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Applications · Chemistry, Physics, and Earth Sciences

Teddy Koker, Abhijeet Gangan, Mit Kotak, Jaime Marian, Tess Smidt

Many materials properties depend on higher-order derivatives of the potential energy surface, yet machine learned interatomic potentials (MLIPs) trained with a standard loss on energy, force, and stress errors can exhibit error in curvature, degrading the prediction of vibrational properties. We introduce phonon fine-tuning (PFT), which directly supervises second-order force constants of materials by matching MLIP energy Hessians to DFT-computed force constants from finite displacement phonon calculations. To scale to large supercells, PFT stochastically samples Hessian columns and computes the loss with a single Hessian-vector product. We also use a simple co-training scheme to incorporate upstream data to mitigate catastrophic forgetting. On the MDR Phonon benchmark, PFT improves Nequix MP by 55% on average across phonon thermodynamic properties and achieves state-of-the-art accuracy among models trained on Materials Project trajectories. PFT also generalizes to improve properties beyond second-derivatives, improving thermal conductivity predictions that rely on third-order derivatives of the potential energy.

Applications · Energy

Siqi Ding, Zitong Zhang, LiXingYu, Shi Guoyang, Xiang Gu, Y.N.Xu, Huasheng Xie, Hanyue Zhao, YUEJIANG SHI, tianyuan liu

Realizing the symbiotic potential of AI and fusion energy requires bridging a critical "sim-to-real" gap. Models trained on simulations must generalize reliably under distribution shifts in safety-critical workflows. Focusing on the strongly nonlinear Grad-Shafranov equation (GSE) for tokamak equilibria, we propose a physics-anchored operator learning framework. Through systematic benchmarking across neural operator instantiations, we identify the Transformer-KAN Neural Operator (TKNO) as the state-of-the-art performer. Crucially, we adopt a semi-supervised paradigm that synergizes sparse data supervision with physical loss constraints. This approach significantly mitigates the catastrophic collapse often observed in purely data-driven methods under boundary-shape distribution shifts, thereby ensuring robust extrapolation. Validated on experimental discharge data from the EXL-50U tokamak, the model achieves high-fidelity equilibrium prediction (RMSE < 1.3%) with millisecond-level inference. These results demonstrate that AI has the potential to significantly accelerate fusion research and development.

Deep Learning · Theory

Qi Sun, Yulei Huang, Zhen Cao, Biao Hou

Spiking neural networks (SNNs) promise energy-efficient inference, yet on static vision benchmarks they often trail matched ANNs under short simulation horizons. Under a matched-backbone and matched-budget protocol without extra tricks, we find that this ANN-SNN accuracy gap is consistently smaller on representative 1D signal classification benchmarks than on image benchmarks. We attribute this to a mechanism-level mismatch: leaky integration naturally implements causal evidence accumulation over time for native temporal signals, while static images typically require amplitude-to-spike encoding, whose finite-window estimation error becomes non-negligible at short horizons. Guided by this view, we propose a plug-and-play framework that combines Multi-Scale Temporal Encoding (MTE) and Sparsity-Regularized Transform Encoding (STE). MTE replaces naive repetition with multi-scale streams and allocates scale-aligned multi-bit integer spikes to increase per-step information density, and STE replaces a controllable fraction of LIF units with a transform-encoding neuron trained using auxiliary reconstruction and sparsity regularization, with a synthesis branch used only during training. Across diverse 1D datasets and backbone families, MTE$\times$STE consistently improves the accuracy-efficiency trade-off over standard SNN baselines and matches or occasionally surpasses ANN counterparts.

Reinforcement Learning · Deep RL

Shaojun Xu, Xiaoling Zhou, Yihan Lin, Yapeng Meng, Xinglong Ji, Luping Shi, Rong Zhao

Model-Based Reinforcement Learning (MBRL) leverages latent imagination for sample efficiency, yet remains constrained by **Historical Tethering**: imagination is typically initialized from observed states. This creates a learning asymmetry, where the world model’s manifold discovery outpaces the policy's sparse-reward optimization. We propose **Mind Dreamer (MD)**, a framework that operationalizes **Active Counterfactual Reasoning (ACR)** to transcend Markovian continuity. MD reformulates discovery as the minimization of a global Relay Manifold Expected Free Energy (R-EFE); by invoking a latent-space $do$-operator, MD utilizes an adversarial generator to synthesize non-continuous **latent jumps** to epistemic blind spots that are physically plausible yet cognitively challenging. To resolve the credit assignment paradox across these spatial ruptures, we derive the **Relay Value Function (RVF)** and **Relay Uncertainty Function (RUF)**. These potentials treat synthesized anchors as latent bridges, propagating pragmatic and epistemic value through a principled Bellman-style formulation. Notably, we prove that the Uncertainty propagation across discontinuities necessitates a quadratic discount $\gamma^2$, establishing a formal epistemic horizon. Theoretically, MD acts as an optimal importance sampler that expands the manifold's spectral gap, reducing the hitting time to critical bottleneck states. Empirically, MD achieves a **1.67$\times$ average speedup** over DreamerV3 on DeepMind Control Suite, reaching **8.8$\times$** in sparse-reward tasks.

General Machine Learning · Representation Learning

Daniil Karzanov, Marcin Detyniecki

Deep neural networks for image classification often exhibit overconfidence on out-of-distribution (OOD) samples. To address this, we introduce Geometrically Constrained Outlier Synthesis (GCOS), a training-time regularization framework aimed at improving OOD robustness during inference. GCOS addresses a limitation of prior synthesis methods by generating virtual outliers in the hidden feature space that respect the learned manifold structure of in-distribution (ID) data. The synthesis proceeds in two stages: (i) a dominant-variance subspace extracted from the training features identifies geometrically informed, off-manifold directions; (ii) a conformally-inspired shell, defined by the empirical quantiles of a nonconformity score from a calibration set, adaptively controls the synthesis magnitude to produce boundary samples. The shell ensures that generated outliers are neither trivially detectable nor indistinguishable from in-distribution data, facilitating smoother learning of robust features. This is combined with a contrastive regularization objective that promotes separability of ID and OOD samples in a chosen score space, such as Mahalanobis or energy-based. Experiments demonstrate that GCOS outperforms state-of-the-art methods using standard energy-based inference on near-OOD benchmarks, defined as tasks where outliers share the same semantic domain as in-distribution data. As an exploratory extension, the framework naturally transitions to conformal OOD inference, which translates uncertainty scores into statistically valid p-values and enables thresholds with formal error guarantees, providing a pathway toward more predictable and reliable OOD detection.

General Machine Learning · Sequential, Network, and Time Series Modeling

SATOSHI NOGUCHI, Yoshinobu Kawahara

We present Mesh Field Theory (MeshFT) and its neural realization, MeshFT-Net: a structure-preserving framework for mesh-based continuum physics that cleanly separates the physics’ topological structure from its metric structure. Imposing minimal physical principles (locality, permutation equivariance, orientation covariance, and energy balance/dissipation inequality), we prove a reduction theorem for mesh-based physics. Under these conditions, the physical dynamics admit a local factorization into a port–Hamiltonian form: the conservative interconnection is fixed uniquely by mesh topology, whereas metric effects enter only through constitutive relations and dissipation. This reduction clarifies what must be fixed and what should be learned, directly informing MeshFT-Net’s design. Across evaluations on analytic and realistic datasets, physics-consistency tests, and out-of-distribution validation, MeshFT-Net achieves near-zero energy drift and strong physical fidelity (correct dispersion and momentum conservation) along with robust extrapolation and high data efficiency. By eliminating non-physical degrees of freedom and learning only metric-dependent structure, MeshFT provides a principled inductive bias for stable, faithful, and data-efficient learning-based physical simulation.

Deep Learning · Graph Neural Networks

Lianze Shan, Ningchong Wang, Jitao Zhao, Di Jin, Dongxiao He

Graph Contrastive Learning (GCL), which trains graph encoders by maximizing similarity between positive samples and minimizing it between negative ones, has emerged as a mainstream graph pre-training paradigm. It is widely recognized that positive samples are essential in GCLs. Ideally, maximizing the similarity of positive samples enables graph encoders to capture intrinsic semantic and patterns of graph data. However, we discover an interesting phenomenon: GCLs can achieve competitive performance even without positive samples. This motivates us to revisit the fundamental mechanism of positive samples in GCLs. From the perspective of Dirichlet energy, we theoretically finds that message passing, a key mechanism in graph encoders, trivializes the maximization of positive samples, preventing GCLs from effectively learning from positive samples. To address this, we propose SPGCL to mitigate the trivialization caused by message passing and restore the learning efficacy of positive samples. Specifically, we find that high Dirichlet energy features help positive samples provide effective learning signals while low Dirichlet energy features contribute little to positive learning signal but is useful for positive sampling. Based on this, SPGCL propagates only high Dirichlet energy features and uses low energy features to construct a probability matrix for reliable positive sampling. Extensive experiments demonstrate the effectiveness of SPGCL.

Deep Learning · Generative Models and Autoencoders

RuiKang OuYang, Louis Grenioux, Jose Miguel Hernandez-Lobato

Score-based generative models have recently achieved remarkable success. While they are usually parameterized by the score, an alternative way is to use a series of time-dependent energy-based models (EBMs), where the score is obtained from the negative input-gradient of the energy. Crucially, EBMs can be leveraged not only for generation, but also for tasks such as compositional sampling or building Boltzmann Generators via Monte Carlo methods. However, training EBMs remains challenging. Direct maximum likelihood is computationally prohibitive due to the need for nested sampling, while score matching, though efficient, suffers from mode blindness. To address these issues, we introduce the Diffusive Classification (DiffCLF) objective, a simple method that avoids blindness while remaining computationally efficient. DiffCLF reframes EBM learning as a supervised classification problem across noise levels, and can be seamlessly combined with standard score-based objectives. We validate the effectiveness of DiffCLF by comparing the estimated energies against ground truth in analytical Gaussian mixture cases, and by applying the trained models to tasks such as model composition and Boltzmann Generator sampling. Our results show that DiffCLF enables EBMs with higher fidelity and broader applicability than existing approaches.

Applications · Chemistry, Physics, and Earth Sciences

Massimo Solinas, Agnes Valenti, Nawaf Bou-Rabee, Roeland Wiersema

Scientific computing has long relied on double precision (64-bit floating point) arithmetic to guarantee accuracy in simulations of real-world phenomena. However, the growing availability of hardware accelerators such as Graphics Processing Units (GPUs) has made low-precision formats attractive due to their superior performance, reduced memory footprint, and improved energy efficiency. In this work, we investigate the role of mixed-precision arithmetic in neural-network based Variational Monte Carlo (VMC), a widely used method for solving computationally otherwise intractable quantum many-body systems. We first derive general analytical bounds on the error introduced by reduced precision on Metropolis-Hastings MCMC, and then empirically validate these bounds on the use-case of VMC. We demonstrate that significant portions of the algorithm, in particular, sampling the quantum state, can be executed in half precision without loss of accuracy. More broadly, this work provides a theoretical framework to assess the applicability of mixed-precision arithmetic in machine-learning approaches that rely on MCMC sampling. In the context of VMC, we additionally demonstrate the practical effectiveness of mixed-precision strategies, enabling more scalable and energy-efficient simulations of quantum many-body systems.

Applications · Time Series

Liu Chong, Yingjie Zhou, Hao Li, Pengyang Wang, Qingsong Wen, Ce Zhu

Time-series forecasting is critical in various scenarios, such as energy, transportation, and public health. However, most existing forecasters rely primarily on one-way inference, \textit{i.e.}, mapping \textbf{history} to \textbf{target}, and overlook the structural information provided by a revised natural chain (``\textbf{history} (model input) -- \textbf{target} (ground-truth output) -- \textbf{post-target continuation}''). The post-target continuation records how trajectories evolve after the target, which can help stabilize forecasting, but it is not observable at inference time. In this work, we aim to obtain an approximate proxy of the post-target continuation for the current input, providing structural knowledge for bidirectional forecasting. This idea is instantiated as KUP-BI (Knowledge Utilization Paradigm with Bidirectional Inspiration), a new time-series modeling paradigm that distills continuation-style knowledge (as an approximate post-target continuation proxy) from a \emph{train-only} historical library and integrates it into standard forecasting backbones. The input stream and the continuation-proxy stream are fused via a lightweight feature-level gating module. This design does not introduce information beyond what is already contained in the training trajectories; instead, it provides a structured inductive bias that helps backbones exploit typical continuation patterns rather than relying solely on parametric extrapolation. Experimental results on six public datasets show that KUP-BI consistently improves the forecasting performance of state-of-the-art models, with small additional overhead.

Optimization · Convex

Aikaterini Karoni, Rajit Rajpal, Benedict Leimkuhler, Gabriel Stoltz

Momentum Stochastic Gradient Descent (mSGD) relies on a fixed momentum coefficient shared across all parameters, failing to account for the heterogeneous structure of modern loss landscapes. In this work, we adopt a continuous-time formulation to introduce individual, adaptive momentum coefficients regulated by the kinetic energy of each model parameter. This mechanism automatically adjusts to local curvature to maintain stability without sacrificing convergence speed. We demonstrate that this adaptive friction is inextricably linked to cubic damping, a suppression mechanism from structural dynamics. We additionally introduce two optimization schemes by augmenting the continuous dynamics of mSGD and Adam with a cubic damping term. Empirically, our methods demonstrate robustness and match or outperform Adam on training ViT, BERT, and GPT2; tasks where mSGD typically struggles. We further provide theoretical results establishing the exponential convergence of the proposed schemes.

Probabilistic Methods · Monte Carlo and Sampling Methods

Emanuel Sommer, Kangning Diao, Jakob Robnik, Uros Seljak, David Rügamer

Scaling inference methods such as Markov chain Monte Carlo to high-dimensional models remains a central challenge in Bayesian deep learning. A promising recent proposal, microcanonical Langevin Monte Carlo, has shown state-of-the-art performance across a wide range of problems. However, its reliance on full-dataset gradients makes it prohibitively expensive for large-scale problems. This paper addresses a fundamental question: Can microcanonical dynamics effectively leverage mini-batch gradient noise? We provide the first systematic study of this problem, establishing a novel continuous-time theoretical analysis of stochastic-gradient microcanonical dynamics. We reveal two critical failure modes: a theoretically derived bias due to anisotropic gradient noise and numerical instabilities in complex high-dimensional posteriors. To tackle these issues, we propose a principled gradient noise preconditioning scheme shown to significantly reduce this bias and develop a novel, energy-variance-based adaptive tuner that automates step size selection and dynamically informs numerical guardrails. The resulting algorithm is a robust and scalable microcanonical Monte Carlo sampler that achieves state-of-the-art performance on challenging high-dimensional inference tasks like Bayesian neural networks. Combined with recent ensemble techniques, our work unlocks a new class of stochastic microcanonical Langevin ensemble (SMILE) samplers for large-scale Bayesian inference.

Deep Learning · Robustness

Bum Jun Kim, Makoto Kawano, Yusuke Iwasawa, Yutaka Matsuo

While the robustness of vision models is often measured, their dependence on specific architectural design choices is rarely dissected. We investigate why certain vision architectures are inherently more robust to additive Gaussian noise and convert these empirical insights into simple, actionable design rules. Specifically, we performed extensive evaluations on 1,174 pretrained vision models, empirically identifying four consistent design patterns for improved robustness against Gaussian noise: larger stem kernels, smaller input resolutions, average pooling, and supervised vision transformers (ViTs) rather than CLIP ViTs, which yield up to 506 rank improvements and 21.6%p accuracy gains. We then develop a theoretical analysis that explains these findings, converting observed correlations into causal mechanisms. First, we prove that low-pass stem kernels attenuate noise with a gain that decreases quadratically with kernel size and that anti-aliased downsampling reduces noise energy roughly in proportion to the square of the downsampling factor. Second, we demonstrate that average pooling is unbiased and suppresses noise in proportion to the pooling window area, whereas max pooling incurs a positive bias that grows slowly with window size and yields a relatively higher mean-squared error and greater worst-case sensitivity. Third, we reveal and explain the vulnerability of CLIP ViTs via a pixel-space Lipschitz bound: The smaller normalization standard deviations used in CLIP preprocessing amplify worst-case sensitivity by up to 1.91 times relative to the Inception-style preprocessing common in supervised ViTs. Our results collectively disentangle robustness into interpretable modules, provide a theory that explains the observed trends, and build practical, plug-and-play guidelines for designing vision models more robust against Gaussian noise.

Deep Learning · Algorithms

Huiyuan Tian, Bonan Xu, Shijian Li

Feature-map knowledge distillation (KD) transfers internal representations well between comparably sized Vision Transformers (ViTs), but it often fails in compression. We revisit this failure and uncover a paradox. Sample-wise SVD shows that each image is highly compressible, which seems to suggest that a narrow student with a linear projector should match the teacher "in principle". However, a dataset-level view contradicts this intuition: PCA shows that the teacher is a union of low-rank subspaces with significant subspace rotation across inputs. We further introduce token-level Spectral Energy Patterns (SEP) and find an architecture-invariant encoding law: tokens spread energy broadly across channel modes even when they live in low-rank subspace, creating a bandwidth mismatch. We refer to this combined phenomenon as an encoding mismatch. We propose two minimal remedies, Lift or WideLast: (i) Lift retains a lightweight lifting projector at inference to provide wider channel, or (ii) WideLast widens only the student’s last block, enabling an input-dependent expansion. On ImageNet-1K, these fixes revive feature KD for ViT compression, improving DeiT-Tiny distilled from CaiT-S24 from 74.86% to 77.53%/78.23% top-1 accuracy, and they also strengthen students trained without distillation. Our analyses clarify when and why feature-map KD fails and then how to fix it. Code and raw data are provided in the supplementary materials.

Applications · Chemistry, Physics, and Earth Sciences

Henrik Schopmans, Christopher von Klitzing, Pascal Friederich

Sampling from unnormalized probability densities is a central challenge in computational science. Boltzmann generators are generative models that enable independent sampling from the Boltzmann distribution of physical systems at a given temperature. However, their practical success depends on data-efficient training, as both simulation data and target energy evaluations are costly. To this end, we propose off-policy log-dispersion regularization (LDR), a novel regularization framework that builds on a generalization of the log-variance objective. We apply LDR in the off-policy setting in combination with standard data-based training objectives, without requiring additional on-policy samples. LDR acts as a shape regularizer of the energy landscape by leveraging additional information in the form of target energy labels. The proposed regularization framework is broadly applicable, supporting unbiased or biased simulation datasets as well as purely variational training without access to target samples. Across all benchmarks, LDR improves both final performance and data efficiency, with sample efficiency gains of up to one order of magnitude.

Deep Learning · Everything Else

Xuandi Luo, Huaidong Zhang, Yi Xie, Shengfeng He

Continual learning seeks to develop models capable of acquiring new tasks sequentially while retaining prior knowledge. A central challenge in this setting is managing inherent knowledge conflicts that arise as overlapping or contradictory information is introduced across tasks. While parameter-efficient fine-tuning (PEFT) techniques, particularly those based on Low-Rank Adaptation (LoRA), have shown promise by reducing interference through parameter isolation or modular architectures, they often treat conflict as something to avoid rather than address directly. In this work, we propose $\underline{S}$ubspace-$\underline{A}$ligned $\underline{B}$alanc$\underline{e}$d $\underline{R}$ecomposition (SABER), a novel method that reframes continual learning as a problem of structured conflict management. SABER introduces a unified subspace alignment framework to support shared task representations, decomposes task-specific knowledge into orthogonal components to preserve distinct information, and recomposes them using an energy-aware balancing mechanism that coordinates contributions without compromising stability. Extensive experiments across multiple continual learning benchmarks show that SABER achieves performance on par with or surpassing state-of-the-art methods, offering a principled approach that directly addresses the root cause of forgetting by managing representational conflict.

Deep Learning · Generative Models and Autoencoders

Sunghyun Kim, Jaehoon Hahm, Jeongwoo Shin, Joonseok Lee

Geometry-aware generative models and novel view synthesis approaches have shown strong potential in visual fidelity and consistency. In parallel, equivariant representation learning has emerged as a powerful framework for constructing latent spaces where analytically known group transformations could act directly, capturing geometric structure in data and enhancing both interpretability and generalization in novel view synthesis. However, we identify that existing approaches often suffer from \textit{latent misalignment}, a discrepancy between the intended group action and the actually required transformations in the latent space. Consequently, the learned latents often fail to consistently preserve the equivariant relations imposed by the underlying group symmetry. To address this, we propose \emph{Residual Latent Flow}, a flow-based framework that corrects the misaligned latents, thereby improving compliance with the underlying equivariance relation. Our comprehensive experiments show that our method significantly reduces latent misalignment and improves novel view synthesis quality, under rotation groups $\mathrm{SO}(n)$.

Optimization · Discrete and Combinatorial Optimization

Yang Huang, Yifan Zhang, Jian Cheng

We propose an OT-guided sampling framework for solving graph combinatorial optimization through exact multilinear relaxation. Graph combinatorial optimization problems can be written as quadratic unconstrained binary optimization(QUBO). Leveraging a classical result in combinatorial optimization, we obtain a continuous multi-linear relaxation of QUBO that is exact, in the sense that it preserves the optimal binary solutions. The challenge is that the resulting energy landscape is highly nonconvex. We address this by treating the objective as an energy function and optimizing via sampling from the induced Boltzmann distribution to escape poor local optima. Viewing sampling as transporting a simple reference distribution to the target distribution, we use optimal transport to characterize more efficient probability flow and derive a stochastic optimal control problem whose solution yields an optimal sampling dynamics. We parameterize the control policy with graph neural networks to approximate the optimal control. Experiments show improved solution quality and efficiency over strong combinatorial and learning-based baselines.

Social Aspects · Accountability, Transparency, and Interpretability

Manjiang Yu, Hongji Li, Junwei Chen, Xue Li, Priyanka Singh, YANG CAO, Lijie Hu

Representation intervention has emerged as a promising paradigm for aligning large language models toward desired behaviors without modifying model weights. Existing methods typically apply a fixed intervention uniformly across all inputs. However, we find that the appropriate intervention direction and strength vary substantially across samples, and such indiscriminate intervention leads to degradation of general capabilities on benign inputs. To address these challenges, we propose Multi-Adapter Representation Interventions via Energy Calibration (MARI). Specifically, we introduce a competitive multi-adapter mechanism in which specialized experts capture non-linear correction patterns and adaptively determine the appropriate intervention direction and strength for different samples. Furthermore, we design an energy-based gating module that leverages internal propagation dynamics to distinguish inputs that are applicable for intervention. Extensive experiments across diverse model families and parameter scales demonstrate that MARI achieves state-of-the-art alignment performance. Our method significantly improves performance on TruthfulQA, BBQ, and safety benchmarks, while maintaining and even improving general capabilities on tasks such as MMLU and ARC. Our code will be released upon acceptance.

General Machine Learning · Causality

Yunfeng Wang, Zhiheng Zhang, Zijun Gao

Partial identification provides informative causal guarantees when point identification is impossible, but existing approaches based on optimal transport (OT) become computationally and statistically intractable in high-dimensional settings. This limitation is particularly severe when both potential outcomes and confounders are high-dimensional, where classical OT-based bounds suffer from the curse of dimensionality and unfavorable convergence rates. To address this challenge, we propose a novel estimator that decomposes the transport problem into a low-dimensional signal subspace and a high-dimensional residual subspace. Unlike existing projection-based methods that discard residual information, we recover the residual transport energy using the Sliced Wasserstein distance, which is computationally efficient and robust to high dimensions. We establish interpretable conditions controlling the approximation gap based on residual structure and provide a data-driven rule for signal dimension selection. Empirical results show that our estimator consistently outperforms projection-only baselines by recovering lost transport energy, yielding more informative causal bounds while remaining computationally tractable in high dimensions.