models with minimal variations.These findings offer strategies to control overfitting in discrete-variable models through empirical shrinkage corrections, improving the management of overfitting in energy-based generative models.Finally, we propose a generalization to arbitrary energy-based models by deriving the neural tangent kernel dynamics of the score function under the score-matching algorithm.

Theory · Learning Theory

Rongzhen Wang, Yan Zhang, Chenyu Zheng, Chongxuan Li, Guoqiang Wu

The success of large generative models has driven a paradigm shift, leveraging massive multi-source data to enhance model capabilities. However, the interaction among these sources remains theoretically underexplored. This paper provides a first attempt to fill this gap by rigorously analyzing multi-source training in conditional generative modeling, where each condition represents a distinct data source. Specifically, we establish a general distribution estimation error bound in average total variation distance for conditional maximum likelihood estimation based on the bracketing number.Our result shows that when source distributions share certain similarities and the model is expressive enough, multi-source training guarantees a sharper bound than single-source training.We further instantiate the general theory on conditional Gaussian estimation and deep generative models including autoregressive and flexible energy-based models, by characterizing their bracketing numbers. The results highlight that the number of sources and similarity among source distributions improve the advantage of multi-source training. Simulations and real-world experiments validate our theory.

Probabilistic Methods · Bayesian Models and Methods

Parikshit Pareek, Abhijith Jayakumar, Kaarthik Sundar, Sidhant Misra, Deepjyoti Deka

Constrained optimization problems arise in various engineering systems such as inventory management and power grids. Standard deep neural network (DNN) based machine learning proxies are ineffective in practical settings where labeled data is scarce and training times are limited. We propose a semi-supervised Bayesian Neural Networks (BNNs) based optimization proxy for this complex regime, wherein training commences in a sandwiched fashion, alternating between a supervised learning step for minimizing cost, and an unsupervised learning step for enforcing constraint feasibility. We show that the proposed semi-supervised BNN outperforms DNN architectures on important non-convex constrained optimization problems from energy network operations, achieving up to a tenfold reduction in expected maximum equality gap and halving the inequality gaps. Further, the BNN's ability to provide posterior samples is leveraged to construct practically meaningful probabilistic confidence bounds on performance using a limited validation data, unlike prior methods.