论文检索

Computer Vision · Classification and Understanding

Chengjie Ge, Yufeng Peng, Zihao Li, Qiyu Kang, Xueyang Fu, Xuhao Li, Qixin ZHANG, Ren Junhao, Zheng-Jun Zha

Spiking Neural Networks (SNNs) draw inspiration from biological neurons to enable brain-like computation, demonstrating effectiveness in processing temporal information with energy efficiency and biological realism. Most existing SNNs are based on neural dynamics such as the (leaky) integrate-and-fire (IF/LIF) models, which are described by *first-order* ordinary differential equations (ODEs) with Markovian characteristics. This means the potential state at any time depends solely on its immediate past value, potentially limiting network expressiveness. Empirical studies of real neurons, however, reveal long-range correlations and fractal dendritic structures, suggesting non-Markovian behavior better modeled by *fractional-order* ODEs. Motivated by this, we propose a *fractional-order* spiking neural network (f-SNN) framework that strictly generalizes integer-order SNNs and captures long-term dependencies in membrane potential and spike trains via fractional dynamics, enabling richer temporal patterns. We also release an open-source toolbox to support the f-SNN framework, applicable to diverse architectures and real-world tasks. Experimentally, fractional adaptations of established SNNs into the f-SNN framework achieve superior accuracy, comparable energy efficiency, and improved robustness to noise, underscoring the promise of f-SNNs as an effective extension of traditional SNNs.

Applications · Language, Speech and Dialog

Yancheng Wang, Osama Hanna, Ruiming Xie, Xianfeng Rui, Maohao Shen, Xuedong Zhang, Christian Fuegen, Jilong Wu, Debjyoti Paul, Arthur Guo 等

Emotion recognition in speech presents a complex multimodal challenge, requiring comprehension of both linguistic content and vocal expressivity, particularly prosodic features such as fundamental frequency, intensity, and temporal dynamics. Although large language models (LLMs) have shown promise in reasoning over textual transcriptions for emotion recognition, they typically neglect fine-grained prosodic information, limiting their effectiveness and interpretability. In this work, we propose VowelPrompt, a linguistically grounded framework that augments LLM-based emotion recognition with interpretable, fine-grained vowel-level prosodic cues. Drawing on phonetic evidence that vowels serve as primary carriers of affective prosody, VowelPrompt extracts pitch-, energy-, and duration-based descriptors from time-aligned vowel segments, and converts these features into natural language descriptions for better interpretability. Such a design enables LLMs to jointly reason over lexical semantics and fine-grained prosodic variation. Moreover, we adopt a two-stage adaptation procedure comprising supervised fine-tuning (SFT) followed by Reinforcement Learning with Verifiable Reward (RLVR), implemented via Group Relative Policy Optimization (GRPO), to enhance reasoning capability, enforce structured output adherence, and improve generalization across domains and speaker variations. Extensive evaluations across diverse benchmark datasets demonstrate that VowelPrompt consistently outperforms state-of-the-art emotion recognition methods under zero-shot, fine-tuned, cross-domain, and cross-linguistic conditions, while enabling the generation of interpretable explanations that are jointly grounded in contextual semantics and fine-grained prosodic structure.

Applications · Everything Else

Nikhil Abhyankar, sanchit kabra, Saaketh Desai, Chandan Reddy

Materials discovery requires navigating vast chemical and structural spaces while satisfying multiple, often conflicting, objectives. We present LLM-guided Evolution for MAterials discovery (**LLEMA**), a unified framework that couples the scientific knowledge embedded in large language models with chemistry-informed evolutionary rules and memory-based refinement. At each iteration, an LLM proposes crystallographically specified candidates under explicit property constraints; a surrogate-augmented oracle estimates physicochemical properties; and a multi-objective scorer updates success/failure memories to guide subsequent generations. Evaluated on **14 realistic tasks** that span electronics, energy, coatings, optics, and aerospace, LLEMA discovers candidates that are chemically plausible, thermodynamically stable, and property-aligned, achieving higher hit rates and improved Pareto front quality relative to generative and LLM-only baselines. Ablation studies confirm the importance of rule-guided generation, memory-based refinement, and surrogate prediction. By enforcing synthesizability and multi-objective trade-offs, LLEMA provides a principled approach to accelerating practical materials discovery. Project website: https://scientific-discovery.github.io/llema-project/

General Machine Learning · Probabilistic Methods

Jiajun He, José Miguel Hernández Lobato, Yuanqi Du, Francisco Vargas

Diffusion models generate data by removing noise gradually, which corresponds to the time-reversal of a noising process. However, access to only the denoising kernels is often insufficient. In many applications, we need the knowledge of the marginal densities along the generation trajectory, which enables tasks such as inference-time control. To address this gap, in this paper, we introduce the Radon-Nikodym Estimator (RNE). Based on the concept of the density ratio between path distributions, it reveals a fundamental connection between marginal densities and transition kernels, providing a flexible plug-and-play framework that unifies (1) diffusion density estimation, (2) inference-time control, and (3) energy-based diffusion training under a single perspective. Experiments demonstrated that RNE delivers strong results in inference-time control applications, such as annealing and model composition, with promising inference-time scaling performance, and achieves simple yet efficient regularisation for training energy-based diffusion models. Additionally, our proposed RNE is modality-agnostic and applicable not only to continuous diffusion models but also to their discrete diffusion counterparts.

Deep Learning · Algorithms

Kenji Kubo, Shunsuke Kamiya, Masanori Koyama, Kohei Hayashi, Yusuke Iwasawa, Yutaka Matsuo

Neural network models with latent recurrent processing, where identical layers are recursively applied to the latent state, have gained attention as promising models for performing reasoning tasks. A strength of such models is that they enable test-time scaling, where the models can enhance their performance in the test phase without additional training. Models such as the Hierarchical Reasoning Model (HRM) and Artificial Kuramoto Oscillatory Neurons (AKOrN) can facilitate deeper reasoning by increasing the number of recurrent steps, thereby enabling the completion of challenging tasks, including Sudoku, Maze solving, and AGI benchmarks. In this work, we introduce confidence-based voting (C-voting), a test-time scaling strategy designed for recurrent models with multiple latent candidate trajectories. Initializing the latent state with multiple candidates using random variables, C-voting selects the one maximizing the average of top-1 probabilities of the predictions, reflecting the model’s confidence. Additionally, it yields $4.9\\%$ higher accuracy on Sudoku-hard than the energy-based voting strategy, which is specific to models with explicit energy functions. An essential advantage of C‑voting is its applicability: it can be applied to recurrent models without requiring an explicit energy function. Finally, we introduce a simple attention-based recurrent model with randomized initial values named ItrSA++, and demonstrate that when combined with C-voting, it outperforms HRM on Sudoku-extreme ($95.2\\%$ vs. $55.0\\%$) and Maze ($78.6\\%$ vs. $74.5\\%$) tasks.

General Machine Learning · Probabilistic Methods

Kirill Tamogashev, Nikolay Malkin

The Schrödinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certain transportation cost. This problem, which represents a generalisation of optimal transport to the stochastic case, has received attention due to its connections to diffusion models and flow matching, as well as its applications in the natural sciences. However, all existing algorithms enable the inference of such dynamics only for cases where samples from both distributions are available. In this paper, we propose the first general method for modelling Schrödinger bridges when one (or both) distributions are given by their unnormalised densities, with no access to data samples. Our algorithm relies on a generalisation of the iterative proportional fitting (IPF) procedure to the data-free case, inspired by recent developments in off-policy reinforcement learning for training of diffusion samplers. We demonstrate the efficacy of the proposed data-to-energy IPF on synthetic problems, finding that it can successfully learn transports between multimodal distributions. As a secondary consequence of our reinforcement learning formulation, which assumes a fixed time discretisation scheme for the dynamics, we find that existing data-to-data Schrödinger bridge algorithms can be substantially improved by learning the diffusion coefficient of the dynamics. Finally, we apply the newly developed algorithm to the problem of sampling posterior distributions in latent spaces of generative models, thus creating a data-free image-to-image translation method.

Deep Learning · Algorithms

Luca Colombo, Fabrizio Pittorino, Daniele Zambon, Carlo Baldassi, Manuel Roveri, Cesare Alippi

Binary Neural Networks (BNNs), which constrain both weights and activations to binary values, offer substantial reductions in computational complexity, memory footprint, and energy consumption. These advantages make them particularly well suited for deployment on resource-constrained devices. However, training BNNs via gradient-based optimization remains challenging due to the discrete nature of their variables. The dominant approach, quantization-aware training, circumvents this issue by employing surrogate gradients. Yet, this method requires maintaining latent full-precision parameters and performing the backward pass with floating-point arithmetic, thereby forfeiting the efficiency of binary operations during training. While alternative approaches based on local learning rules exist, they are unsuitable for global credit assignment and for back-propagating errors in multi-layer architectures. This paper introduces Binary Error Propagation (BEP), the first learning algorithm to establish a principled, discrete analog of the backpropagation chain rule. This mechanism enables error signals, represented as binary vectors, to be propagated backward through multiple layers of a neural network. BEP operates entirely on binary variables, with all forward and backward computations performed using only bitwise operations. Crucially, this makes BEP the first solution to enable end-to-end binary training for recurrent neural network architectures. We validate the effectiveness of BEP on both multi-layer perceptrons and recurrent neural networks, demonstrating gains of up to $+6.89$% and $+10.57$% in test accuracy, respectively. The proposed algorithm is released as an open-source repository.

Applications · Chemistry and Drug Discovery

Seonghyun Park, Kiyoung Seong, Soojung Yang, Rafael Gomez-Bombarelli, Sungsoo Ahn

Molecular dynamics is crucial for understanding molecular systems but its applicability is often limited by the vast timescales of rare events like protein folding. Enhanced sampling techniques overcome this by accelerating the simulation along key reaction pathways, which are defined by collective variables (CVs). However, identifying effective CVs that capture the slow, macroscopic dynamics of a system remains a major bottleneck. This work proposes a novel framework coined BioEmu-CV that learns these essential CVs automatically from BioEmu, a recently proposed foundation model for generating protein equilibrium samples. In particular, we re-purpose BioEmu to learn time-lagged generation conditioned on the learned CV, i.e., predict the distribution of molecular states after a certain amount of time. This training process promotes the CV to encode only the slow, long-term information while disregarding fast, random fluctuations. We validate our learned CV on fast-folding proteins with two key applications: (1) estimating free energy differences using on-the-fly probability enhanced sampling and (2) sampling transition paths with steered molecular dynamics. Our empirical study also serves as a new systematic and comprehensive benchmark for MLCVs on fast-folding proteins larger than Alanine Dipeptide.

Deep Learning · Graph Neural Networks

Kai Yang, Yuqi Huang, Junheng Tao, Wanyu Wang, Qitian Wu

Modeling 3D dynamics is a fundamental problem in multi-body systems across scientific and engineering domains and has important practical implications in trajectory prediction and simulation. While recent GNN-based approaches have achieved strong performance by enforcing geometric symmetries, encoding high-order features or incorporating neural-ODE mechanics, they typically depend on explicitly observed structures and inherently fail to capture the unobserved interactions that are crucial to complex physical behaviors and dynamics mechanism. In this paper, we propose PAINET, a principled SE(3)-equivariant neural architecture for learning all-pair interactions in multi-body systems. The model comprises: (1) a novel physics-inspired attention network derived from the minimization trajectory of an energy function, and (2) a parallel decoder that preserves equivariance while enabling efficient inference. Empirical results on diverse real-world benchmarks, including human motion capture, molecular dynamics, and large-scale protein simulations, show that PAINET consistently outperforms recently proposed models, yielding 4.7% to 41.5% error reductions in 3D dynamics prediction with comparable computation costs in terms of time and memory. Our codes, baseline models and datasets are available at https://github.com/Icarus1411/PAINET.

Theory · Learning Theory

Kazushi Mimura, Junichi Takeuchi, Yuto Sumikawa, Yoshiyuki Kabashima, Anthony CC Coolen

Dense associative memory, a fundamental instance of modern Hopfield networks, can store a large number of memory patterns as equilibrium states of recurrent networks. While the stationary-state storage capacity has been investigated, its dynamical properties have not yet been discussed. In this paper, we analyze the dynamics using an exact approach based on generating functional analysis. We show results on convergence properties of memory retrieval, such as the convergence time and the size of the attraction basins. Our analysis enables a quantitative evaluation of the convergence time and the storage capacity of dense associative memory, which is useful for model design. Unlike the traditional Hopfield model, the retrieval of a pattern does not act as additional noise to itself, suggesting that the structure of modern networks makes recall more robust. Furthermore, the methodology addressed here can be applied to other energy-based models, and thus has the potential to contribute to the design of future architectures.

Applications · Climate

Guowen Li, Xintong Liu, Yang Liu, Mengxuan Chen, Shilei Cao, Xuehe Wang, Juepeng Zheng, Jinxiao Zhang, Haoyuan Liang, Lixian Zhang 等

Accurate Subseasonal-to-Seasonal (S2S) forecasting is vital for decision-making in agriculture, energy production, and emergency management. However, it remains a challenging and underexplored problem due to the chaotic nature of the weather system. Recent data-driven studies have shown promising results, but their performance is limited by the inadequate incorporation of climate states and a model tendency to degrade, progressively losing fine-scale details and yielding over-smoothed forecasts. To overcome these limitations, we propose TianQuan-S2S, a global S2S forecasting model that integrates initial weather states with climatological means via incorporating climatology into patch embedding and enhancing variability capture through an uncertainty-augmented Transformer. Extensive experiments on the Earth Reanalysis 5 (ERA5) reanalysis dataset demonstrate that our model yields a significant improvement in both deterministic and ensemble forecasting over the climatology mean, traditional numerical methods, and data-driven models. Ablation studies empirically show the effectiveness of our model designs. Remarkably, our model outperforms skillful numerical ECMWF-S2S and advanced data-driven Fuxi-S2S in key meteorological variables. The code implementation can be found in https://github.com/zhangminglang42/TianQuan.

General Machine Learning · Transfer, Multitask and Meta-learning

Zhengyan Wan, Yidong Ouyang, Liyan Xie, Fang Fang, Hongyuan Zha, Guang Cheng

Guidance provides a simple and effective framework for posterior sampling by steering the generation process towards the desired distribution. When modeling discrete data, existing approaches mostly focus on guidance with the first-order approximation to improve the sampling efficiency. However, such an approximation is inappropriate in discrete state spaces since the approximation error could be large. A novel guidance framework for discrete data is proposed to address this problem: we derive the exact transition rate for the desired distribution given a learned discrete flow matching model, leading to guidance that only requires a single forward pass in each sampling step, significantly improving efficiency. This unified novel framework is general enough, encompassing existing guidance methods as special cases, and it can also be seamlessly applied to the masked diffusion model. We demonstrate the effectiveness of our proposed guidance on energy-guided simulations and preference alignment on text-to-image generation and multimodal understanding tasks.

Theory · Everything Else

Ernesto Araya, Massimiliano Datres, Gitta Kutyniok

Spiking neural networks (SNNs) are a promising paradigm for energy-efficient computation, yet their theoretical foundations—especially regarding stability and robustness—remain limited compared to artificial neural networks. In this work, we study discrete-time leaky integrate-and-fire (LIF) SNNs through the lens of Boolean function analysis. We focus on noise sensitivity and stability in classification tasks, quantifying how input perturbations affect outputs. Our main result shows that wide LIF-SNN classifiers are stable on average, a property explained by the concentration of their Fourier spectrum on low-frequency components. Motivated by this, we introduce the notion of *spectral simplicity*, which formalizes simplicity in terms of Fourier spectrum concentration and connects our analysis to the *simplicity bias* observed in deep networks. Within this framework, we show that random LIF-SNNs are biased toward simple functions. Experiments on trained networks confirm that these stability properties persist in practice. Together, these results provide new insights into the stability and robustness properties of SNNs.

Deep Learning · Theory

Yuandong Tian

While the phenomenon of grokking, i.e., delayed generalization, has been studied extensively, it remains an open problem whether there is a mathematical framework that characterizes what kind of features will emerge, how and in which conditions it happens, and is still closely connected with the gradient dynamics of the training, for complex structured inputs. We propose a novel framework, named \ours{}, that captures three key stages for the grokking behavior of 2-layer nonlinear networks: (I) \underline{\textbf{L}}azy learning, (II) \underline{\textbf{i}}ndependent feature learning and (III) \underline{\textbf{i}}nteractive feature learning. At the lazy learning stage, top layer overfits to random hidden representation and the model appears to memorize. During lazy learning, the \emph{backpropagated gradient} $G_F$ from the top layer carries information about the target label, with a specific structure that enables each hidden node to learn their representation \emph{independently}. Interestingly, the independent dynamics follows exactly the \emph{gradient ascent} of an energy function $\mathcal{E}$, and its local maxima are precisely the emerging features. We study whether these local-optima induced features are generalizable, their representation power, and how they change on sample size, in group arithmetic tasks. When hidden nodes start to interact in the later stage of learning, we provably show how $G_F$ changes to focus on missing features that need to be learned. Our study sheds lights on roles played by key hyperparameters such as weight decay, learning rate and sample sizes in grokking, leads to provable scaling laws of feature emergence, memorization and generalization, and reveals the underlying cause why recent optimizers such as Muon can be effective, from the first principles of gradient dynamics. Our analysis can be extended to multi-layer architectures.

Deep Learning · Attention Mechanisms

Nima Dehmamy, Benjamin Hoover, Bishwajit Saha, Leo Kozachkov, Jean-Jacques Slotine, Dmitry Krotov

Generative Pre-trained Transformer (GPT) architectures are the most popular design for language modeling. Energy-based modeling is a different paradigm that views inference as a dynamical process operating on an energy landscape. We propose a minimal modification of the GPT setting to unify it with the EBM framework. The inference step of our model, which we call eNeRgy-GPT (NRGPT), is conceptualized as an exploration of the tokens on the energy landscape. We prove, and verify empirically, that under certain circumstances this exploration becomes gradient descent, although they don’t necessarily lead to the best performing models. We demonstrate that our model performs well for simple language (Shakespeare dataset), algebraic ListOPS tasks, and richer settings such as OpenWebText language modeling. We also observe that our models may be more resistant to overfitting, doing so only during very long training.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Mohammad M Maheri, Xavier Cadet, Peter Chin, Hamed Haddadi

Approximate machine unlearning aims to efficiently remove the influence of specific data points from a trained model, offering a practical alternative to full retraining. However, it introduces privacy risks: an adversary with access to both the original and unlearned models can exploit their differences for membership inference or data reconstruction. We show these vulnerabilities arise from two factors: large gradient norms of forgotten samples and the close proximity of the unlearned model to the original. To demonstrate their severity, we design unlearning-specific membership inference and reconstruction attacks, showing that several state-of-the-art methods (such as NGP and SCRUB) remain vulnerable. To mitigate this leakage, we introduce WARP, a plug-and-play teleportation defense that leverages neural network symmetries to reduce gradient energy of forgotten samples and increase parameter dispersion while preserving accuracy. This reparameterization hides the signal of forgotten data, making it harder for attackers to distinguish forgotten samples from non-members or to recover them through reconstruction. Across six unlearning algorithms, our approach achieves consistent privacy gains, reducing adversarial advantage by up to 64% in black-box settings and 92% in white-box settings, while maintaining accuracy on retained data. These results highlight teleportation as a general tool for improving privacy in approximate unlearning.

Applications · Neuroscience, Cognitive Science

Gaspard Oliviers, Mufeng Tang, Rafal Bogacz

Predictive coding (PC) is an influential computational model of visual learning and inference in the brain. Classical PC was proposed as a top-down generative model, where the brain actively predicts upcoming visual inputs, and inference minimises the prediction errors. Recent studies have also shown that PC can be formulated as a discriminative model, where sensory inputs predict neural activities in a feedforward manner. However, experimental evidence suggests that the brain employs both generative and discriminative inference, while unidirectional PC models show degraded performance in tasks requiring bidirectional processing. In this work, we propose bidirectional PC (bPC), a PC model that incorporates both generative and discriminative inference while maintaining a biologically plausible circuit implementation. We show that bPC matches or outperforms unidirectional models in their specialised generative or discriminative tasks, by developing an energy landscape that simultaneously suits both tasks. We also demonstrate bPC's superior performance in two biologically relevant tasks including multimodal learning and inference with missing information, suggesting that bPC resembles biological visual inference more closely.

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

As AI increasingly shapes daily life, energy consumption and data privacy have become pressing concerns. On-device learning trains models directly on edge devices, cutting energy consumption and safeguarding data privacy. However, the expanding scale of modern neural networks creates a major obstacle for on-device training. Although prior work has concentrated on compact convolutional architectures, we instead apply subspace-based training to transformer models. Motivated by the idea that a model's essential information lies in a fixed subspace, we introduce Weight-Activation Subspace Iteration (WASI), a method that mitigates the memory bottleneck of backpropagation and boosts inference efficiency in transformer models by restricting training to this subspace. Our results demonstrate that WASI maintains accuracy comparable to vanilla training while reducing memory usage by up to $62\times$ and computational cost (FLOPs) by up to $2\times$. On a Raspberry Pi 5, WASI achieves roughly $1.4\times$ faster training and inference than vanilla training. The code is available at https://github.com/Le-TrungNguyen/ICLR2026-WASI.git.

Shijie Zhao, Xuanyu Zhang, Weiqi Li, Junlin Li, Li zhang, Tianfan Xue, Jian Zhang

Reasoning-based image quality assessment (IQA) models trained through reinforcement learning (RL) exhibit exceptional generalization, yet the underlying mechanisms and critical factors driving this capability remain underexplored in current research. Moreover, despite their superior performance, these models incur inference energy usage and latency orders of magnitude higher than their earlier counterparts, restricting their deployment in specific scenarios. Through extensive experiments, this paper verifies and elaborates that through RL training, MLLMs leverage their reasoning capability to convert redundant visual representations into compact, cross-domain aligned text representations. This conversion is precisely the source of the generalization exhibited by these reasoning-based IQA models. Building on this fundamental insight, we propose a novel algorithm, RALI, which employs contrastive learning to directly align images with these generalizable text representations learned by RL. This approach eliminates the reliance on reasoning processes and even obviates the need to load an LLM. For the quality scoring task, this framework achieves generalization performance comparable to reasoning-based models while requiring less than 5% of their model parameters and inference time.

Mingyu Kim, Young-Heon Kim, Mijung Park

Safety mechanisms for diffusion and flow models have recently been developed along two distinct paths. In robot planning, control barrier functions are employed to guide generative trajectories away from obstacles at every denoising step by explicitly imposing geometric constraints. In parallel, recent data-driven, negative guidance approaches have been shown to suppress harmful content and promote diversity in generated samples. However, they rely on heuristics without clearly stating when safety guidance is actually necessary. In this paper, we first introduce a unified probabilistic framework using a Maximum Mean Discrepancy (MMD) potential for image generation tasks that recasts both Shielded Diffusion and Safe Denoiser as instances of our energy-based negative guidance against unsafe data samples. Furthermore, we leverage control-barrier functions analysis to justify the existence of a critical time window in which negative guidance must be strong; outside of this window, the guidance should decay to zero to ensure safe and high-quality generation. We evaluate our unified framework on several realistic safe generation scenarios, confirming that negative guidance should be applied in the early stages of the denoising process for successful safe generation.