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Reinforcement Learning · Deep RL

Aditya Ellendula, Yi Wang, Minh Nguyen, Chandrajit Bajaj

We present GRL-SNAM, a geometric reinforcement learning framework for Simultaneous Navigation and Mapping in unknown environments. GRL-SNAM differs from traditional SLAM and other reinforcement learning methods by relying exclusively on local sensory observations without constructing a global map. Our approach formulates navigation and mapping as coupled dynamics on generalized Hamiltonian manifolds: sensory inputs are translated into local energy landscapes that encode reachability, obstacle barriers, and deformation constraints, while policies for sensing, planning, and reconfiguration evolve stagewise under Differential Policy Optimization. A reduced Hamiltonian serves as an adaptive score function, updating kinetic/potential terms, embedding barrier constraints, and continuously refining trajectories as new local information arrives. We evaluate GRL-SNAM on 2D deformable navigation tasks, where a hyperelastic robot learns to squeeze through narrow gaps, detour around obstacles, and generalize to unseen environments. We compare our method against local reactive baselines (PF, CBF, staged DWA), global A* references (rigid, clearance-aware), and deep RL baselines (PPO, TRPO, SAC) under identical stagewise sensing constraints. GRL-SNAM achieves strong path quality while using the minimal map coverage, preserves clearance, and generalizes to unseen layouts. This demonstrates that our Hamiltonian-structured RL framework enables high-quality navigation through minimal exploration via local energy refinement rather than global mapping.

Jing Gu, Xian Liu, Yu Zeng, Ashwin Nagarajan, Fangrui Zhu, Daniel Hong, Yue Fan, Qianqi Yan, Kaiwen Zhou, Ming-Yu Liu 等

Video generation models have achieved remarkable progress in creating high-quality, photorealistic content. However, their ability to accurately simulate physical phenomena remains a critical and unresolved challenge. This paper presents $PhyWorldBench$ , a comprehensive benchmark designed to evaluate video generation models based on their adherence to the laws of physics. The benchmark covers multiple levels of physical phenomena, ranging from fundamental principles like object motion and energy conservation to more complex scenarios involving rigid body interactions and human or animal motion. Additionally, we introduce a novel "Anti-Physics" category, where prompts intentionally violate real-world physics, enabling the assessment of whether models can follow such instructions while maintaining logical consistency. Besides large-scale human evaluation, we also design a simple yet effective method that could utilize current MLLM to evaluate the physics realism in a zero-shot fashion. We evaluate 10 state-of-the-art text-to-video generation models, including five open-source and five proprietary models, with a detailed comparison and analysis. we identify pivotal challenges models face in adhering to real-world physics. Through systematic testing of their outputs across 1,050 curated prompts—spanning fundamental, composite, and anti-physics scenarios—we identify pivotal challenges these models face in adhering to real-world physics. We then rigorously examine their performance on diverse physical phenomena with varying prompt types, deriving targeted recommendations for crafting prompts that enhance fidelity to physical principles.

Jing Gu, Xian Liu, Yu Zeng, Ashwin Nagarajan, Fangrui Zhu, Daniel Hong, Yue Fan, Qianqi Yan, Kaiwen Zhou, Ming-Yu Liu 等

Video generation models have achieved remarkable progress in creating high-quality, photorealistic content. However, their ability to accurately simulate physical phenomena remains a critical and unresolved challenge. This paper presents $PhyWorldBench$ , a comprehensive benchmark designed to evaluate video generation models based on their adherence to the laws of physics. The benchmark covers multiple levels of physical phenomena, ranging from fundamental principles like object motion and energy conservation to more complex scenarios involving rigid body interactions and human or animal motion. Additionally, we introduce a novel "Anti-Physics" category, where prompts intentionally violate real-world physics, enabling the assessment of whether models can follow such instructions while maintaining logical consistency. Besides large-scale human evaluation, we also design a simple yet effective method that could utilize current MLLM to evaluate the physics realism in a zero-shot fashion. We evaluate 10 state-of-the-art text-to-video generation models, including five open-source and five proprietary models, with a detailed comparison and analysis. we identify pivotal challenges models face in adhering to real-world physics. Through systematic testing of their outputs across 1,050 curated prompts—spanning fundamental, composite, and anti-physics scenarios—we identify pivotal challenges these models face in adhering to real-world physics. We then rigorously examine their performance on diverse physical phenomena with varying prompt types, deriving targeted recommendations for crafting prompts that enhance fidelity to physical principles.

Robert Ganian, Frank Sommer, Manuel Sorge

The training of neural networks has been extensively studied from both algorithmic and complexity-theoretic perspectives, yet recent results in this direction almost exclusively concern real-valued networks. In contrast, advances in machine learning practice highlight the benefits of quantization, where network parameters and data are restricted to finite integer domains, yielding significant improvements in speed and energy efficiency. Motivated by this gap, we initiate a systematic complexity-theoretic study of ReLU Neural Network Training in the full quantization mode. We establish strong lower bounds by showing that hardness already arises in the binary setting and under highly restrictive structural assumptions on the architecture, thereby excluding parameterized tractability for natural measures such as depth and width. On the positive side, we identify nontrivial fixed-parameter tractable cases when parameterizing by input dimensionality in combination with width and either output dimensionality or error bound, and further strengthen these results by replacing width with the more general treewidth.

Applications · Physics

Youngwoo Cho, Seunghoon Yi, Wooil Yang, Sungmo Kang, Young-Woo Son, Jaegul Choo, Joonseok Lee, Soo Kyung Kim, Hongkee Yoon

Pre-trained materials foundation models, or machine learning interatomic potentials, leverage general physicochemical knowledge to effectively approximate potential energy surfaces. However, they often require domain-specific calibration due to physicochemical diversity as well as mismatches between practical computational settings and those used in constructing the pre-training data. To address this, we propose a sparsity-promoting fine-tuning method that selectively updates model parameters by exploiting the structural properties of E(3)-equivariant materials foundation models. On energy and force prediction tasks across molecular and crystalline benchmarks, our method matches or surpasses full fine-tuning and equivariant low-rank adaptation while updating only ~3 \% of parameters, and in some cases as little as \~0.5 \%. Beyond energy and force calibration, we further demonstrate task generalizability by applying our method to magnetic moment prediction and magnetism-aware total energy modeling. Finally, analysis of sparsity patterns reveals physically interpretable signatures, such as enhanced $d$-orbital contributions in transition metal systems. Overall, our results establish sparsity-promoting fine-tuning as a flexible and interpretable method for domain specialization of equivariant materials foundation models.

Applications · Climate

Chenrui Xu, Xi Huang, Ying-Jun Zhang, Jianwei Huang

Accurate prediction of extreme wind velocities has substantial significance in industry, particularly for the operation management of wind power plants. Although the state-of-the-art data-driven models perform well for general meteorological forecasting, they may exhibit large errors for extreme weather—for example, systematically underestimating the magnitudes and short-term variation of extreme winds. To address this issue, we conduct a theoretical analysis of how the data frequency spectrum influences errors in extreme wind prediction. Based on these insights, we propose a novel loss function that incorporates a gradient penalty to mitigate the magnitude shrinkage of extreme weather, and we theoretically justify its effectiveness via a PDE-based energy–enstrophy analysis. To capture more precise short-term wind velocity variations, we design a novel structure of physics-embedded machine learning models with frequency reweighting. Experiments demonstrate that, compared to the baseline models, our approach achieves significant improvements in predicting extreme wind velocities while maintaining robust overall performance.

Applications · Chemistry and Drug Discovery

Pablo Lemos, Zane Beckwith, Sasaank Bandi, Maarten Van Damme, Jordan Crivelli-Decker, Benjamin Shields, Thomas Merth, Punit Jha, Nicola De Mitri, Tiffany Callahan 等

Accurate prediction of protein-ligand binding affinities remains a cornerstone problem in drug discovery. While binding affinity is inherently dictated by the 3D structure and dynamics of protein-ligand complexes, current deep learning approaches are limited by the lack of high-quality experimental structures with annotated binding affinities. To address this limitation, we introduce the Structurally Augmented IC50 Repository (SAIR), the largest publicly available dataset of protein-ligand 3D structures with associated activity data. The dataset comprises $5,244,285$ structures across $1,048,857$ unique protein-ligand systems, curated from the ChEMBL and BindingDB databases, which were then computationally folded using the Boltz-1x model. We provide a comprehensive characterization of the dataset, including distributional statistics of proteins and ligands, and evaluate the structural fidelity of the folded complexes using PoseBusters. Our analysis reveals that approximately $3 \%$ of structures exhibit physical anomalies, predominantly related to internal energy violations. As an initial demonstration, we benchmark several binding affinity prediction methods, including empirical scoring functions (Vina, Vinardo), a 3D convolutional neural network (Onionnet-2), and a graph neural network (AEV-PLIG). While machine learning-based models consistently outperform traditional scoring function methods, neither exhibit a high correlation with ground truth affinities, highlighting the need for models specifically fine-tuned to synthetic structure distributions. This work provides a foundation for developing and evaluating next-generation structure and binding-affinity prediction models and offers insights into the structural and physical underpinnings of protein-ligand interactions. The link to the data will be added upon publication, to preserve anonymity of the submission.

Social Aspects · Trustworthy Machine Learning

Robert Adrian Minut, Hazem Dewidar, Iacopo Masi

We reinterpret the final Large Language Model (LLM) softmax classifier as an Energy-Based Model (EBM), decomposing the sequence-to-sequence probability chain into multiple interacting EBMs at inference. This principled approach allows us to track “energy spills” during decoding, which we empirically show correlate with factual errors, biases, and failures. Similar to Orgad et al. (2025), our method localizes the exact answer token and subsequently tests for hallucinations. Crucially, however, we achieve this without requiring trained probe classifiers or activation ablations. Instead, we introduce two completely training-free metrics derived directly from output logits: **spilled energy**, which captures the discrepancy between energy values across consecutive generation steps that should theoretically match, and **marginalized energy**, which is measurable at a single step. Evaluated on nine benchmarks across state-of-the-art LLMs (including LLaMA, Mistral, and Gemma) and on synthetic algebraic operations (Qwen3), our approach demonstrates robust, competitive hallucination detection and cross-task generalization. Notably, these results hold for both pretrained and instruction-tuned variants without introducing any training overhead. Code available at [github.com/OmnAI-Lab/spilled-energy/](https://github.com/OmnAI-Lab/spilled-energy/)

Reinforcement Learning · Everything Else

Kejie He, Yi-Chen Li, Yang Yu

Model fusion has emerged as a promising research direction, offering a resource-efficient paradigm that leverages existing pre-trained models to circumvent the need for training from scratch. In this work, we investigate the fusion of models specifically adapted for decision-making tasks. This challenge divides into two distinct, yet related subproblems: the direct fusion of models that act as policy and the fusion of dynamics models that subsequently induce a policy. We suggest that these seemingly divergent subproblems can be unified through the lens of energy-based models (EBMs), which parameterizes a conditional distribution via an energy function where lower energy implies higher probability. Our framework, \textbf{EMFuse}, provides this convergence by leveraging the concept of energy as a common currency for fusion. For direct fusion of policies, such as those in language models, the output distribution is commonly softmax (Boltzmann), which essentially defines the negative logarithmic probability as an energy function. For dynamics models, existing works often train a set of models on the same dataset to obtain robust uncertainty estimation; such an ensemble approach leads to an exponential explosion in computational complexity when it comes to dynamics fusion across multiple sets of models. To overcome this, we introduce the Any-step Dynamics Energy-based Transition Model (ADETM), a novel architecture that performs efficient single-model-per-dataset uncertainty estimation with its energy-based backbone, thereby avoiding this computational explosion. Our EMFuse framework surpasses other baselines by 0.34\% to 6.63\% on single/cross domain discrete decision-making benchmarks, and achieved an extra 2.3 to 7.4 normalized points on average in D4RL MuJoCo continuous-control scenarios. Our code is available at https://github.com/LAMDA-RL/EMFuse.

Deep Learning · Generative Models and Autoencoders

Junn Yong Loo, Leong Yu, Michelle Adeline, Julia Lau, Hwa Hui Tew, Arghya Pal, VISHNU MONN BASKARAN, Chee-Ming Ting, Raphaël Phan

Energy-based models (EBMs) are a powerful class of probabilistic generative models due to their flexibility and interpretability. However, relationships between potential flows and explicit EBMs remain underexplored, while contrastive divergence training via implicit Markov chain Monte Carlo (MCMC) sampling is often unstable and expensive in high-dimensional settings. In this paper, we propose Variational Potential (VAPO) Flow Bayes, a new energy-based generative framework that eliminates the need for implicit MCMC sampling and does not rely on auxiliary networks or cooperative training. VAPO learns an energy-parameterized potential flow by constructing a flow-driven density homotopy that is matched to the data distribution through a variational loss minimizing the Kullback-Leibler divergence between the flow-driven and marginal homotopies. This principled formulation enables robust and efficient generative modeling while preserving the interpretability of EBMs. Experimental results on image generation, interpolation, out-of-distribution detection, and compositional generation confirm the effectiveness of VAPO, showing that our method performs competitively with existing approaches in terms of sample quality and versatility across diverse generative modeling tasks.

Deep Learning · Generative Models and Autoencoders

Mikhail Persiianov, Jiawei Chen, Petr Mokrov, Alexander Tyurin, Evgeny Burnaev, Aleksandr Korotin

Learning population dynamics involves recovering the underlying process that governs particle evolution, given evolutionary snapshots of samples at discrete time points. Recent methods frame this as an energy minimization problem in probability space and leverage the celebrated JKO scheme for efficient time discretization. In this work, we introduce ``iJKOnet``, an approach that combines the JKO framework with inverse optimization techniques to learn population dynamics. Our method relies on a conventional *end-to-end* adversarial training procedure and does not require restrictive architectural choices, e.g., input-convex neural networks. We establish theoretical guarantees for our methodology and demonstrate improved performance over prior JKO-based methods.

Applications · Physics

Ying Pang, Jingyuan Wang, Jiahao Ji, Fanhao Mu

Proper Orthogonal Decomposition (POD) is a cornerstone reduced-order modeling technique for accelerating the solution of partial differential equations (PDEs) by extracting energy-optimal orthogonal bases. However, POD's inherent linear assumption limits its expressive power for complex nonlinear dynamics, and its snapshot-based fixed bases generalize poorly to unseen scenarios. Meanwhile, emerging deep learning solvers have explored integrating decomposition architectures, yet their purely data-driven nature lacks essential physical priors and leads to modal collapse, where decomposed modes lose discriminative power. To address these challenges, we revisit POD from an information-theoretic perspective. We theoretically establish that POD's classical energy-maximization criterion is, in essence, a principle of maximizing mutual information. Guided by this insight, we propose OrthoSolver, a neural POD framework that generalizes this core information-theoretic principle to the nonlinear domain. OrthoSolver iteratively and adaptively extracts a set of compact and expressive nonlinear basis modes by directly maximizing their mutual information with the data field. Furthermore, an orthogonality regularization is imposed to preserve the diversity of the learned modes and effectively mitigate mode collapse. Extensive experiments on seven PDE benchmarks demonstrate that OrthoSolver consistently outperforms state-of-the-art deep learning baselines.

Applications · Physics

Xianquan Yan, Hakan Akgün, Kenji Kawaguchi, Duane Loh, Ching Lee

AI is transforming scientific research by revealing new ways to understand complex physical systems, but its impact remains constrained by the lack of large, high-quality domain-specific datasets. A rich, largely untapped resource lies in non-Hermitian quantum physics, where the energy spectra of crystals form intricate geometries on the complex plane—termed as $\textit{Hamiltonian spectral graphs}$. Despite their significance as fingerprints for electronic behavior, their systematic study has been intractable due to the reliance on manual extraction. To unlock this potential, we introduce $\textbf{Poly2Graph}$ (https://github.com/sarinstein-yan/Poly2Graph): a high-performance, open-source pipeline that automates the mapping of 1-D crystal Hamiltonians to spectral graphs. Using this tool, we present $\textbf{HSG-12M}$ (https://github.com/sarinstein-yan/HSG-12M): a dataset containing 11.6 million static and 5.1 million dynamic Hamiltonian spectral graphs across 1401 characteristic-polynomial classes, distilled from 177 TB of spectral potential data. Crucially, HSG-12M is the first large-scale dataset of $\textit{spatial multigraphs}$—graphs embedded in a metric space where multiple geometrically distinct trajectories between two nodes are retained as separate edges. This simultaneously addresses a critical gap, as existing graph benchmarks overwhelmingly assume simple, non-spatial edges, discarding vital geometric information. Benchmarks with popular GNNs expose new challenges in learning spatial multi-edges at scale. Beyond its practical utility, we show that spectral graphs serve as universal topological fingerprints of polynomials, vectors, and matrices, forging a new algebra-to-graph link. HSG-12M lays the groundwork for data-driven scientific discovery in condensed matter physics, new opportunities in geometry-aware graph learning and beyond.

Applications · Neuroscience, Cognitive Science

Mingqing Xiao, Qingyan Meng, Zongpeng Zhang, Di He, Dongsheng Li, Zhouchen Lin

Brain-inspired neuromorphic computing with spiking neural networks (SNNs) is a promising energy-efficient computational approach. However, successfully training deep SNNs in a more biologically plausible and neuromorphic-hardware-friendly way is still challenging. Most recent methods leverage spatial and temporal backpropagation (BP), not adhering to neuromorphic properties. Despite the efforts of some online training methods, tackling spatial credit assignments by alternatives with competitive performance as spatial BP remains a significant problem. In this work, we propose a novel method, online pseudo-zeroth-order (OPZO) training. Our method only requires a single forward propagation with noise injection and direct top-down signals for spatial credit assignment, avoiding spatial BP's problem of symmetric weights and separate phases for layer-by-layer forward-backward propagation. OPZO solves the large variance problem of zeroth-order methods by the pseudo-zeroth-order formulation and momentum feedback connections, while having more guarantees than random feedback. Combining online training, OPZO can pave paths to on-chip SNN training. Experiments on neuromorphic and static datasets with both fully connected and convolutional networks demonstrate the effectiveness of OPZO with competitive performance compared with spatial BP, as well as estimated low training costs.

Applications · Chemistry and Drug Discovery

Lars Holdijk, Nithishwer Mouroug Anand, Michael Bronstein, Max Welling

Estimating relative free energy differences between multiple thermodynamic states lies at the core of numerous problems in computational biochemistry. Traditional estimators, such as Free Energy Perturbation and its non-equilibrium counterpart based on the Jarzynski equality, rely on defining a switching protocol between thermodynamic states and computing the free energy difference from the work performed during this process. In this work, we present a method for learning such switching protocols within the class of escorted protocols that combine deterministic and stochastic steps. For this purpose, we use Conditional Flow Matching, and introduce Conditional Density Matching (CDM) for the purpose of estimating the change in Free-Energy. We further reduce the variance in the multistate setting by coupling multiple flows between thermodynamic states into a Flow Graph, enforcing estimator consistency across different transition paths.

Deep Learning · Everything Else

Makram Chahine, Philipp Nazari, Daniela Rus, T. Konstantin Rusch

State Space Models (SSMs), developed to tackle long sequence modeling tasks efficiently, offer both parallelizable training and fast inference. At their core are recurrent dynamical systems that maintain a hidden state, with update costs scaling with the state dimension. A key design challenge is striking the right balance between maximizing expressivity and limiting this computational burden. Control theory, and more specifically Hankel singular value analysis, provides a potent framework for the measure of energy for each state, as well as the balanced truncation of the original system down to a smaller representation with performance guarantees. Leveraging the eigenvalue stability properties of Hankel matrices, we apply this lens to SSMs $\textit{during training}$, where only dimensions of high influence are identified and preserved. Our approach, CompreSSM, applies to Linear Time-Invariant SSMs such as Linear Recurrent Units, but is also extendable to selective models. Experiments show that in-training reduction significantly accelerates optimization while preserving expressivity, with compressed models retaining task-critical structure lost by models trained directly at smaller dimension. In other words, SSMs that begin large and shrink during training achieve computational efficiency while maintaining higher performance. Project code is available at https://github.com/camail-official/compressm.

Applications · Physics

Hanming Yang, Antonio Moretti, Sebastian Macaluso, Philippe Chlenski, Christian A. Naesseth, Itsik Pe'er

Reconstructing jets, which provide vital insights into the properties and histories of subatomic particles produced in high-energy collisions, is a main problem in data analyses of collider physics. This intricate task deals with estimating the latent structure of a jet (binary tree) and involves parameters such as particle energy, momentum, and types. While Bayesian methods offer a natural approach for handling uncertainty and leveraging prior knowledge, they face significant challenges due to the super-exponential growth of potential jet topologies as the number of observed particles increases. To address this, we introduce a Combinatorial Sequential Monte Carlo approach for inferring jet latent structures. As a second contribution, we leverage the resulting estimator to develop a variational inference algorithm for parameter learning. Building on this, we introduce a variational family using a pseudo-marginal framework for a fully Bayesian treatment of all variables, unifying the generative model with the inference process. We illustrate our method's effectiveness through experiments using data generated with a collider physics generative model, highlighting superior speed and accuracy across a range of tasks.

Applications · Time Series

Ao Hu, Liangjian Wen, Jiang Duan, Yong Dai, HE YAN, Dongkai Wang, Jun Wang, Yukun Zhang, Ruoxi Jiang, Zenglin Xu

Long-term time series forecasting (LTSF) plays a crucial role in fields such as energy management, finance, and traffic prediction. Transformer-based models have adopted patch-based strategies to capture long-range dependencies, but accurately modeling shape similarities across patches and variables remains challenging due to scale differences. To address this, we introduce patch-mean decoupling (PMD), which separates the trend and residual shape information by subtracting the mean of each patch, preserving the original structure and ensuring that the attention mechanism captures true shape similarities. Futhermore, to more effectively model long-range dependencies and capture cross-variable relationships, we propose Trend Restoration Attention (TRA) and Proximal Variable Attention (PVA). The former module reintegrates the decoupled trend from PMD while calculating attention output. And the latter focuses cross-variable attention on the most relevant, recent time segments to avoid overfitting on outdated correlations. Combining these components, we propose PMDformer, a model designed to effectively capture shape similarity in long-term forecasting scenarios. Extensive experiments indicate that PMDformer outperforms existing state-of-the-art methods in stability and accuracy across multiple LTSF benchmarks. The code is available at https://github.com/aohu1105/PMDformer.

General Machine Learning · Representation Learning

Gong Zhiren, Chao Yang, Wendi Ren, Shuang Li

Humans navigate daily life by combining two modes of behavior: deliberate planning in novel situations and fast, automatic responses in familiar ones. Modeling human decision-making therefore requires capturing how people switch between these modes. We present a framework for learning human habits with rule-guided active inference, extending the view of the brain as a prediction machine that minimizes mismatches between expectations and observations, and computationally modeling of human(-like) behavior and habits. In our approach, habits emerge as symbolic rules that serve as compact, interpretable shortcuts for action. To learn these rules alongside the human models, we design a biologically inspired wake--sleep algorithm. In the wake phase, the agent engages in active inference on real trajectories: reconstructing states, updating beliefs, and harvesting candidate rules that reliably reduce free energy. In the sleep phase, the agent performs generative replay with its world model, refining parameters and consolidating or pruning rules by minimizing joint free energy. This alternating rule–model consolidation lets the agent build a reusable habit library while preserving the flexibility to plan. Experiments on basketball player movements, car-following behavior, medical diagnosis, and visual game strategy demonstrate that our framework improves predictive accuracy and efficiency compared to logic-based, deep learning, LLM-based, model-based RL, and prior active inference baselines, while producing interpretable rules that mirror human-like habits.

Computer Vision · Image and Video Generation

Luigi Sigillo, Shengfeng He, Danilo Comminiello

High-resolution image synthesis remains a core challenge in generative modeling, particularly in balancing computational efficiency with the preservation of fine-grained visual detail. We present $\textit{Latent Wavelet Diffusion (LWD)}$, a lightweight training framework that significantly improves detail and texture fidelity in ultra-high-resolution (2K-4K) image synthesis. LWD introduces a novel, frequency-aware masking strategy derived from wavelet energy maps, which dynamically focuses the training process on detail-rich regions of the latent space. This is complemented by a scale-consistent VAE objective to ensure high spectral fidelity. The primary advantage of our approach is its efficiency: LWD requires no architectural modifications and adds zero additional cost during inference, making it a practical solution for scaling existing models. Across multiple strong baselines, LWD consistently improves perceptual quality and FID scores, demonstrating the power of signal-driven supervision as a principled and efficient path toward high-resolution generative modeling.