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Physical Models

Mengyi Chen, Qianxiao Li

Macroscopic observables of a system are of keen interest in real applications such as the design of novel materials. Current methods rely on microscopic trajectory simulations, where the forces on all microscopic coordinates need to be computed or measured. However, this can be computationally prohibitive for realistic systems. In this paper, we propose a method to learn macroscopic dynamics requiring only force computations on a subset of the microscopic coordinates. Our method relies on a sparsity assumption: the force on each microscopic coordinate relies only on a small number of other coordinates. The main idea of our approach is to map the training procedure on the macroscopic coordinates back to the microscopic coordinates, on which partial force computations can be used as stochastic estimation to update model parameters. We provide a theoretical justification of this under suitable conditions. We demonstrate the accuracy, force computation efficiency, and robustness of our method on learning macroscopic closure models from a variety of microscopic systems, including those modeled by partial differential equations or molecular dynamics simulations.

Neuroscience, Cognitive Science

Shuangpeng Han, Ziyu Wang, Mengmi Zhang

Biological motion perception (BMP) refers to humans' ability to perceive and recognize the actions of living beings solely from their motion patterns, sometimes as minimal as those depicted on point-light displays. While humans excel at these tasks \textit{without any prior training}, current AI models struggle with poor generalization performance. To close this research gap, we propose the Motion Perceiver (MP). MP solely relies on patch-level optical flows from video clips as inputs. During training, it learns prototypical flow snapshots through a competitive binding mechanism and integrates invariant motion representations to predict action labels for the given video. During inference, we evaluate the generalization ability of all AI models and humans on 62,656 video stimuli spanning 24 BMP conditions using point-light displays in neuroscience. Remarkably, MP outperforms all existing AI models with a maximum improvement of 29\% in top-1 action recognition accuracy on these conditions. Moreover, we benchmark all AI models in point-light displays of two standard video datasets in computer vision. MP also demonstrates superior performance in these cases. More interestingly, via psychophysics experiments, we found that MP recognizes biological movements in a way that aligns with human behaviors. Our data and code are available at https://github.com/ZhangLab-DeepNeuroCogLab/MotionPerceiver.

Physical Models · Physics

Timothy Nest, Maxence Ernoult

Power efficiency is plateauing in the standard digital electronics realm such that new hardware, models, and algorithms are needed to reduce the costs of AI training. The combination of energy-based analog circuits and the Equilibrium Propagation (EP) algorithm constitutes a compelling alternative compute paradigm for gradient-based optimization of neural nets. Existing analog hardware accelerators, however, typically incorporate digital circuitry to sustain auxiliary non-weight-stationary operations, mitigate analog device imperfections, and leverage existing digital platforms. Such heterogeneous hardware lacks a supporting theoretical framework. In this work, we introduce \emph{Feedforward-tied Energy-based Models} (ff-EBMs), a hybrid model comprised of feedforward and energy-based blocks housed on digital and analog circuits. We derive a novel algorithm to compute gradients end-to-end in ff-EBMs by backpropagating and ``eq-propagating'' through feedforward and energy-based parts respectively, enabling EP to be applied flexibly on realistic architectures. We experimentally demonstrate the effectiveness of this approach on ff-EBMs using Deep Hopfield Networks (DHNs) as energy-based blocks, and show that a standard DHN can be arbitrarily split into any uniform size while maintaining or improving performance with increases in simulation speed of up to four times. We then train ff-EBMs on ImageNet32 where we establish a new state-of-the-art performance for the EP literature (46 top-1 \%). Our approach offers a principled, scalable, and incremental roadmap for the gradual integration of self-trainable analog computational primitives into existing digital accelerators.

Jianke Yang, Wang Rao, Nima Dehmamy, Robin Walters, Rose Yu

Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may search an unnecessarily large space and discover less accurate or overly complex equations. In this paper, we propose to leverage symmetry in automated equation discovery to compress the equation search space and improve the accuracy and simplicity of the learned equations. Specifically, we derive equivariance constraints from the time-independent symmetries of ODEs. Depending on the types of symmetries, we develop a pipeline for incorporating symmetry constraints into various equation discovery algorithms, including sparse regression and genetic programming. In experiments across diverse dynamical systems, our approach demonstrates better robustness against noise and recovers governing equations with significantly higher probability than baselines without symmetry.

Computer Vision

Linye Lyu, Jiawei Zhou, Daojing He, YU LI

Prior works on physical adversarial camouflage against vehicle detectors mainly focus on the effectiveness and robustness of the attack. The current most successful methods optimize 3D vehicle texture at a pixel level. However, this results in conspicuous and attention-grabbing patterns in the generated camouflage, which humans can easily identify. To address this issue, we propose a Customizable and Natural Camouflage Attack (CNCA) method by leveraging an off-the-shelf pre-trained diffusion model. By sampling the optimal texture image from the diffusion model with a user-specific text prompt, our method can generate natural and customizable adversarial camouflage while maintaining high attack performance. With extensive experiments on the digital and physical worlds and user studies, the results demonstrate that our proposed method can generate significantly more natural-looking camouflage than the state-of-the-art baselines while achieving competitive attack performance.

Physical Models

Michal Balcerak, Tamaz Amiranashvili, Andreas Wagner, Jonas Weidner, Petr Karnakov, Johannes C. Paetzold, Ivan Ezhov, Petros Koumoutsakos, Benedikt Wiestler, bjoern menze

Physical models in the form of partial differential equations serve as important priors for many under-constrained problems. One such application is tumor treatment planning, which relies on accurately estimating the spatial distribution of tumor cells within a patient’s anatomy. While medical imaging can detect the bulk of a tumor, it cannot capture the full extent of its spread, as low-concentration tumor cells often remain undetectable, particularly in glioblastoma, the most common primary brain tumor. Machine learning approaches struggle to estimate the complete tumor cell distribution due to a lack of appropriate training data. Consequently, most existing methods rely on physics-based simulations to generate anatomically and physiologically plausible estimations. However, these approaches face challenges with complex and unknown initial conditions and are constrained by overly rigid physical models. In this work, we introduce a novel method that integrates data-driven and physics-based cost functions, akin to Physics-Informed Neural Networks (PINNs). However, our approach parametrizes the solution directly on a dynamic discrete mesh, allowing for the effective modeling of complex biomechanical behaviors. Specifically, we propose a unique discretization scheme that quantifies how well the learned spatiotemporal distributions of tumor and brain tissues adhere to their respective growth and elasticity equations. This quantification acts as a regularization term, offering greater flexibility and improved integration of patient data compared to existing models. We demonstrate enhanced coverage of tumor recurrence areas using real-world data from a patient cohort, highlighting the potential of our method to improve model-driven treatment planning for glioblastoma in clinical practice.

ZAIXI ZHANG, Marinka Zitnik, Qi Liu

Designing ligand-binding proteins, such as enzymes and biosensors, is essential in bioengineering and protein biology. One critical step in this process involves designing protein pockets, the protein interface binding with the ligand. Current approaches to pocket generation often suffer from time-intensive physical computations or template-based methods, as well as compromised generation quality due to the overlooking of domain knowledge. To tackle these challenges, we propose PocketFlow, a generative model that incorporates protein-ligand interaction priors based on flow matching. During training, PocketFlow learns to model key types of protein-ligand interactions, such as hydrogen bonds. In the sampling, PocketFlow leverages multi-granularity guidance (overall binding affinity and interaction geometry constraints) to facilitate generating high-affinity and valid pockets. Extensive experiments show that PocketFlow outperforms baselines on multiple benchmarks, e.g., achieving an average improvement of 1.29 in Vina Score and 0.05 in scRMSD. Moreover, modeling interactions make PocketFlow a generalized generative model across multiple ligand modalities, including small molecules, peptides, and RNA.

Neuroscience, Cognitive Science

Luis Cubillos, Guy Revach, Matthew Mender, Joseph Costello, Hisham Temmar, Aren Hite, Diksha Anoop Kumar Zutshi, Dylan Wallace, Xiaoyong Ni, Madison Kelberman 等

People with brain or spinal cord-related paralysis often need to rely on others for basic tasks, limiting their independence. A potential solution is brain-machine interfaces (BMIs), which could allow them to voluntarily control external devices (e.g., robotic arm) by decoding brain activity to movement commands. In the past decade, deep-learning decoders have achieved state-of-the-art results in most BMI applications, ranging from speech production to finger control. However, the 'black-box' nature of deep-learning decoders could lead to unexpected behaviors, resulting in major safety concerns in real-world physical control scenarios. In these applications, explainable but lower-performing decoders, such as the Kalman filter (KF), remain the norm. In this study, we designed a BMI decoder based on KalmanNet, an extension of the KF that augments its operation with recurrent neural networks to compute the Kalman gain. This results in a varying “trust” that shifts between inputs and dynamics. We used this algorithm to predict finger movements from the brain activity of two monkeys. We compared KalmanNet results offline (pre-recorded data, $n=13$ days) and online (real-time predictions, $n=5$ days) with a simple KF and two recent deep-learning algorithms: tcFNN (non-ReFIT version) and LSTM. KalmanNet achieved comparable or better results than other deep learning models in offline and online modes, relying on the dynamical model for stopping while depending more on neural inputs for initiating movements. We further validated this mechanism by implementing a heteroscedastic KF that used the same strategy, and it also approached state-of-the-art performance while remaining in the explainable domain of standard KFs. However, we also see two downsides to KalmanNet. KalmanNet shares the limited generalization ability of existing deep-learning decoders, and its usage of the KF as an inductive bias limits its performance in the presence of unseen noise distributions. Despite this trade-off, our analysis successfully integrates traditional controls and modern deep-learning approaches to motivate high-performing yet still explainable BMI designs.

Physical Models · Physics

Timothée Devergne, Vladimir Kostic, Michele Parrinello, Massimiliano Pontil

We investigate learning the eigenfunctions of evolution operators for time-reversal invariant stochastic processes, a prime example being the Langevin equation used in molecular dynamics. Many physical or chemical processes described by this equation involve transitions between metastable states separated by high potential barriers that can hardly be crossed during a simulation. To overcome this bottleneck, data are collected via biased simulations that explore the state space more rapidly. We propose a framework for learning from biased simulations rooted in the infinitesimal generator of the process {and the associated resolvent operator}. We contrast our approach to more common ones based on the transfer operator, showing that it can provably learn the spectral properties of the unbiased system from biased data. In experiments, we highlight the advantages of our method over transfer operator approaches and recent developments based on generator learning, demonstrating its effectiveness in estimating eigenfunctions and eigenvalues. Importantly, we show that even with datasets containing only a few relevant transitions due to sub-optimal biasing, our approachrecovers relevant information about the transition mechanism.

Computer Vision

Junfeng Ni, Yixin Chen, Bohan Jing, Nan Jiang, Bin Wang, Bo Dai, Puhao Li, Yixin Zhu, Song-Chun Zhu, Siyuan Huang

We address the issue of physical implausibility in multi-view neural reconstruction. While implicit representations have gained popularity in multi-view 3D reconstruction, previous work struggles to yield physically plausible results, limiting their utility in domains requiring rigorous physical accuracy. This lack of plausibility stems from the absence of physics modeling in existing methods and their inability to recover intricate geometrical structures. In this paper, we introduce PHYRECON, the first approach to leverage both differentiable rendering and differentiable physics simulation to learn implicit surface representations. PHYRECON features a novel differentiable particle-based physical simulator built on neural implicit representations. Central to this design is an efficient transformation between SDF-based implicit representations and explicit surface points via our proposed Surface Points Marching Cubes (SP-MC), enabling differentiable learning with both rendering and physical losses. Additionally, PHYRECON models both rendering and physical uncertainty to identify and compensate for inconsistent and inaccurate monocular geometric priors. The physical uncertainty further facilitates physics-guided pixel sampling to enhance the learning of slender structures. By integrating these techniques, our model supports differentiable joint modeling of appearance, geometry, and physics. Extensive experiments demonstrate that PHYRECON significantly improves the reconstruction quality. Our results also exhibit superior physical stability in physical simulators, with at least a 40% improvement across all datasets, paving the way for future physics-based applications.

Physical Models · Physics

Yue Li, Yi Sun, Shida Sun, Juntian Ye, Yueyi Zhang, Feihu Xu, Zhiwei Xiong

Dynamic reconstruction in confocal non-line-of-sight imaging encounters great challenges since the dense raster-scanning manner limits the practical frame rate. A fewer pioneer works reconstruct high-resolution volumes from the under-scanning transient measurements but overlook temporal consistency among transient frames. To fully exploit multi-frame information, we propose the first spatial-temporal Mamba (ST-Mamba) based method tailored for dynamic reconstruction of transient videos. Our method capitalizes on neighbouring transient frames to aggregate the target 3D hidden volume. Specifically, the interleaved features extracted from the input transient frames are fed to the proposed ST-Mamba blocks, which leverage the time-resolving causality in transient measurement. The cross ST-Mamba blocks are then devised to integrate the adjacent transient features. The target high-resolution transient frame is subsequently recovered by the transient spreading module. After transient fusion and recovery, a physical-based network is employed to reconstruct the hidden volume. To tackle the substantial noise inherent in transient videos, we propose a wave-based loss function to impose constraints within the phasor field. Besides, we introduce a new dataset, comprising synthetic videos for training and real-world videos for evaluation. Extensive experiments showcase the superior performance of our method on both synthetic data and real world data captured by different imaging setups. The code and data are available at https://github.com/Depth2World/Dynamic_NLOS.

Physical Models · Physics

Takeshi Koshizuka, Masahiro Fujisawa, Yusuke Tanaka, Issei Sato

In this paper, we explores the expressivity and trainability of the Fourier Neural Operator (FNO). We establish a mean-field theory for the FNO, analyzing the behavior of the random FNO from an \emph{edge of chaos} perspective. Our investigation into the expressivity of a random FNO involves examining the ordered-chaos phase transition of the network based on the weight distribution. This phase transition demonstrates characteristics unique to the FNO, induced by mode truncation, while also showcasing similarities to those of densely connected networks. Furthermore, we identify a connection between expressivity and trainability: the ordered and chaotic phases correspond to regions of vanishing and exploding gradients, respectively. This finding provides a practical prerequisite for the stable training of the FNO. Our experimental results corroborate our theoretical findings.

Haoran He, Chenjia Bai, Ling Pan, Weinan Zhang, Bin Zhao, Xuelong Li

Learning a generalist embodied agent capable of completing multiple tasks poses challenges, primarily stemming from the scarcity of action-labeled robotic datasets. In contrast, a vast amount of human videos exist, capturing intricate tasks and interactions with the physical world. Promising prospects arise for utilizing actionless human videos for pre-training and transferring the knowledge to facilitate robot policy learning through limited robot demonstrations. However, it remains a challenge due to the domain gap between humans and robots. Moreover, it is difficult to extract useful information representing the dynamic world from human videos, because of its noisy and multimodal data structure. In this paper, we introduce a novel framework to tackle these challenges, which leverages a unified discrete diffusion to combine generative pre-training on human videos and policy fine-tuning on a small number of action-labeled robot videos. We start by compressing both human and robot videos into unified video tokens. In the pre-training stage, we employ a discrete diffusion model with a mask-and-replace diffusion strategy to predict future video tokens in the latent space. In the fine-tuning stage, we harness the imagined future videos to guide low-level action learning with a limited set of robot data. Experiments demonstrate that our method generates high-fidelity future videos for planning and enhances the fine-tuned policies compared to previous state-of-the-art approaches with superior performance.

Jiaqi Han, Minkai Xu, Aaron Lou, Haotian Ye, Stefano Ermon

Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. In this work, we propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories. Modeling such distribution is challenging as it requires capturing both the complex spatial interactions with physical symmetries and temporal correspondence encapsulated in the dynamics. We theoretically justify that diffusion models with equivariant temporal kernels can lead to density with desired symmetry, and develop a novel transition kernel leveraging SE(3)-equivariant spatial convolution and temporal attention. Furthermore, to induce an expressive trajectory distribution for conditional generation, we introduce a generalized learnable geometric prior into the forward diffusion process to enhance temporal conditioning. We conduct extensive experiments on both unconditional and conditional generation in various scenarios, including physical simulation, molecular dynamics, and pedestrian motion. Empirical results on a wide suite of metrics demonstrate that GeoTDM can generate realistic geometric trajectories with significantly higher quality.

Computer Vision · Image Generation

Qiyao Liang, Ziming Liu, Mitchell Ostrow, Ila Fiete

Diffusion models are capable of generating photo-realistic images that combine elements which do not appear together in natural images, demonstrating their ability to compositionally generalize. Nonetheless, the precise mechanism of compositionality and how it is acquired through training remains elusive. Here, we consider a highly reduced setting to examine whether diffusion models learn semantically meaningful and fully factorized representations of composable features. We performed extensive controlled experiments on conditional DDPMs trained to generate various forms of 2D Gaussian data. We demonstrate that the models learn factorized, semi-continuous manifold representations that are orthogonal in underlying continuous latent features of independent variations but are not aligned for different values of the same feature. With such representations, models demonstrate superior compositionality but have limited ability to interpolate over unseen values of a given feature. Our experimental results further demonstrate that diffusion models can attain compositionality with a small amount of compositional examples, suggesting a novel way to train DDPMs. Finally, we connect manifold formation in diffusion models to percolation theory in physics, thereby offering insights into the sudden onset of factorized representation learning. Our thorough toy experiments thus contribute a deeper understanding of how diffusion models capture compositional structure in data, paving the way for future research aimed at enhancing factorization and compositional generalization in generative models for real-world applications.

Theory · Statistics

Yihan Zhang, Marco Mondelli

We study the matrix denoising problem of estimating the singular vectors of a rank-$1$ signal corrupted by noise with both column and row correlations. Existing works are either unable to pinpoint the exact asymptotic estimation error or, when they do so, the resulting approaches (e.g., based on whitening or singular value shrinkage) remain vastly suboptimal. On top of this, most of the literature has focused on the special case of estimating the left singular vector of the signal when the noise only possesses row correlation (one-sided heteroscedasticity). In contrast, our work establishes the information-theoretic and algorithmic limits of matrix denoising with doubly heteroscedastic noise. We characterize the exact asymptotic minimum mean square error, and design a novel spectral estimator with rigorous optimality guarantees: under a technical condition, it attains positive correlation with the signals whenever information-theoretically possible and, for one-sided heteroscedasticity, it also achieves the Bayes-optimal error. Numerical experiments demonstrate the significant advantage of our theoretically principled method with the state of the art. The proofs draw connections with statistical physics and approximate message passing, departing drastically from standard random matrix theory techniques.

Interpretability

Xinyue Luo, Jin Cheng, Yu Chen

Lossless compression of large-scale scientific floating-point data is critical yet challenging due to the presence of high-order information and noise that arises from model truncation and discretization errors. Existing entropy coding techniques fail to effectively leverage the mechanisms underlying the data generation process. This paper introduces MeLLoC(Mechanism Learning for Lossless Compression), a novel approach that combines high-order mechanism learning with classical encoding to enhance lossless compression for scientific data. The key idea is to treat the data as discrete samples from an underlying physical field described by differential equations and solve an inverse problem to identify the governing equation coefficients exhibiting more compressible numeric representations. Periodic extension techniques are employed to accelerate the decompression. Through extensive experiments on various scientific datasets, MeLLoC consistently outperforms state-of-the-art lossless compressors while offering compelling trade-offs between compression ratios and computational costs. This work opens up new avenues for exploiting domain knowledge and high-order information to improve data compression in scientific computing.

Human-computer interaction

Zhenyu Lou, Qiongjie Cui, Tuo Wang, Zhenbo Song, Luoming Zhang, Cheng Cheng, Haofan Wang, Xu Tang, Huaxia Li, Hong Zhou

Diverse human motion prediction (HMP) is a fundamental application in computer vision that has recently attracted considerable interest. Prior methods primarily focus on the stochastic nature of human motion, while neglecting the specific impact of external environment, leading to the pronounced artifacts in prediction when applied to real-world scenarios. To fill this gap, this work introduces a novel task: predicting diverse human motion within real-world 3D scenes. In contrast to prior works, it requires harmonizing the deterministic constraints imposed by the surrounding 3D scenes with the stochastic aspect of human motion. For this purpose, we propose DiMoP3D, a diverse motion prediction framework with 3D scene awareness, which leverages the 3D point cloud and observed sequence to generate diverse and high-fidelity predictions. DiMoP3D is able to comprehend the 3D scene, and determines the probable target objects and their desired interactive pose based on the historical motion. Then, it plans the obstacle-free trajectory towards these interested objects, and generates diverse and physically-consistent future motions. On top of that, DiMoP3D identifies deterministic factors in the scene and integrates them into the stochastic modeling, making the diverse HMP in realistic scenes become a controllable stochastic generation process. On two real-captured benchmarks, DiMoP3D has demonstrated significant improvements over state-of-the-art methods, showcasing its effectiveness in generating diverse and physically-consistent motion predictions within real-world 3D environments.

Wuyang Chen, Jialin Song, Pu Ren, Shashank Subramanian, Dmitriy Morozov, Michael Mahoney

Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insights for solving scientific problems based on partial differential equations (PDEs). However, being data-intensive, these methods still require a large amount of PDE data. This reintroduces the need for expensive numerical PDE solutions, partially undermining the original goal of avoiding these expensive simulations. In this work, seeking data efficiency, we design unsupervised pretraining for PDE operator learning. To reduce the need for training data with heavy simulation costs, we mine unlabeled PDE data without simulated solutions,and we pretrain neural operators with physics-inspired reconstruction-based proxy tasks. To improve out-of-distribution performance, we further assist neural operators in flexibly leveraging a similarity-based method that learns in-context examples, without incurring extra training costs or designs. Extensive empirical evaluations on a diverse set of PDEs demonstrate that our method is highly data-efficient, more generalizable, and even outperforms conventional vision-pretrained models. We provide our code at https://github.com/delta-lab-ai/data_efficient_nopt.

Deep Learning · Representation Learning

Gunshi Gupta, Karmesh Yadav, Yarin Gal, Dhruv Batra, Zsolt Kira, Cong Lu, Tim G. J. Rudner

Embodied AI agents require a fine-grained understanding of the physical world mediated through visual and language inputs. Such capabilities are difficult to learn solely from task-specific data. This has led to the emergence of pre-trained vision-language models as a tool for transferring representations learned from internet-scale data to downstream tasks and new domains. However, commonly used contrastively trained representations such as in CLIP have been shown to fail at enabling embodied agents to gain a sufficiently fine-grained scene understanding—a capability vital for control. To address this shortcoming, we consider representations from pre-trained text-to-image diffusion models, which are explicitly optimized to generate images from text prompts and as such, contain text-conditioned representations that reflect highly fine-grained visuo-spatial information. Using pre-trained text-to-image diffusion models, we construct Stable Control Representations which allow learning downstream control policies that generalize to complex, open-ended environments. We show that policies learned using Stable Control Representations are competitive with state-of-the-art representation learning approaches across a broad range of simulated control settings, encompassing challenging manipulation and navigation tasks. Most notably, we show that Stable Control Representations enable learning policies that exhibit state-of-the-art performance on OVMM, a difficult open-vocabulary navigation benchmark.