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Applications · Computer Vision

Pierrick Leroy, Antonio Mastropietro, Marco Nurisso, Francesco Vaccarino

Face Recognition (FR) tasks have made significant progress with the advent of Deep Neural Networks, particularly through margin-based triplet losses that embed facial images into high-dimensional feature spaces. During training, these contrastive losses focus exclusively on identity information as labels. However, we observe a multiscale geometric structure emerging in the embedding space, influenced by interpretable facial (e.g., hair color) and image attributes (e.g., contrast).We propose a geometric approach to describe the dependence or invariance of FR models to these attributes and introduce a physics-inspired alignment metric. We evaluate the proposed metric on controlled, simplified models and widely used FR models fine-tuned with synthetic data for targeted attribute augmentation. Our findings reveal that the models exhibit varying degrees of invariance across different attributes, providing insight into their strengths and weaknesses and enabling deeper interpretability.Code available here: https://github.com/mantonios107/attrs-fr-embs.

Deep Learning

Shiba Biswal, Karthik Elamvazhuthi, Rishi Sonthalia

This paper investigates the use of transformers to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in modeling phenomena across physics, biology, and engineering, including opinion formation, biological networks, and swarm robotics. The key characteristic of these systems is that the particles are indistinguishable, leading to permutation-equivariant dynamics. First, we empirically demonstrate that transformers are well-suited for approximating a variety of mean field models, including the Cucker-Smale model for flocking and milling, and the mean-field system for training two-layer neural networks. We validate our numerical experiments via mathematical theory. Specifically, we prove that if a finite-dimensional transformer effectively approximates the finite-dimensional vector field governing the particle system, then the $L_\infty$ distance between the \textit{expected transformer} and the infinite-dimensional mean-field vector field can be bounded by a function of the number of particles observed during training. Leveraging this result, we establish theoretical bounds on the distance between the true mean-field dynamics and those obtained using the transformer.

Applications · Chemistry, Physics, and Earth Sciences

Philipp Höllmer, Thomas Egg, Maya Martirossyan, Eric Fuemmeler, Zeren Shui, Amit Gupta, Pawan Prakash, Adrian Roitberg, Mingjie Liu, George Karypis 等

The discovery of new materials is essential for enabling technological advancements. Computational approaches for predicting novel materials must effectively learn the manifold of stable crystal structures within an infinite design space. We introduce Open Materials Generation (OMatG), a unifying framework for the generative design and discovery of inorganic crystalline materials. OMatG employs stochastic interpolants (SI) to bridge an arbitrary base distribution to the target distribution of inorganic crystals via a broad class of tunable stochastic processes, encompassing both diffusion models and flow matching as special cases. In this work, we adapt the SI framework by integrating an equivariant graph representation of crystal structures and extending it to account for periodic boundary conditions in unit cell representations. Additionally, we couple the SI flow over spatial coordinates and lattice vectors with discrete flow matching for atomic species. We benchmark OMatG's performance on two tasks: Crystal Structure Prediction (CSP) for specified compositions, and de novo generation (DNG) aimed at discovering stable, novel, and unique structures. In our ground-up implementation of OMatG, we refine and extend both CSP and DNG metrics compared to previous works. OMatG establishes a new state of the art in generative modeling for materials discovery, outperforming purely flow-based and diffusion-based implementations. These results underscore the importance of designing flexible deep learning frameworks to accelerate progress in materials science. The OMatG code is available at https://github.com/FERMat-ML/OMatG.

Deep Learning · Graph Neural Networks

Zongzhao Li, Jiacheng Cen, Bing Su, Tingyang Xu, Yu Rong, Deli Zhao, Wenbing Huang

Accurately predicting 3D structures and dynamics of physical systems is crucial in scientific applications. Existing approaches that rely on geometric Graph Neural Networks (GNNs) effectively enforce $\mathrm{E}(3)$-equivariance, but they often fail in leveraging extensive broader information. While direct application of Large Language Models (LLMs) can incorporate external knowledge, they lack the capability for spatial reasoning with guaranteed equivariance. In this paper, we propose EquiLLM, a novel framework for representing 3D physical systems that seamlessly integrates $\mathrm{E}(3)$-equivariance with LLM capabilities. Specifically, EquiLLM comprises four key components: geometry-aware prompting, an equivariant encoder, an LLM, and an equivariant adapter. Essentially, the LLM guided by the instructive prompt serves as a sophisticated invariant feature processor, while 3D directional information is exclusively handled by the equivariant encoder and adapter modules. Experimental results demonstrate that EquiLLM delivers significant improvements over previous methods across molecular dynamics simulation, human motion simulation, and antibody design, highlighting its promising generalizability.

Applications · Chemistry, Physics, and Earth Sciences

Prateek Gupta, Andrea Ferrari, Nabil Iqbal

The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction of a dual Hamiltonian and a map from the original to the dual observables. By using neural networks to parameterize these maps and introducing a loss function that penalises the difference between correlation functions in original and dual models, we formulate the process of duality discovery as an optimization problem. We numerically solve this problem and show that our framework can rediscover the celebrated Kramers-Wannier duality for the 2d Ising model, numerically reconstructing the known mapping of temperatures. We further investigate the 2d Ising model deformed by a plaquette coupling and find families of ``approximate duals''. We discuss future directions and prospects for discovering new dualities within this framework.

Deep Learning · Sequential Models, Time series

Weiwei Ye, Zhuopeng Xu, Ning Gui

Due to the dynamics of underlying physics and external influences, the uncertainty of time series often varies over time. However, existing Denoising Diffusion Probabilistic Models (DDPMs) often fail to capture this non-stationary nature, constrained by their constant variance assumption from the additive noise model (ANM). In this paper, we innovatively utilize the Location-Scale Noise Model (LSNM) to relax the fixed uncertainty assumption of ANM. A diffusion-based probabilistic forecasting framework, termed Non-stationary Diffusion (NsDiff), is designed based on LSNM that is capable of modeling the changing pattern of uncertainty. Specifically, NsDiff combines a denoising diffusion-based conditional generative model with a pre-trained conditional mean and variance estimator, enabling adaptive endpoint distribution modeling. Furthermore, we propose an uncertainty-aware noise schedule, which dynamically adjusts the noise levels to accurately reflect the data uncertainty at each step and integrates the time-varying variances into the diffusion process. Extensive experiments conducted on nine real-world and synthetic datasets demonstrate the superior performance of NsDiff compared to existing approaches. Code is available at https://github.com/wwy155/NsDiff.

Reinforcement Learning · Deep RL

Brett Barkley, David Fridovich-Keil

Dyna-style off-policy model-based reinforcement learning (DMBRL) algorithms are a family of techniques for generating synthetic state transition data and thereby enhancing the sample efficiency of off-policy RL algorithms. This paper identifies and investigates a surprising performance gap observed when applying DMBRL algorithms across different benchmark environments with proprioceptive observations. We show that, while DMBRL algorithms perform well in control tasks in OpenAI Gym, their performance can drop significantly in DeepMind Control Suite (DMC), even though these settings offer similar tasks and identical physics backends. Modern techniques designed to address several key issues that arise in these settings do not provide a consistent improvement across all environments, and overall our results show that adding synthetic rollouts to the training process --- the backbone of Dyna-style algorithms --- significantly degrades performance across most DMC environments. Our findings contribute to a deeper understanding of several fundamental challenges in model-based RL and show that, like many optimization fields, there is no free lunch when evaluating performance across diverse benchmarks in RL.

Applications · Chemistry, Physics, and Earth Sciences

Shuqi Lu, Xiaohong Ji, Bohang Zhang, Lin Yao, Siyuan Liu, Zhifeng Gao, Linfeng Zhang, Guolin Ke

Molecular pretrained representations (MPR) has emerged as a powerful approach for addressing the challenge of limited supervised data in applications such as drug discovery and material design. While early MPR methods relied on 1D sequences and 2D graphs, recent advancements have incorporated 3D conformational information to capture rich atomic interactions. However, these prior models treat molecules merely as discrete atom sets, overlooking the space surrounding them. We argue from a physical perspective that only modeling these discrete points is insufficient. We first present a simple yet insightful observation: naively adding randomly sampled virtual points beyond atoms can surprisingly enhance MPR performance. In light of this, we propose a principled framework that incorporates the entire 3D space spanned by molecules. We implement the framework via a novel Transformer-based architecture, dubbed SpaceFormer, with three key components:(1)grid-based space discretization; (2)grid sampling/merging; and (3)efficient 3D positional encoding.Extensive experiments show that SpaceFormer significantly outperforms previous 3D MPR models across various downstream tasks with limited data, validating the benefit of leveraging the additional 3D space beyond atoms in MPR models.

Applications · Chemistry, Physics, and Earth Sciences

Tianyu Chen, Haoyi Zhou, Ying Li, Hao Wang, Chonghan Gao, Rongye Shi, Shanghang Zhang, Jianxin Li

Foundation models have revolutionized language modeling, while whether this success is replicated in scientific computing remains unexplored. We present OmniArch, the first prototype aiming at solving multi-scale and multi-physics scientific computing problems with physical alignment. We addressed all three challenges with one unified architecture. Its pre-training stage contains a Fourier Encoder-decoder fading out the disharmony across separated dimensions and a Transformer backbone integrating quantities through temporal dynamics, and the novel PDE-Aligner performs physics-informed fine-tuning under flexible conditions. As far as we know, we first conduct 1D-2D-3D united pre-training on the PDEBench, and it sets not only new performance benchmarks for 1D, 2D, and 3D PDEs but also demonstrates exceptional adaptability to new physics via in-context and zero-shot learning approaches, which supports realistic engineering applications and foresight physics discovery.

Applications · Chemistry, Physics, and Earth Sciences

Zhang Jiasheng, Delvin Zhang, Shuang Liang, Zhengpin Li, ZHITAO YING, Jie Shao

Protein language models often struggle to capture biological functions due to their lack of factual knowledge (e.g., gene descriptions). Existing solutions leverage protein knowledge graphs (PKGs) as auxiliary pre-training objectives, but lack explicit integration of task-oriented knowledge, making them suffer from limited knowledge exploitation and catastrophic forgetting. The root cause is that they fail to align PKGs with task-specific data, forcing their knowledge modeling to adapt to the knowledge-isolated nature of downstream tasks. In this paper, we propose Knowledge-aware retrieval augmented protein language model (Kara), achieving the first task-oriented and explicit integration of PKGs and protein language models. With a knowledge retriever learning to predict linkages between PKG and task proteins, Kara unifies the knowledge integration of the pre-training and fine-tuning stages with a structure-based regularization, mitigating catastrophic forgetting. To ensure task-oriented integration, Kara uses contextualized virtual tokens to extract graph context as task-specific knowledge for new proteins. Experiments show that Kara outperforms existing knowledge-enhanced models in 6 representative tasks, achieving on average 5.1% improvements.

Applications · Chemistry, Physics, and Earth Sciences

Parshin Shojaee, Ngoc Hieu Nguyen, Kazem Meidani, Amir Barati Farimani, Khoa Doan, Chandan Reddy

Scientific equation discovery is a fundamental task in the history of scientific progress, enabling the derivation of laws governing natural phenomena. Recently, Large Language Models (LLMs) have gained interest for this task due to their potential to leverage embedded scientific knowledge for hypothesis generation. However, evaluating the true discovery capabilities of these methods remains challenging, as existing benchmarks often rely on common equations that are susceptible to memorization by LLMs, leading to inflated performance metrics that do not reflect actual discovery. In this paper, we introduce LLM-SRBench, a comprehensive benchmark with 239 challenging problems across four scientific domains specifically designed to evaluate LLM-based scientific equation discovery methods while preventing trivial memorization. Our benchmark comprises two main categories: LSR-Transform, which transforms common physical models into less common mathematical representations to test reasoning beyond memorization, and LSR-Synth, which introduces synthetic, discovery-driven problems requiring data-driven reasoning. Through extensive evaluation of several state-of-the-art methods on LLM-SRBench, using both open and closed LLMs, we find that the best-performing system so far achieves only 31.5% symbolic accuracy.These findings highlight the challenges of scientific equation discovery, positioning LLM-SRBench as a valuable resource for future research.

Applications · Computer Vision

Chenyu Li, Oscar Michel, Xichen Pan, Sainan Liu, Mike Roberts, Saining Xie

Large-scale pre-trained video generation models excel in content creation but are not reliable as physically accurate world simulators out of the box. This work studies the process of post-training these models for accurate world modeling through the lens of the simple, yet fundamental, physics task of modeling object freefall. We show state-of-the-art video generation models struggle with this basic task, despite their visually impressive outputs. To remedy this problem, we find that fine-tuning on a relatively small amount of simulated videos is effective in inducing the dropping behavior in the model, and we can further improve results through a novel reward modeling procedure we introduce. Our study also reveals key limitations of post-training in generalization and distribution modeling. Additionally, we release a benchmark for this task that may serve as a useful diagnostic tool for tracking physical accuracy in large-scale video generative model development. Code is available at this repository: https://github.com/vision-x-nyu/pisa-experiments.

Applications · Chemistry, Physics, and Earth Sciences

Dapeng Jiang, Xiangzhe Kong, Jiaqi Han, Mingyu Li, Rui Jiao, Wenbing Huang, Stefano Ermon, Jianzhu Ma, Yang Liu

Cyclic peptides, characterized by geometric constraints absent in linear peptides, offer enhanced biochemical properties, presenting new opportunities to address unmet medical needs. However, designing target-specific cyclic peptides remains underexplored due to limited training data. To bridge the gap, we propose CP-Composer, a novel generative framework that enables zero-shot cyclic peptide generation via composable geometric constraints. Our approach decomposes complex cyclization patterns into unit constraints, which are incorporated into a diffusion model through geometric conditioning on nodes and edges. During training, the model learns from unit constraints and their random combinations in linear peptides, while at inference, novel constraint combinations required for cyclization are imposed as input. Experiments show that our model, despite trained with linear peptides, is capable of generating diverse target-binding cyclic peptides, reaching success rates from 38\% to 84\% on different cyclization strategies.

Applications · Health / Medicine

Dayang Wang, Srivathsa Pasumarthi Venkata, Ajit Shankaranarayanan, Greg Zaharchuk

Contrast-enhanced MRI enhances pathological visualization but often necessitates Pre-Contrast images for accurate quantitative analysis and comparative assessment. However, Pre-Contrast images are frequently unavailable due to time, cost, or safety constraints, or they may suffer from degradation, making alignment challenging. This limitation hinders clinical diagnostics and the performance of tools requiring combined image types. To address this challenge, we propose a novel staged, physics-grounded learning framework with a hyperintensity prior to synthesize Pre-Contrast images directly from Post-Contrast MRIs. The proposed method can generate high-quality Pre-Contrast images, thus, enabling comprehensive diagnostics while reducing the need for additional imaging sessions, costs, and patient risks. To the best of our knowledge, this is the first Pre-Contrast synthesis model capable of generating images that may be interchangeably used with standard-of-care Pre-Contrast images. Extensive evaluations across multiple datasets, sites, anatomies, and downstream tasks demonstrate the model’s robustness and clinical applicability, positioning it as a valuable tool for contrast-enhanced MRI workflows.

Applications · Chemistry, Physics, and Earth Sciences

Manwen Liao, Yan Zhu, Weitian Zhang, Yuxiang Yang

Characterizing quantum states is essential for advancing many quantum technologies. Recently, deep neural networks have been applied to learn quantum states by generating compressed implicit representations. Despite their success in predicting properties of the states, these representations remain a black box, lacking insights into strategies for experimental reconstruction. In this work, we aim to open this black box by developing explicit representations through generating surrogate state preparation circuits for property estimation. We design a reinforcement learning agent equipped with a Transformer-based architecture and a local fidelity reward function. Relying solely on measurement data from a few neighboring qubits, our agent accurately recovers properties of target states. We also theoretically analyze the global fidelity the agent can achieve when it learns a good local approximation. Extensive experiments demonstrate the effectiveness of our framework in learning various states of up to 100 qubits, including those generated by shallow Instantaneous Quantum Polynomial circuits, evolved by Ising Hamiltonians, and many-body ground states. Furthermore, the learned circuit representations can be applied to Hamiltonian learning as a downstream task utilizing a simple linear model.

Applications · Chemistry, Physics, and Earth Sciences

In Huh, Changwook Jeong, Muhammad Alam

Out-Of-Domain (OOD) generalization is a significant challenge in learning dynamical systems, especially when they exhibit bifurcation, a sudden topological transition triggered by a model parameter crossing a critical threshold. A prevailing belief is that machine learning models, unless equipped with strong priors, struggle to generalize across bifurcations due to the abrupt changes in data characteristics. Contrary to this belief, we demonstrate that context-dependent Neural Ordinary Differential Equations (NODEs), trained solely on localized, pre-bifurcation, symmetric data and without physics-based priors, can still identify post-bifurcation, symmetry-breaking behaviors, even in a zero-shot manner. We interpret this capability to the model's implicit utilization of topological invariants, particularly the Poincaré index, and offer a formal explanation based on the Poincaré–Hopf theorem. We derive the conditions under which NODEs can recover—or erroneously hallucinate—broken symmetries without explicit training. Building on this insight, we showcase a topological regularizer inspired by the Poincaré–Hopf theorem and validate it empirically on phase transitions of systems described by the Landau–Khalatnikov equation.

Deep Learning · Foundation Models

Bingyi Kang, Yang Yue, Rui Lu, Zhijie Lin, Yang Zhao, Kaixin Wang, Gao Huang, Jiashi Feng

Scaling video generation models is believed to be promising in building world models that adhere to fundamental physical laws. However, whether these models can discover physical laws purely from vision can be questioned. A world model learning the true law should give predictions robust to nuances and correctly extrapolate on unseen scenarios.In this work, we evaluate across three key scenarios: in-distribution, out-of-distribution, and combinatorial generalization.We developed a 2D simulation testbed for object movement and collisions to generate videos deterministically governed by one or more classical mechanics laws.We focus on the scaling behavior of trainingdiffusion-based video generation models to predict object movements based on initial frames.Our scaling experiments show perfect generalization within the distribution, measurable scaling behavior for combinatorial generalization, but failure in out-of-distribution scenarios.Further experiments reveal two key insights about the generalization mechanisms of these models: (1) the models fail to abstract general physical rules and instead exhibit "case-based" generalization behavior, i.e., mimicking the closest training example; (2) when generalizing to new cases, models are observed to prioritize different factors when referencing training data: color $>$ size $>$ velocity $>$ shape.Our study suggests that scaling alone is insufficient for video generation models to uncover fundamental physical laws.

Applications · Chemistry, Physics, and Earth Sciences

Ning Liu, Yue Yu

Attention mechanisms have emerged as transformative tools in core AI domains such as natural language processing and computer vision. Yet, their largely untapped potential for modeling intricate physical systems presents a compelling frontier. Learning such systems often entails discovering operators that map between functional spaces using limited instances of function pairs---a task commonly framed as a severely ill-posed inverse PDE problem. In this work, we introduce Neural Interpretable PDEs (NIPS), a novel neural operator architecture that builds upon and enhances Nonlocal Attention Operators (NAO) in both predictive accuracy and computational efficiency. NIPS employs a linear attention mechanism to enable scalable learning and integrates a learnable kernel network that acts as a channel-independent convolution in Fourier space. As a consequence, NIPS eliminates the need to explicitly compute and store large pairwise interactions, effectively amortizing the cost of handling spatial interactions into the Fourier transform. Empirical evaluations demonstrate that NIPS consistently surpasses NAO and other baselines across diverse benchmarks, heralding a substantial leap in scalable, interpretable, and efficient physics learning. Our code and data accompanying this paper are available at https://github.com/fishmoon1234/Nonlocal-Attention-Operator.

Applications · Chemistry, Physics, and Earth Sciences

Ibrahim Fayad, Max Zimmer, Martin Schwartz, Fabian Gieseke, Philippe CIAIS, Gabriel Belouze, Sarah Brood, Aurélien de Truchis, Alexandre d'Aspremont

Significant efforts have been directed towards adapting self-supervised multimodal learning for Earth observation applications. However, most current methods produce coarse patch-sized embeddings, limiting their effectiveness and integration with other modalities like LiDAR. To close this gap, we present DUNIA, an approach to learn pixel-sized embeddings through cross-modal alignment between images and full-waveform LiDAR data. As the model is trained in a contrastive manner, the embeddings can be directly leveraged in the context of a variety of environmental monitoring tasks in a zero-shot setting. In our experiments, we demonstrate the effectiveness of the embeddings for seven such tasks: canopy height mapping, fractional canopy cover, land cover mapping, tree species identification, plant area index, crop type classification, and per-pixel waveform-based vertical structure mapping. The results show that the embeddings, along with zero-shot classifiers, often outperform specialized supervised models, even in low-data regimes. In the fine-tuning setting, we show strong performances near or better than the state-of-the-art on five out of six tasks.

Applications · Chemistry, Physics, and Earth Sciences

Michael Sun, Weize Yuan, Gang Liu, Wojciech Matusik, Jie Chen

Recent data-efficient molecular generation approaches exploit graph grammars to introduce interpretability into the generative models. However, grammar learning therein relies on expert annotation or unreliable heuristics for algorithmic inference. We propose Foundation Molecular Grammar (FMG), which leverages multi-modal foundation models (MMFMs) to induce an interpretable molecular language. By exploiting the chemical knowledge of an MMFM, FMG renders molecules as images, describes them as text, and aligns information across modalities using prompt learning. FMG can be used as a drop-in replacement for the prior grammar learning approaches in molecular generation and property prediction. We show that FMG not only excels in synthesizability, diversity, and data efficiency but also offers built-in chemical interpretability for automated molecular discovery workflows. Code is available at https://github.com/shiningsunnyday/induction.