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Probabilistic Methods · Monte Carlo and Sampling Methods

Yuanqi Du, Jiajun He, Francisco Vargas, Yuanqing Wang, Carla Gomes, José Miguel Hernández-Lobato, Eric Vanden-Eijnden

We present Free energy Estimators with Adaptive Transport (FEAT), a novel framework for free energy estimation---a critical challenge across scientific domains. FEAT leverages learned transports implemented via stochastic interpolants and provides consistent, minimum-variance estimators based on escorted Jarzynski equality and controlled Crooks theorem, alongside variational upper and lower bounds on free energy differences. Unifying equilibrium and non-equilibrium methods under a single theoretical framework, FEAT establishes a principled foundation for neural free energy calculations. Experimental validation on toy examples, molecular simulations, and quantum field theory demonstrates promising improvements over existing learning-based methods. Our PyTorch implementation is available at https://github.com/jiajunhe98/FEAT.

Data-centric AI · Data-centric AI methods and tools

Adrian Mirza, Nawaf Alampara, Martiño Ríos-García, Mohamed Abdelalim, Jack Butler, Bethany Connolly, Tunca Dogan, Marianna Nezhurina, Bünyamin Şen, Santosh Tirunagari 等

Foundation models have shown remarkable success across scientific domains, yet their impact in chemistry remains limited due to the absence of diverse, large-scale, high-quality datasets that reflect the field's multifaceted nature. We present the ChemPile, an open dataset containing over 75 billion tokens of curated chemical data, specifically built for training and evaluating general-purpose models in the chemical sciences. The dataset mirrors the human learning journey through chemistry---from educational foundations to specialized expertise---spanning multiple modalities and content types including structured data in diverse chemical representations (SMILES, SELFIES, IUPAC names, InChI, molecular renderings), scientific and educational text, executable code, and chemical images. ChemPile integrates foundational knowledge (textbooks, lecture notes), specialized expertise (scientific articles and language-interfaced data), visual understanding (molecular structures, diagrams), and advanced reasoning (problem-solving traces and code)---mirroring how human chemists develop expertise through diverse learning materials and experiences. Constructed through hundreds of hours of expert curation, the ChemPile captures both foundational concepts and domain-specific complexity. We provide standardized training, validation, and test splits, enabling robust benchmarking. ChemPile is openly released via HuggingFace with a consistent API, permissive license, and detailed documentation. We hope the ChemPile will serve as a catalyst for chemical AI, enabling the development of the next generation of chemical foundation models.

Reinforcement Learning · Multi-agent

Yi-Chen Li, Zhongxiang Ling, Tao Jiang, Fuxiang Zhang, Pengyuan Wang, Lei Yuan, Zongzhang Zhang, Yang Yu

Learning from multi-agent expert demonstrations, known as Multi-Agent Imitation Learning (MAIL), provides a promising approach to sequential decision-making. However, existing MAIL methods including Behavior Cloning (BC) and Adversarial Imitation Learning (AIL) face significant challenges: BC suffers from the compounding error issue, while the very nature of adversarial optimization makes AIL prone to instability. In this work, we propose \textbf{M}ulti-\textbf{A}gent imitation by learning and sampling from \textbf{F}actor\textbf{I}zed \textbf{S}oft Q-function (MAFIS), a novel method that addresses these limitations for both online and offline MAIL settings. Built upon the single-agent IQ-Learn framework, MAFIS introduces the value decomposition network to factorize the imitation objective at agent level, thus enabling scalable training for multi-agent systems. Moreover, we observe that the soft Q-function implicitly defines the optimal policy as an energy-based model, from which we can sample actions via stochastic gradient Langevin dynamics. This allows us to estimate the gradient of the factorized optimization objective for continuous control tasks, avoiding the adversarial optimization between the soft Q-function and the policy required by prior work. By doing so, we obtain a tractable and \emph{non-adversarial} objective for both discrete and continuous multi-agent control. Experiments on common benchmarks including the discrete control tasks StarCraft Multi-Agent Challenge v2 (SMACv2), Gold Miner, and Multi Particle Environments (MPE), as well as the continuous control task Multi-Agent MuJoCo (MaMuJoCo), demonstrate that MAFIS achieves superior performance compared with baselines. Our code is available at https://github.com/LAMDA-RL/MAFIS.

Probabilistic Methods · Gaussian Processes

Amon Lahr, Johannes Köhler, Anna Scampicchio, Melanie Zeilinger

Non-conservative uncertainty bounds are key for both assessing an estimation algorithm’s accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic uncertainty bound for kernel-based estimation, which can also handle correlated noise sequences. Its computation relies on a mild norm-boundedness assumption on the unknown function and the noise, returning the worst-case function realization within the hypothesis class at an arbitrary query input location. The value of this function is shown to be given in terms of the posterior mean and covariance of a Gaussian process for an optimal choice of the measurement noise covariance. By rigorously analyzing the proposed approach and comparing it with other results in the literature, we show its effectiveness in returning tight and easy-to-compute bounds for kernel-based estimates.

Applications · Physics

Stephen Zhang, Michael Stumpf

We consider the Schrödinger bridge problem which, given ensemble measurements of the initial and final configurations of a stochastic dynamical system and some prior knowledge on the dynamics, aims to reconstruct the "most likely" evolution of the system compatible with the data. Most existing literature assume Brownian reference dynamics, and are implicitly limited to modelling systems driven by the gradient of a potential energy. We depart from this regime and consider reference processes described by a multivariate Ornstein-Uhlenbeck process with generic drift matrix $\mathbf{A} \in \mathbb{R}^{d \times d}$. When $\mathbf{A}$ is asymmetric, this corresponds to a non-equilibrium system in which non-gradient forces are at play: this is important for applications to biological systems, which naturally exist out-of-equilibrium. In the case of Gaussian marginals, we derive explicit expressions that characterise exactly the solution of both the static and dynamic Schrödinger bridge. For general marginals, we propose mvOU-OTFM, a simulation-free algorithm based on flow and score matching for learning an approximation to the Schrödinger bridge. In application to a range of problems based on synthetic and real single cell data, we demonstrate that mvOU-OTFM achieves higher accuracy compared to competing methods, whilst being significantly faster to train.

Bo Peng, Jie Lu, Guangquan Zhang, Zhen Fang

Out-of-distribution (OOD) detection, recognized for its ability to identify samples of unknown classes, provides solid advantages in ensuring the reliability of machine learning models. Among existing OOD detection methods, pre-trained vision-language models have emerged as powerful post-hoc OOD detectors by leveraging textual and visual information. Despite the empirical success, there still remains a lack of research on a formal understanding of their effectiveness. This paper bridges the gap by theoretically demonstrating that existing CLIP-based post-hoc methods effectively perform a stochastic estimation of the point-wise mutual information (PMI) between the input image and each in-distribution label. This estimation is then utilized to construct energy functions for modeling in-distribution distributions. Different from prior methods that inherently consider PMI estimation as a whole task, we, motivated by the divide-and-conquer philosophy, decompose PMI estimation into multiple easier sub-tasks by applying the chain rule of PMI, which not only reduces the estimation complexity but also provably increases the estimation upper bound to reduce the underestimation bias. Extensive evaluations across mainstream benchmarks empirically manifest that our method establishes a new state-of-the-art in a variety of OOD detection setups.

Deep Learning · Robustness

Wei Chen, Yuxuan Liang

Spatio-temporal forecasting is crucial in many domains, such as transportation, meteorology, and energy. However, real-world scenarios frequently present challenges such as signal anomalies, noise, and distributional shifts. Existing solutions primarily enhance robustness by modifying network architectures or training procedures. Nevertheless, these approaches are computationally intensive and resource-demanding, especially for large-scale applications. In this paper, we explore a _novel **t**est-**t**ime **c**omputing paradigm, namely learning with calibration, **ST-TTC**_, for **s**patio-**t**emporal forecasting. Through learning with calibration, we aim to capture periodic structural biases arising from non-stationarity during the testing phase and perform real-time bias correction on predictions to improve accuracy. Specifically, we first introduce a spectral-domain calibrator with phase-amplitude modulation to mitigate periodic shift and then propose a flash updating mechanism with a streaming memory queue for efficient test-time computation. _**ST-TTC**_ effectively bypasses complex training-stage techniques, offering an efficient and generalizable paradigm. Extensive experiments on real-world datasets demonstrate the effectiveness, universality, flexibility and efficiency of our proposed method.

Computer Vision · Everything Else

Shuteng Wang, Christian Theobalt, Vladislav Golyanik

Quantum Implicit Neural Representations (QINRs) have emerged as a promising paradigm that leverages parametrised quantum circuits to encode and process classical information. However, significant challenges remain in areas such as ansatz architecture design, the effective utility of quantum-mechanical properties, training efficiency, and the integration with classical modules. This paper advances the field by introducing a novel QINR architecture for 2D image and 3D geometric field learning, which we collectively refer to as Quantum Visual Field (QVF). QVF encodes classical data into quantum statevectors using neural amplitude encoding grounded in a learnable energy manifold, ensuring meaningful Hilbert space embeddings. Our ansatz follows a fully entangled design of learnable parametrised quantum circuits, with quantum (unitary) operations performed in the real Hilbert space, resulting in numerically stable training with fast convergence. QVF does not rely on classical post-processing---in contrast to the previous QINR learning approach---and directly employs measurements to extract learned signals encoded in the ansatz. Experiments on a quantum hardware simulator demonstrate that QVF outperforms existing quantum approach and competes widely used classical foundational baselines in terms of visual representation accuracy across various metrics and model characteristics. We also show applications of QVF in 2D and 3D field completion and 3D shape interpolation, highlighting its practical potential. Project page: \url{https://4dqv.mpi-inf.mpg.de/QVF/}.

Probabilistic Methods · Bayesian Models and Methods

Hadi Vafaii, Dekel Galor, Jacob Yates

Inference in both brains and machines can be formalized by optimizing a shared objective: maximizing the evidence lower bound (ELBO) in machine learning, or minimizing variational free energy ($\mathcal{F}$) in neuroscience (ELBO = $-\mathcal{F}$). While this equivalence suggests a unifying framework, it leaves open how inference is implemented in neural systems. Here, we introduce FOND (*Free energy Online Natural-gradient Dynamics*), a framework that derives neural inference dynamics from three principles: (1) natural gradients on $\mathcal{F}$, (2) online belief updating, and (3) iterative refinement. We apply FOND to derive iP-VAE (*iterative Poisson variational autoencoder*), a recurrent spiking neural network that performs variational inference through membrane potential dynamics, replacing amortized encoders with iterative inference updates. Theoretically, iP-VAE yields several desirable features such as emergent normalization via lateral competition, and hardware-efficient integer spike count representations. Empirically, iP-VAE outperforms both standard VAEs and Gaussian-based predictive coding models in sparsity, reconstruction, and biological plausibility, and scales to complex color image datasets such as CelebA. iP-VAE also exhibits strong generalization to out-of-distribution inputs, exceeding hybrid iterative-amortized VAEs. These results demonstrate how deriving inference algorithms from first principles can yield concrete architectures that are simultaneously biologically plausible and empirically effective.

Applications · Chemistry and Drug Discovery

Yibo Wen, Chenwei Xu, Jerry Yao-Chieh Hu, Kaize Ding, Han Liu

We present a three-stage framework for training deep learning models specializing in antibody sequence-structure co-design. We first pre-train a language model using millions of antibody sequence data. Then, we employ the learned representations to guide the training of a diffusion model for joint optimization over both sequence and structure of antibodies. During the final alignment stage, we optimize the model to favor antibodies with low repulsion and high attraction to the antigen binding site, enhancing the rationality and functionality of the designs. To mitigate conflicting energy preferences, we extend AbDPO (Antibody Direct Preference Optimization) to guide the model toward Pareto optimality under multiple energy-based alignment objectives. Furthermore, we adopt an iterative learning paradigm with temperature scaling, enabling the model to benefit from diverse online datasets without requiring additional data. In practice, our proposed methods achieve high stability and efficiency in producing a better Pareto front of antibody designs compared to top samples generated by baselines and previous alignment techniques. Through extensive experiments, we showcase the superior performance of our methods in generating nature-like antibodies with high binding affinity.

Applications · Neuroscience, Cognitive Science

Hongzhi Wang, Xiubo Liang, Jinxing Han, Weidong Geng

Low-light image enhancement (LLIE) aims to improve the visibility and quality of images captured under poor illumination. However, existing deep enhancement methods often underemphasize computational efficiency, leading to high energy and memory costs. We propose \textbf{Spike-RetinexFormer}, a novel LLIE architecture that synergistically integrates Retinex theory, spiking neural networks (SNNs) and a Transformer-based design. Leveraging sparse spike-driven computation, the model reduces theoretical compute energy and memory traffic relative to ANN counterparts. Across standard benchmarks, the method matches or surpasses strong ANNs (25.50 dB on LOL-v1; 30.37 dB on SDSD-out) with comparable parameters and lower theoretical energy. Our work pioneers the synergistic integration of SNNs into Transformer architectures for LLIE, establishing a compelling pathway toward powerful, energy-efficient low-level vision on resource-constrained platforms.

Deep Learning · Everything Else

Yiyang Gu, Bohan Wu, Qinghua Ran, Rong-Cheng Tu, Xiao Luo, Zhiping Xiao, Wei Ju, Dacheng Tao, Ming Zhang

This paper studies the problem of learning hash codes from noisy supervision, which is a practical yet challenging task. This problem is important in extensive real-world applications such as image retrieval and cross-modal retrieval. However, most of the existing methods focus on label denoising to address this problem, but ignore the geometric structure of the hash space, which is critical for learning stable hash codes. Towards this end, this paper proposes a novel framework named Semantic Geometry Shaping (SEGA) that explicitly refines the semantic geometry of hash space. Specifically, we first learn dynamic class prototypes as semantic anchors and cluster hash embeddings around these prototypes to keep structural stability. We then leverage both the energy of predicted distributions and structure-based divergence to estimate the uncertainty of instances and calibrate the supervision in a soft manner. Moreover, we introduce structure-aware interpolation to improve the class boundaries. To verify the effectiveness of our design, we give the theoretical analysis for the proposed framework. Experiments on a range of widely-used retrieval datasets justify the superiority of our SEGA over extensive strong baselines under noisy supervision.

Applications · Time Series

Xiangfei Qiu, Xingjian Wu, Hanyin Cheng, Xvyuan Liu, Chenjuan Guo, Jilin Hu, Bin Yang

Time series forecasting holds significant value in various domains such as economics, traffic, energy, and AIOps, as accurate predictions facilitate informed decision-making. However, the existing Mean Squared Error (MSE) loss function sometimes fails to accurately capture the seasonality or trend within the forecasting horizon, even when decomposition modules are used in the forward propagation to model the trend and seasonality separately. To address these challenges, we propose a simple yet effective Decomposition-Based Loss function called DBLoss. This method uses exponential moving averages to decompose the time series into seasonal and trend components within the forecasting horizon, and then calculates the loss for each of these components separately, followed by weighting them. As a general loss function, DBLoss can be combined with any deep learning forecasting model. Extensive experiments demonstrate that DBLoss significantly improves the performance of state-of-the-art models across diverse real-world datasets and provides a new perspective on the design of time series loss functions.

Optimization

Mincheol Park, Heeji Won, Won Woo Ro, Suhyun Kim

Test-time adaptation (TTA) aims to preserve model performance under distribution shifts. Yet, most existing methods rely on entropy minimization for confident predictions. This paper re-examines the sufficiency of entropy minimization by analyzing its dual relationship with energy. We view energy as a proxy for likelihood, where lower energy indicates higher observability under the learned distribution. We uncover that entropy and energy are tightly associated, controlled by the model’s confidence or ambiguity, and show that simultaneous reduction of both is essential. Importantly, we reveal that entropy minimization alone neither ensures energy reduction nor supports reliable likelihood estimation, and it requires explicit discriminative guidance to reach zero entropy. To combat these problems, we propose a twofold solution. First, we introduce a likelihood-based objective grounded in energy-based models, which reshape the energy landscape to favor test samples. For stable and scalable training, we adopt sliced score matching—a sampling-free, Hessian-insensitive approximation of Fisher divergence. Second, we enhance entropy minimization with a cross-entropy that treats the predicted class as a target to promote discriminability. By counterbalancing entropy and energy through the solution of multi-objective optimization, our unified TTA, ReTTA, outperforms existing entropy- or energy-based approaches across diverse distribution shifts.

Applications · Genetics, Cell Biology, etc

Yuanxi Yu, Fan Jiang, Xinzhu Ma, Liang Zhang, Bozitao Zhong, Wanli Ouyang, Guisheng Fan, Huiqun Yu, Liang Hong, Mingchen Li

In-silico prediction of protein mutant stability, measured by the difference in Gibbs free energy change ($\Delta \Delta G$), is fundamental for protein engineering. Current sequence-to-label methods typically employ two-stage pipelines: (i) encoding mutant sequences using neural networks (e.g., transformers), followed by (ii) the $\Delta \Delta G$ regression from the latent representations. Although these methods have demonstrated promising performance, their dependence on specialized neural network encoders significantly increases the complexity. Additionally, the requirement to compute latent representations individually for each mutant sequence negatively impacts computational efficiency and poses the risk of overfitting. This work proposes the Venus-MAXWELL framework, which reformulates mutation $\Delta \Delta G$ prediction as a sequence-to-landscape task. In Venus-MAXWELL, mutations of a protein and their corresponding $\Delta \Delta G$ values are organized into a landscape matrix, allowing our framework to learn the $\Delta \Delta G$ landscape of a protein with a single forward and backward pass during training. To this end, we curated a new $\Delta \Delta G$ benchmark dataset with strict controls on data leakage and redundancy to ensure robust evaluation. Leveraging the zero-shot scoring capability of protein language models (PLMs), Venus-MAXWELL effectively utilizes the evolutionary patterns learned by PLMs during pre-training. More importantly, Venus-MAXWELL is compatible with multiple protein language models. For example, when integrated with the ESM-IF, Venus-MAXWELL achieves higher accuracy than ThermoMPNN with 10$\times$ faster in inference speed (despite having 50$\times$ more parameters than ThermoMPNN). The training codes, model weights, and datasets are publicly available at https://github.com/ai4protein/Venus-MAXWELL.

Applications · Physics

Sheikh Md Shakeel Hassan, Xianwei Zou, Akash Dhruv, Aparna Chandramowlishwaran

Modeling boiling---an inherently chaotic, multiphase process central to energy and thermal systems---remains a significant challenge for neural PDE surrogates. Existing models require future input (e.g., bubble positions) during inference because they fail to learn nucleation from past states, limiting their ability to autonomously forecast boiling dynamics. They also fail to model flow boiling velocity fields, where sharp interface–momentum coupling demands long-range and directional inductive biases. We introduce Bubbleformer, a transformer-based spatiotemporal model that forecasts stable and long-range boiling dynamics including nucleation, interface evolution, and heat transfer without dependence on simulation data during inference. Bubbleformer integrates factorized axial attention, frequency-aware scaling, and conditions on thermophysical parameters to generalize across fluids, geometries, and operating conditions.To evaluate physical fidelity in chaotic systems, we propose interpretable physics-based metrics that evaluate heat flux consistency, interface geometry, and mass conservation. We also release BubbleML 2.0, a high-fidelity dataset that spans diverse working fluids (cryogens, refrigerants, dielectrics), boiling configurations (pool and flow boiling), flow regimes (bubbly, slug, annular), and boundary conditions. Bubbleformer sets new benchmark results in both prediction and forecasting of two-phase boiling flows.

Applications · Time Series

Xinghong Chen, Weilin Wu, Kunping Yang, Guannan Chen

Forecasting real-world time series requires modeling both short-term fluctuations and long-term evolutions, as these signals typically exhibit multiscale temporal structures. A core challenge lies in reconciling such dynamics: high-frequency seasonality demands local precision, while low-frequency trends require global robustness. However, most existing methods adopt a unified loss function across all temporal components, overlooking their structural differences. This misalignment often causes overfitting to seasonal noise or underfitting of long-term trends, leading to suboptimal forecasting performance. To address this issue, we propose a Physics-guided Multiscale Loss Framework (PMLF) that decomposes time series into seasonal and trend components and assigns component-specific objectives grounded in the distinct energy responses of oscillatory and drift dynamics. Specifically, we assign a quadratic loss to seasonal components, reflecting the quadratic potential energy profile of molecular vibration, while a logarithmic loss is used for trend components to capture the sublinear energy profile of molecular drift under sustained external forces. Furthermore, we introduce a softmax-based strategy that adaptively balances the unequal energetic responses of these two physical processes. Experiments on different public benchmarks show that PMLF improves the performance of diverse baselines, demonstrating the effectiveness of physics-guided loss design in modeling structural heterogeneity in time series forecasting.

Computer Vision · Everything Else

Yi Xiao, Qiangqiang Yuan, Kui Jiang, Wenke Huang, Qiang Zhang, Tingting Zheng, Chia-Wen Lin, Liangpei Zhang

Spiking neural networks (SNNs) are emerging as a promising alternative to traditional artificial neural networks (ANNs), offering biological plausibility and energy efficiency. Despite these merits, SNNs are frequently hampered by limited capacity and insufficient representation power, yet remain underexplored in remote sensing image (RSI) super-resolution (SR) tasks. In this paper, we first observe that spiking signals exhibit drastic intensity variations across diverse textures, highlighting an active learning state of the neurons. This observation motivates us to apply SNNs for efficient SR of RSIs. Inspired by the success of attention mechanisms in representing salient information, we devise the spiking attention block (SAB), a concise yet effective component that optimizes membrane potentials through inferred attention weights, which, in turn, regulates spiking activity for superior feature representation. Our key contributions include: 1) we bridge the independent modulation between temporal and channel dimensions, facilitating joint feature correlation learning, and 2) we access the global self-similar patterns in large-scale remote sensing imagery to infer spatial attention weights, incorporating effective priors for realistic and faithful reconstruction. Building upon SAB, we proposed SpikeSR, which achieves state-of-the-art performance across various remote sensing benchmarks such as AID, DOTA, and DIOR, while maintaining high computational efficiency. Code of SpikeSR will be available at https://github.com/XY-boy/SpikeSR.

Reinforcement Learning · Deep RL

Felix Chalumeau, Daniel Rajaonarivonivelomanantsoa, Ruan John de Kock, Juan Formanek, Sasha Abramowitz, Omayma Mahjoub, Wiem Khlifi, Simon Du Toit, Louay Nessir, Refiloe Shabe 等

Reinforcement learning (RL) systems have countless applications, from energy-grid management to protein design. However, such real-world scenarios are often extremely difficult, combinatorial in nature, and require complex coordination between multiple agents. This level of complexity can cause even state-of-the-art RL systems, trained until convergence, to hit a performance ceiling which they are unable to break out of with zero-shot inference. Meanwhile, many digital or simulation-based applications allow for an inference phase that utilises a specific time and compute budget to explore multiple attempts before outputting a final solution. In this work, we show that such an inference phase employed at execution time, and the choice of a corresponding inference strategy, are key to breaking the performance ceiling observed in complex multi-agent RL problems. Our main result is striking: we can obtain up to a 126% and, on average, a 45% improvement over the previous state-of-the-art across 17 tasks, using only a couple seconds of extra wall-clock time during execution. We also demonstrate promising compute scaling properties, supported by over 60k experiments, making it the largest study on inference strategies for complex RL to date. We make all of our experimental data and code available.

Guan-Horng Liu, Jaemoo Choi, Yongxin Chen, Benjamin K Miller, Ricky T. Q. Chen

Computational methods for learning to sample from the Boltzmann distribution—where the target distribution is known only up to an unnormalized energy function—have advanced significantly recently. Due to the lack of explicit target samples, however, prior diffusion-based methods, known as _diffusion samplers_, often require importance-weighted estimation or complicated learning processes. Both trade off scalability with extensive evaluations of the energy and model, thereby limiting their practical usage. In this work, we propose **Adjoint Schrödinger Bridge Sampler (ASBS)**, a new diffusion sampler that employs simple and scalable matching-based objectives yet without the need to estimate target samples during training. ASBS is grounded on a mathematical model—the Schrödinger Bridge—which enhances sampling efficiency via kinetic-optimal transportation. Through a new lens of stochastic optimal control theory, we demonstrate how SB-based diffusion samplers can be learned at scale via Adjoint Matching and prove convergence to the global solution. Notably, ASBS generalizes the recent Adjoint Sampling (Havens et al., 2025) to arbitrary source distributions by relaxing the so-called memoryless condition that largely restricts the design space. Through extensive experiments, we demonstrate the effectiveness of ASBS on sampling from classical energy functions, amortized conformer generation, and molecular Boltzmann distributions. Codes are available at https://github.com/facebookresearch/adjoint_samplers