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Probabilistic Methods · Bayesian Models and Methods

Nicolas M Zilberstein, Florentin Guth, Santiago Segarra, Eero Simoncelli

Generative diffusion models can provide powerful priors for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ they learn only an implicit approximation of the prior density, and $(ii)$ they rely on crude likelihood approximations that introduce biases in the sampling. We address these challenges by introducing a new energy-based model trained using denoising score matching with a covariance-based regularization that enforces consistency across different inverse problems. Our approach learns explicit, normalized posterior densities for diverse linear inverse problems using a single model, while preserving the sampling capabilities of diffusion models. This enables new capabilities unavailable to score-based diffusion models: energy-guided adaptive sampling that adjusts schedules on-the-fly, unbiased MCMC correction with Metropolis-Hastings acceptance, and blind degradation estimation via Bayes rule. We validate our method on multiple datasets (MNIST, CelebA, ImageNet) and tasks (inpainting, deblurring), demonstrating competitive or superior performance to established baselines.

Deep Learning · Generative Models and Autoencoders

Xiao Li, Yixuan Jia, Zekai Zhang, Xiang Li, Lianghe Shi, Jinxin Zhou, Zhihui Zhu, Liyue Shen, Qing Qu

Diffusion models are effective generative frameworks with strong representation learning capabilities, yet the intrinsic properties that govern their semantic structure and generalization remain poorly understood. Drawing inspiration from self-supervised representation learning (SSL), we introduce an evaluation framework that decomposes diffusion features into a perturbation invariant component and a residual component induced by noise and augmentations. From this decomposition we derive the Invariant Contamination Ratio (ICR), a Fisher-based metric that measures how residual, augmentation-sensitive energy contaminates invariant signal in feature space. We use this framework to analyze both discriminative and generative behavior. On the representation side, we find invariance peaks at intermediate noise levels, which also yield the best downstream classification performance. On the generative side, we study how training transitions from genuine generalization to memorization in data-limited regimes, and find that $\mathrm{ICR}$ serves as a sensitive training time indicator of the early learning phenomenon: rising residual energy along Fisher directions marks the onset of memorization, detectable from training features alone without external evaluators or held-out test sets. Overall, our results show diffusion models can be monitored from a self-supervised perspective via the geometry of their learned representations.

Applications · Neuroscience, Cognitive Science

Francesco Innocenti, El Mehdi Achour, Rafal Bogacz

Predictive coding (PC) is a biologically plausible alternative to standard backpropagation (BP) that minimises an energy function with respect to network activities before updating weights. Recent work has improved the training stability of deep PC networks (PCNs) by leveraging some BP-inspired reparameterisations. However, the full scalability and theoretical basis of these approaches remains unclear. To address this, we study the infinite width and depth limits of PCNs. For linear residual networks, we show that the set of width- and depth-stable feature-learning parameterisations for PC is exactly the same as for BP. Moreover, under any of these parameterisations, the PC energy with equilibrated activities converges to the BP loss in a regime where the model width is much larger than the depth, resulting in PC computing the same gradients as BP. Experiments show that these results hold in practice for deep nonlinear networks as long as an activity equilibrium is reached. Overall, this work unifies various previous theoretical and empirical results and has important practical implications for the scaling of PCNs.

Deep Learning · Graph Neural Networks

Yilin Liu, Hongchao Zhang, Ahmad Taha, Taylor T Johnson, Meiyi Ma

Graph anomaly detection methods aim to distinguish anomalous nodes. While prior methods characterize anomalies through increased variation in the spectral energy distributions, they overlook those that result in decreased variation, i.e., camouflaged anomalies that appear normal. We show that this type of anomaly persists across multiple datasets and remains undetectable by existing spectral approaches. To address this limitation, we propose a node-level spectral energy formulation that is fully compatible with message passing and enables the detection of camouflaged anomalies. Building on this formulation, we introduce an energy-aware graph learning framework that models spectral shifts through energy-driven message passing in both static and time-series graphs. Besides, our unified architecture extends to temporal settings without introducing specialized sequence modules, enabling efficient learning under long sliding windows. Extensive experiments on large-scale benchmarks demonstrate the effectiveness and scalability of our approach.

Deep Learning · Large Language Models

Md Kowsher, Ali Polat, Ehsan Ardehaly, Mehrdad Salehi, Zia Ghiasi, Prasanth Murali, Chen Chen

This paper presents a theoretical framework that explains why fine-tuning small, randomly selected subnetworks (slices) within pre-trained models is sufficient for downstream adaptation. We prove that pretrained networks exhibit a universal winning slice property, arising from two phenomena: (1) spectral balance— the eigenspectra of different weight matrix slices are remarkably similar—and (2) high task energy—their backbone representations (pretrained weights) retain rich, task-relevant features. This leads to the Universal Winning Slice Hypothesis, which provides a theoretical foundation for parameter-efficient fine-tuning (PEFT) in large-scale models. Inspired by this, we propose SliceFine, a PEFT method that uses this inherent redundancy by updating only selected slices of the origi- nal weights—introducing zero new parameters, unlike adapter-based approaches. Empirically, SliceFine matches the performance of SOTA PEFT methods across various language and vision tasks, while significantly improving training speed, memory efficiency, and model compactness. Our work bridges theory and prac- tice, offering a theoretically grounded alternative to existing PEFT techniques.

Deep Learning · Large Language Models

Yoonjun Cho, Dongjae Jeon, Soeun Kim, Moongyu Jeon, Albert No

Quantization Error Reconstruction (QER) reduces accuracy loss in Post-Training Quantization (PTQ) by approximating weights as $\mathbf{W} \approx \mathbf{Q} + \mathbf{L}\mathbf{R}$, using a rank-$r$ correction to reconstruct quantization error. Prior methods devote the full rank budget to error reconstruction, which is suboptimal when $\mathbf{W}$ has intrinsic low-rank structure and quantization corrupts dominant directions. We propose Structured Residual Reconstruction (SRR), a rank-allocation framework that preserves the top-$k$ singular subspace of the activation-scaled weight before quantization, quantizes only the residual, and uses the remaining rank $r-k$ for error reconstruction. We derive a theory-guided criterion for selecting $k$ by balancing quantization-exposed energy and unrecoverable error under rank constraints. We further show that resulting $\mathbf{Q}+\mathbf{L}\mathbf{R}$ parameterization naturally supports Quantized Parameter-Efficient Fine-Tuning (QPEFT), and stabilizes fine-tuning via gradient scaling along preserved directions. Experiments demonstrate consistent perplexity reductions across diverse models and quantization settings in PTQ, along with a 5.9 percentage-point average gain on GLUE under 2-bit QPEFT.

Deep Learning · Large Language Models

GuanHao Zhao, Wenbo Lu, Cheng Cheng, Zhenya Huang, Wei Song, Zhiding Liu, Runze Wu, Enhong Chen

The collective intelligence of Large Language Model (LLM)-based Multi-Agent Systems (MAS) is fundamentally governed by the underlying communication graph. However, discovering task-adaptive structures within this combinatorial search space remains a significant challenge. Existing methods, ranging from heuristic pruning to autoregressive generation, often lack a unified theoretical framework to guide the self-organization of agents into efficient teams. In this paper, we bridge non-equilibrium thermodynamics and generative modeling to formalize multi-agent graph generation as an energy minimization process. Specifically, we frame the emergence of efficient collaboration as a thermodynamic "cooling" process, where initially stochastic interactions converge to a low-energy, structured equilibrium. To implement this, We propose MAGE (Multi-Agent Communication Graph Generation), a score-based diffusion framework that constructs communication graphs by navigating the energy landscape via iterative denoising and first-order gradient guidance. Extensive experiments on representative benchmarks demonstrate that MAGE achieves state-of-the-art performance. Furthermore, qualitative analysis reveals that the generated graphs mirroring the functional specialization of human organizations, validating our thermodynamic hypothesis.

Qing Zhou, Hongyuan Zhang, Tao Yang, Junyu Gao, Qi Wang

Token merging accelerates Transformer inference by clustering similar tokens to reduce sequence length (retention ratio $r$), but distorts attention outputs, inducing covariate shift in residual streams and performance collapse under high compression. Existing heuristics, such as proportional attention, mitigate mild compression effectively but degrade sharply at aggressive ratios due to unaddressed energy drift and biased attention distributions. We reframe token merging as a statistical reconstruction problem in high dimensions and introduce an asymptotic radial-angular decomposition of the reconstruction error, an analytical framework decoupling magnitude and distributional distortions. Minimizing this decomposed risk under minimal assumptions of finite second moments and variance stationarity yields closed-form optimal corrections governed by a single scaling factor $\sqrt{r}$: scaling merged values and shrinking merged logits toward the cluster-size prior. This calibrates both energy balance and distributional fidelity. Extensive experiments on vision Transformers demonstrate superior accuracy and robustness across compression levels.

Applications · Health / Medicine

Ruihan Guo, Chaoran Cheng, Zhanghan Ni, Neil He, Bangji Yang, Ge Liu

Predicting protein mutation effects is fundamental to protein engineering and disease variant interpretation, yet experimental mutation data remain accurate but extremely sparse. Large-scale computational augmentation offers scalability, but introduces heterogeneous and poorly calibrated supervision signals arising from distinct modeling paradigms. We construct a PDB-wide, structure-aligned mutation augmentation dataset that exhaustively enumerates single-site substitutions and aligns mutation signals from physics-based energy models, protein language models, and structure-conditioned inverse folding models. Large-scale analysis under a unified mutation preference representation reveals substantial differences in preference structure, confidence, and cross-model agreement, indicating that disagreement is pervasive and reflects conflicting inductive biases rather than random noise. Motivated by these observations, we propose an unsupervised multi-source mutation preference distillation framework that learns from relative mutation preferences while explicitly modeling cross-source disagreement. Without using any experimental mutation labels during training, our approach achieves consistent improvements on the ProteinGym benchmark over zero-shot baselines and naive multi-source fusion strategies. We release the dataset and evaluation pipeline to support reproducible studies of protein mutation effects.

Applications · Computer Vision

Shangze Li, Yifan Xu, Jingmiao Liang, Yongfei Zhang, Yuzhuo Ma, Yingbo Qu

While Vision Transformers (ViTs) offer strong global modeling, their quadratic computational cost limits utility in latency-sensitive applications like person re-identification (ReID). Existing compression strategies, such as token pruning or generic merging, typically rely on coarse-grained criteria tailored for image classification. In fine-grained retrieval, these approaches often discard or smooth out subtle but discriminative local details. To resolve this, we propose SRE-Merge, a training-free framework designed for discriminative token compression. SRE-Merge injects spatial priors into the merging process through three mechanisms: (i) Spatial-Entropy Saliency Assessment (SES-Assess), which quantifies token importance as Spatial-Entropic Mass (SE-Mass) by coupling spatial structure with local attention entropy; (ii) Hybrid Context-Affinity Matching (HCA-Match), which guides precise pair selection by combining feature similarity with mass-derived context; and (iii) Energy-Preserving Weighted Fusion (EPW-Fuse), which incorporates SE-Mass weighting to counteract feature variance reduction. Extensive experiments on standard benchmarks show that SRE-Merge reduces GFLOPs of the base ViT model by about 24\% while maintaining state-of-the-art accuracy, establishing a superior accuracy-efficiency trade-off.

Applications · Neuroscience, Cognitive Science

Dongyang Ma, Zhengyu Ma, Yifan Huang, Chenlin Zhou, Wei Zhang, Yonghong Tian

Retina-like event cameras and brain-inspired Spiking Neural Networks (SNNs) demonstrate exceptional energy efficiency through bio-inspired sensing and computation. While SNNs are naturally well-suited to the asynchronous nature of event data, their practical applications face the following challenges: sensitivity to noise, dense representations that disrupt spike pathways, and insufficient multi-scale feature perception. To address the aforementioned challenges, we propose a bio-vision-inspired object detection method motivated by biological (bio) vision systems. First, at the micro level, this paper proposes a noise-filtering STATNF-Neuron architecture to address the current sensitivity of basic neurons to noise. Based on STATNF-Neurons, the paper introduces two bio-vision-inspired macro-structures: Events-to-Spikes Representation (E2S), which preserves spiking characteristics while mimicking the memory and noise-filtering abilities of retinal neurons; Bidirectional Multi-Scale Spiking Network (BiSNet), which simulates cortical information flow pathways to integrate multi-scale features in both directions, enhancing the network's ability to perceive information at multiple scales. Extensive experiments show that the proposed bio-vision-inspired method achieving state-of-the-art performance. Notably, it reaches 96.1\% accuracy on NCAR, 63.5\% mAP\textsubscript{50} on N-Caltech101, and 69.1\% mAP\textsubscript{50} on Gen1.

Applications · Robotics

Kaijun Zhou, Da Peng, Qiwei Chen, Zhiyang Li, Xijun Li, Jinyu Gu

Vision-Language-Action (VLA) models are promising for generalist robot control, but on-robot deployment is bottlenecked by real-time inference under tight cost and energy budgets. Most prior evaluations rely on desktop-grade GPUs, obscuring the trade-offs and opportunities offered by heterogeneous edge accelerators (GPUs/XPUs/NPUs). We present a systematic framework for low-cost VLA deployment via model--hardware co-characterization. First, we build a cross-accelerator leaderboard and evaluate model--hardware pairs under \textbf{CET} (Cost, Energy, Time), showing that ``right-sized'' edge devices can be more cost-/energy-efficient than flagship GPUs while meeting control-rate constraints. Second, using fine-grained SM tracing and Roofline analysis, we uncover a consistent two-phase inference pattern: a compute-bound VLM backbone followed by a memory-bound Action Expert, which induces phase-dependent underutilization and hardware inefficiency. Finally, guided by these insights, we propose \textbf{DP-Cache} and \textbf{V-AEFusion} to reduce diffusion redundancy and enable asynchronous pipeline parallelism, achieving up to \(2.9\times\) speedup on GPUs and \(3.3\times\) on edge NPUs with only marginal success degradation. The code will be publicly available once the acceptance of the paper. The example leaderboard website is: \url{https://vla-leaderboard-01.vercel.app/}.

Deep Learning · Sequential Models, Time series

Matteo Pinna, Giacomo Lagomarsini, Andrea Ceni, Claudio Gallicchio

Reservoir Computing (RC) has established itself as an efficient paradigm for temporal processing. However, its scalability remains severely constrained by (i) the necessity of processing temporal data sequentially and (ii) the prohibitive memory footprint of high-dimensional reservoirs. In this work, we revisit RC through the lens of structured operators and state space modeling to address these limitations, introducing Parallel Echo State Network (ParalESN). ParalESN enables the construction of high-dimensional and efficient reservoirs based on diagonal linear recurrence in the complex space, enabling parallel processing of temporal data. We provide a theoretical analysis demonstrating that ParalESN preserves the Echo State Property and the universality guarantees of traditional Echo State Networks while admitting an equivalent representation of arbitrary linear reservoirs in the complex diagonal form. Empirically, ParalESN matches the predictive accuracy of traditional RC on time series benchmarks, while delivering substantial computational savings. On 1-D pixel-level classification tasks, ParalESN achieves competitive accuracy with fully trainable neural networks while reducing computational costs and energy consumption by orders of magnitude. Overall, ParalESN offers a promising, scalable, and principled pathway for integrating RC within the deep learning landscape.

Deep Learning · Other Representation Learning

Boliang Hao, Bailing Zhang, Fangyu Wu

Modern Hopfield Networks (MHNs) have achieved widespread success across various domains but are confined to Euclidean/Hilbert spaces, failing to preserve the hierarchical structure of data due to geometric constraints—arbitrary tree structures cannot be embedded with low distortion, while hyperbolic spaces can naturally accommodate hierarchical structures through exponential volume growth. To address this issue, we propose Hyperbolic Associative Memory Networks (HAMNs), the first framework to embed modern associative memory into hyperbolic space: we map query and memory vectors from Euclidean space to a constant negative curvature manifold via exponential maps, define a regularized energy function based on the Minkowski inner product, and adopt curvature-aware Riemannian optimization combined with exponential map updates to achieve stable on-manifold retrieval. We put forward a hierarchy-sensitivity hypothesis—HAMNs outperform Euclidean MHNs on data with deep hierarchies but exhibit comparable performance on data with weak or shallow hierarchies, which is validated by depth-controlled experiments and cross-level metrics. As a plug-and-play, model-agnostic module, HAMNs are suitable for the storage and retrieval of representations in task architectures requiring hierarchical understanding, instantiated with the Poincaré ball in experiments, and also applicable to any hyperbolic model with constant negative curvature.

Applications · Computer Vision

Lingfeng He, De Cheng, Huaijie Wang, Xi Yang, Nannan Wang, Xinbo Gao

Continual Learning (CL) requires models to sequentially adapt to new tasks without forgetting old knowledge. Recently, Low-Rank Adaptation (LoRA), a representative Parameter-Efficient Fine-Tuning (PEFT) method, has gained increasing attention in CL. Several LoRA-based CL methods reduce interference across tasks by separating their update spaces, typically building the new space from the estimated null space of past tasks. However, they (i) overlook task-shared directions, which suppresses knowledge transfer, and (ii) fail to capture truly effective task-specific directions since these ``null bases" of old tasks can remain nearly inactive for new task under correlated tasks. To address this, we study LoRA learning capability from a projection energy perspective, and propose Low-rank Decomposition and Adaptation (LoDA). It performs a task-driven decomposition to build general and truly task-specific LoRA subspaces by solving two energy-based objectives, decoupling directions for knowledge sharing and isolation. LoDA fixes LoRA down-projections on two subspaces and learns robust up-projections via a Gradient-Aligned Optimization (GAO) approach. After each task, before integrating the LoRA updates into the backbone, LoDA derives a closed-form recalibration for the general update, approximating a feature-level joint optimum along this task-shared direction. Experiments indicate that LoDA outperforms existing CL methods.

Reinforcement Learning · Multi-agent

Jiajun Wu, Xuefeng Du, Yuduo Zheng, Fengqi Li

Decentralized multi-agent reinforcement learning faces a persistent exploration–coordination tension: intrinsic rewards promote exploration under sparse feedback, yet effective cooperation requires agents’ behaviors to remain consistent over a limited communication graph. Existing methods often combine exploration bonuses and coordination regularizers with fixed-weight schedules, making them hard to tune and prone to either fragmented conventions or premature behavioral collapse. We propose the IEC (Isomorphic Exploration-Consensus) framework that couples exploration and coordination through a single constrained objective: maximize task return augmented with two complementary exploration signals, dynamics-based information gain and state-coverage novelty, while constraining graph-induced policy disagreement via a spectral smoothness penalty on neighboring agents, which can be interpreted as a Dirichlet-energy regularizer on the communication graph. IEC optimizes the resulting Lagrangian with a lightweight primal–dual update that adapts the consensus multiplier from observed constraint violations, yielding an automatic shift from diverse exploration to stable cooperative conventions. Across three distinct benchmarks, IEC achieves superior performance.

Optimization · Zero-order and Black-box Optimization

Yan Zhang, Xuefeng Liu, Sipeng Chen, Sascha Ranftl, Chong Liu, Shibo Li

Standard Bayesian Optimization (BO) assumes uniform smoothness across the search space—an assumption violated in multi-regime problems such as molecular conformation search through distinct energy basins or drug discovery across heterogeneous molecular scaffolds. A single GP either oversmooths sharp transitions or hallucinates noise in smooth regions, yielding miscalibrated uncertainty. We propose RAMBO, a Dirichlet Process Mixture of Gaussian Processes that automatically discovers latent regimes during optimization, each modeled by an independent GP with locally-optimized hyperparameters. We derive collapsed Gibbs sampling that analytically marginalizes latent functions for efficient inference, and introduce adaptive concentration parameter scheduling for coarse-to-fine regime discovery. Our acquisition functions decompose uncertainty into intra-regime and inter-regime components. Experiments on synthetic benchmarks and real-world applications—including molecular conformer optimization, virtual screening for drug discovery, and fusion reactor design—demonstrate consistent improvements over state-of-the-art baselines on multi-regime objectives.

Applications · Robotics

Dezhong Tong, Jiawen Wang, Hengyi Zhou, Yinlong Shen, Xiaonan Huang, Mohammad Khalid Jawed

Many physical AI tasks are governed by implicit equilibrium: an agent actuates a subset of degrees of freedom (boundary DoFs), while the remaining free DoFs settle by minimizing a total potential energy. Even seemingly basic tasks such as bending a deformable linear object (DLO) to a target shape can exhibit strongly nonlinear behavior due to multi-stability: the same boundary conditions may yield multiple equilibrium shapes depending on the actuation trajectory. However, learning and control in such systems is brittle because the actuation-to-configuration map is defined only implicitly, and naive backpropagation through iterative equilibrium solvers is memory- and compute-intensive. We propose Neural Control, a boundary-control framework that computes trajectory-dependent, memory-efficient proxy gradients by differentiating equilibrium conditions via an adjoint formulation, avoiding unrolling of solver iterations. To improve robustness over long horizons, we integrate these sensitivities into a receding-horizon MPC scheme that repeatedly re-anchors optimization to realized equilibria and mitigates basin-switching in multi-stable regimes. We evaluate Neural Control in simulation and on physical robots manipulating DLOs, and show improved performance over gradient-free baselines such as SPSA and CEM.

Applications · Chemistry, Physics, and Earth Sciences

Yue Yu, Weiqi Chen, Binqing Wu, Dongliang Cui, Wanyi Jiang, Zongjiang Shang, Bo Wu, Liang Sun, Ling Chen

Accurate seasonal‑to‑interannual climate forecasting provides critical support for decision-making in agriculture, energy, and disaster preparedness. Current deterministic models often fail to capture climate uncertainty, while existing generative approaches oversimplify the system by neglecting key spatiotemporal dependencies and cross-scale interactions. To address these limitations, we introduce ClimateAR, an AutoRegressive generative model for probabilistic seasonal-to-interannual Climate forecasting. The framework incorporates two novel components: (1) an aligned tokenizer that bridges and aligns heterogeneous simulation and real-world data to improve transferability across domains, and (2) a mixed-scale conditioning mechanism that captures multi-scale climate interactions for robust probabilistic forecasting. Extensive evaluations on the ERA5 reanalysis dataset show that ClimateAR achieves state-of-the-art performance, improving anomaly correlation skill by 37.56\% on average compared to leading baselines. The Code is available at https://anonymous.4open.science/r/ClimateAR-956D.

Applications · Chemistry, Physics, and Earth Sciences

Zhichao Han, Mengyi Chen, Qianxiao Li

Accurately modeling the macroscopic dynamics of high-dimensional microscopic systems is of broad interest across the sciences. Many data-driven approaches learn a low-dimensional latent state through an autoencoder trained for pointwise input reconstruction. These methods typically assume a fixed ordering of microscopic degrees of freedom in the input. However, in many settings such as particle systems the microscopic state is inherently unordered. This motivates an autoencoder framework that learns permutation-invariant latent representations. To this end, we adopt a permutation-invariant encoder and design the decoder to reconstruct the mass distribution centered at the observed points rather than per-sample reconstruction. We then jointly learn the macroscopic dynamics of the observables together with the latent states. We demonstrate the effectiveness and robustness of the proposed method across a range of microscopic settings, including learning the energy in interacting particle systems, predicting mixing dynamics in Lennard–Jones fluids, and modeling the stretching dynamics from videos of a more realistic polymer system.