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Applications

Bodhisattwa Prasad Majumder, Harshit Surana, Dhruv Agarwal, Sanchaita Hazra, Ashish Sabharwal, Peter Clark

With the accumulation of data at an unprecedented rate, its potential to fuel scientific discovery is growing exponentially. This position paper urges the Machine Learning (ML) community to exploit the capabilities of large generative models (LGMs) to develop automated systems for end-to-end data-driven discovery—a paradigm encompassing the search and verification of hypotheses purely from a set of provided datasets, without the need for additional data collection or physical experiments. We first outline several desiderata for an ideal data-driven discovery system. Then, through DataVoyager, a proof-of-concept utilizing GPT-4, we demonstrate how LGMs fulfill several of these desiderata—a feat previously unattainable—while also highlighting important limitations in the current system that open up opportunities for novel ML research. We contend that achieving accurate, reliable, and robust end-to-end discovery systems solely through the current capabilities of LGMs is challenging. We instead advocate for fail-proof tool integration, along with active user moderation through feedback mechanisms, to foster data-driven scientific discoveries with efficiency and reproducibility.

Reinforcement Learning · Multi-agent

Dingyang Chen, Qi Zhang

Identification and analysis of symmetrical patterns in the natural world have led to significant discoveries across various scientific fields, such as the formulation of gravitational laws in physics and advancements in the study of chemical structures. In this paper, we focus on exploiting Euclidean symmetries inherent in certain cooperative multi-agent reinforcement learning (MARL) problems and prevalent in many applications. We begin by formally characterizing a subclass of Markov games with a general notion of symmetries that admits the existence of symmetric optimal values and policies. Motivated by these properties, we design neural network architectures with symmetric constraints embedded as an inductive bias for multi-agent actor-critic methods. This inductive bias results in superior performance in various cooperative MARL benchmarks and impressive generalization capabilities such as zero-shot learning and transfer learning in unseen scenarios with repeated symmetric patterns.

Reinforcement Learning · Function Approximation

Ehsan Saleh, Saba Ghaffari, Timothy Bretl, Luke Olson, Matthew West

This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for training. As a result, accurate evaluation may be impractical, and we show that naive approximations at replacing these integrals with unbiased estimates lead to biased loss functions and solutions. To overcome this bias, we investigate three types of potential solutions: the deterministic sampling approaches, the double-sampling trick, and the delayed target method. We consider three classes of PDEs for benchmarking; one defining Poisson problems with singular charges and weak solutions of up to 10 dimensions, another involving weak solutions on electro-magnetic fields and a Maxwell equation, and a third one defining a Smoluchowski coagulation problem. Our numerical results confirm the existence of the aforementioned bias in practice and also show that our proposed delayed target approach can lead to accurate solutions with comparable quality to ones estimated with a large sample size integral. Our implementation is open-source and available at https://github.com/ehsansaleh/btspinn.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Gabriela Kadlecová, Jovita Lukasik, Martin Pilát, Petra Vidnerová, Mahmoud Safari, Roman Neruda, Frank Hutter

Performance prediction has been a key part of the neural architecture search (NAS) process, allowing to speed up NAS algorithms by avoiding resource-consuming network training. Although many performance predictors correlate well with ground truth performance, they require training data in the form of trained networks. Recently, zero-cost proxies have been proposed as an efficient method to estimate network performance without any training. However, they are still poorly understood, exhibit biases with network properties, and their performance is limited. Inspired by the drawbacks of zero-cost proxies, we propose neural graph features (GRAF), simple to compute properties of architectural graphs. GRAF offers fast and interpretable performance prediction while outperforming zero-cost proxies and other common encodings. In combination with other zero-cost proxies, GRAF outperforms most existing performance predictors at a fraction of the cost.

Probabilistic Methods · Monte Carlo and Sampling Methods

Haoyang Zheng, Hengrong Du, Qi Feng, Wei Deng, Guang Lin

Replica exchange stochastic gradient Langevin dynamics (reSGLD) is an effective sampler for non-convex learning in large-scale datasets. However, the simulation may encounter stagnation issues when the high-temperature chain delves too deeply into the distribution tails. To tackle this issue, we propose reflected reSGLD (r2SGLD): an algorithm tailored for constrained non-convex exploration by utilizing reflection steps within a bounded domain. Theoretically, we observe that reducing the diameter of the domain enhances mixing rates, exhibiting a *quadratic* behavior. Empirically, we test its performance through extensive experiments, including identifying dynamical systems with physical constraints, simulations of constrained multi-modal distributions, and image classification tasks. The theoretical and empirical findings highlight the crucial role of constrained exploration in improving the simulation efficiency.

Miscellaneous Aspects of Machine Learning · Representation Learning

Zhengqi Pei, Anran Zhang, Shuhui Wang, Xiangyang Ji, Qingming Huang

Neural models are equivalent to dynamic systems from a physics-inspired view, implying that computation on neural networks can be interpreted as the dynamical interactions between neurons. However, existing work models neuronal interaction as a weight-based linear transformation, and the nonlinearity comes from the nonlinear activation functions, which leads to limited nonlinearity and data-fitting ability of the whole neural model. Inspired by Riemannian geometry, we interpret neural structures by projecting neurons onto the Riemannian neuronal state space and model neuronal interaction with Riemannian metric (${\it RieM}$), which provides a more efficient neural representation with higher parameter efficiency. With ${\it RieM}$, we further design a novel data-free neural compression mechanism that does not require additional fine-tuning with real data. Using backbones like ResNet and Vision Transformer, we conduct extensive experiments on datasets such as MNIST, CIFAR-100, ImageNet-1k, and COCO object detection. Empirical results show that, under equal compression rates and computational complexity, models compressed with ${\it RieM}$ achieve superior inference accuracy compared to existing data-free compression methods.

Social Aspects · Trustworthy Machine Learning

Luca Masserano, Alexander Shen, Michele Doro, Tommaso Dorigo, Rafael Izbicki, Ann Lee

An open scientific challenge is how to classify events with reliable measures of uncertainty, when we have a mechanistic model of the data-generating process but the distribution over both labels and latent nuisance parameters is different between train and target data. We refer to this type of distributional shift as generalized label shift (GLS). Direct classification using observed data $\mathbf{X}$ as covariates leads to biased predictions and invalid uncertainty estimates of labels $Y$. We overcome these biases by proposing a new method for robust uncertainty quantification that casts classification as a hypothesis testing problem under nuisance parameters. The key idea is to estimate the classifier's receiver operating characteristic (ROC) across the entire nuisance parameter space, which allows us to devise cutoffs that are invariant under GLS. Our method effectively endows a pre-trained classifier with domain adaptation capabilities and returns valid prediction sets while maintaining high power. We demonstrate its performance on two challenging scientific problems in biology and astroparticle physics with data from realistic mechanistic models.

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Jongha (Jon) Ryu, Xiangxiang Xu, Hasan Sabri Melihcan Erol, Yuheng Bu, Lizhong Zheng, Gregory Wornell

Computing eigenvalue decomposition (EVD) of a given linear operator, or finding its leading eigenvalues and eigenfunctions, is a fundamental task in many machine learning and scientific simulation problems. For high-dimensional eigenvalue problems, training neural networks to parameterize the eigenfunctions is considered as a promising alternative to the classical numerical linear algebra techniques. This paper proposes a new optimization framework based on the low-rank approximation characterization of a truncated singular value decomposition, accompanied by new techniques called *nesting* for learning the top-$L$ singular values and singular functions in the correct order. The proposed method promotes the desired orthogonality in the learned functions implicitly and efficiently via an unconstrained optimization formulation, which is easy to solve with off-the-shelf gradient-based optimization algorithms. We demonstrate the effectiveness of the proposed optimization framework for use cases in computational physics and machine learning.

Optimization

Shirin Shoushtari, JIAMING LIU, Edward Chandler, Salman Asif, Ulugbek Kamilov

Plug-and-Play (PnP) priors is a widely-used family of methods for solving imaging inverse problems by integrating physical measurement models with image priors specified using image denoisers. PnP methods have been shown to achieve state-of-the-art performance when the prior is obtained using powerful deep denoisers. Despite extensive work on PnP, the topic of distribution mismatch between the training and testing data has often been overlooked in the PnP literature. This paper presents a set of new theoretical and numerical results on the topic of prior distribution mismatch and domain adaptation for the alternating direction method of multipliers (ADMM) variant of PnP. Our theoretical result provides an explicit error bound for PnP-ADMM due to the mismatch between the desired denoiser and the one used for inference. Our analysis contributes to the work in the area by considering the mismatch under nonconvex data-fidelity terms and expansive denoisers. Our first set of numerical results quantifies the impact of the prior distribution mismatch on the performance of PnP-ADMM on the problem of image super-resolution. Our second set of numerical results considers a simple and effective domain adaption strategy that closes the performance gap due to the use of mismatched denoisers. Our results suggest the relative robustness of PnP-ADMM to prior distribution mismatch, while also showing that the performance gap can be significantly reduced with only a few training samples from the desired distribution.

Applications · Physics

Hong Chul Nam, Julius Berner, Anima Anandkumar

We propose Neural Walk-on-Spheres (NWoS), a novel neural PDE solver for the efficient solution of high-dimensional Poisson equations. Leveraging stochastic representations and Walk-on-Spheres methods, we develop novel losses for neural networks based on the recursive solution of Poisson equations on spheres inside the domain. The resulting method is highly parallelizable and does not require spatial gradients for the loss. We provide a comprehensive comparison against competing methods based on PINNs, the Deep Ritz method, and (backward) stochastic differential equations. In several challenging, high-dimensional numerical examples, we demonstrate the superiority of NWoS in accuracy, speed, and computational costs. Compared to commonly used PINNs, our approach can reduce memory usage and errors by orders of magnitude. Furthermore, we apply NWoS to problems in PDE-constrained optimization and molecular dynamics to show its efficiency in practical applications.

Applications · Chemistry and Drug Discovery

Bowen Jing, Bonnie Berger, Tommi Jaakkola

The biological functions of proteins often depend on dynamic structural ensembles. In this work, we develop a flow-based generative modeling approach for learning and sampling the conformational landscapes of proteins. We repurpose highly accurate single-state predictors such as AlphaFold and ESMFold and fine-tune them under a custom flow matching framework to obtain sequence-conditioned generative models of protein structure called AlphaFlow and ESMFlow. When trained and evaluated on the PDB, our method provides a superior combination of precision and diversity compared to AlphaFold with MSA subsampling. When further trained on ensembles from all-atom MD, our method accurately captures conformational flexibility, positional distributions, and higher-order ensemble observables for unseen proteins. Moreover, our method can diversify a static PDB structure with faster wall-clock convergence to certain equilibrium properties than replicate MD trajectories, demonstrating its potential as a proxy for expensive physics-based simulations. Code is available at https://github.com/bjing2016/alphaflow.

Applications · Everything Else

Yoni Choukroun, Lior Wolf

Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern, especially for short block lengths. While neural decoders have recently demonstrated their advantage over classical decoding techniques, the neural design of the codes remains a challenge. In this work, we propose for the first time a unified encoder-decoder training of binary linear block codes. To this end, we adapt the coding setting to support efficient and differentiable training of the code for end-to-end optimization over the order two Galois field. We also propose a novel Transformer model in which the self-attention masking is performed in a differentiable fashion for the efficient backpropagation of the code gradient. Our results show that (i) the proposed decoder outperforms existing neural decoding on conventional codes, (ii) the suggested framework generates codes that outperform the analogous conventional codes, and (iii) the codes we developed not only excel with our decoder but also show enhanced performance with traditional decoding techniques.

Sherry Yang, Jacob C Walker, Jack Parker-Holder, Yilun Du, Jake Bruce, Andre Barreto, Pieter Abbeel, Dale Schuurmans

Both text and video data are abundant on the internet and support large-scale self-supervised learning through next token or frame prediction. However, they have not been equally leveraged: language models have had significant real-world impact, whereas video generation has remained largely limited to media entertainment. Yet video data captures important information about the physical world that is difficult to express in language. To address this gap, we discuss an under-appreciated opportunity to extend video generation to solve tasks in the real world. We observe how, akin to language, video can serve as a unified interface that can absorb internet knowledge and represent diverse tasks. Moreover, we demonstrate how, like language models, video generation can serve as planners, agents, compute engines, and environment simulators through techniques such as in-context learning, planning and reinforcement learning. We identify major impact opportunities in domains such as robotics, self-driving, and science, supported by recent work that demonstrates how such advanced capabilities in video generation are plausibly within reach. Lastly, we identify key challenges in video generation that mitigate progress. Addressing these challenges will enable video generation models to demonstrate unique value alongside language models in a wider array of AI applications.

Deep Learning · Large Language Models

Xiaoxuan Wang, ziniu hu, Pan Lu, Yanqiao Zhu, Jieyu Zhang, Satyen Subramaniam, Arjun Loomba, Shichang Zhang, Yizhou Sun, Wei Wang

Most existing Large Language Model (LLM) benchmarks on scientific problem reasoning focus on problems grounded in high-school subjects and are confined to elementary algebraic operations. To systematically examine the reasoning capabilities required for solving complex scientific problems, we introduce an expansive benchmark suite SciBench for LLMs. SciBench contains a carefully curated dataset featuring a range of collegiate-level scientific problems from mathematics, chemistry, and physics domains. Based on the dataset, we conduct an in-depth benchmarking study of representative open-source and proprietary LLMs with various prompting strategies. The results reveal that current LLMs fall short of delivering satisfactory performance, with the best overall score of merely 43.22%. Furthermore, through a detailed user study, we categorize the errors made by LLMs into ten problem-solving abilities. Our analysis indicates that no single prompting strategy significantly outperforms the others and some strategies that demonstrate improvements in certain problem-solving skills could result in declines in other skills. We envision that SciBench will catalyze further developments in the reasoning abilities of LLMs, thereby ultimately contributing to scientific research and discovery.

Deep Learning · Graph Neural Networks

Alexandre Duval, Victor Schmidt, Santiago Miret, Yoshua Bengio, Alex Hernandez-Garcia, David Rolnick

Mitigating the climate crisis requires a rapid transition towards lower-carbon energy. Catalyst materials play a crucial role in the electrochemical reactions involved in numerous industrial processes key to this transition, such as renewable energy storage and electrofuel synthesis. To reduce the energy spent on such activities, we must quickly discover more efficient catalysts to drive electrochemical reactions. Machine learning (ML) holds the potential to efficiently model materials properties from large amounts of data, accelerating electrocatalyst design. The Open Catalyst Project OC20 dataset was constructed to that end. However, ML models trained on OC20 are still neither scalable nor accurate enough for practical applications. In this paper, we propose task-specific innovations applicable to most architectures, enhancing both computational efficiency and accuracy. This includes improvements in (1) the graph creation step, (2) atom representations, (3) the energy prediction head, and (4) the force prediction head. We describe these contributions, referred to as PhAST, and evaluate them thoroughly on multiple architectures. Overall, PhAST improves energy MAE by 4 to 42% while dividing compute time by 3 to 8× depending on the targeted task/model. PhAST also enables CPU training, leading to 40× speedups in highly parallelized settings. Python package: https://phast.readthedocs.io.

Probabilistic Methods

Kirill Neklyudov, Rob Brekelmans, Alexander Tong, Lazar Atanackovic, qiang liu, Alireza Makhzani

The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (*kinetic energy*), and the regularization of density paths (*potential energy*). These combinations yield different variational problems (*Lagrangians*), encompassing many variations of the optimal transport problem such as the Schrödinger bridge, unbalanced optimal transport, and optimal transport with physical constraints, among others. In general, the optimal density path is unknown, and solving these variational problems can be computationally challenging. We propose a novel deep learning based framework approaching all of these problems from a unified perspective. Leveraging the dual formulation of the Lagrangians, our method does not require simulating or backpropagating through the trajectories of the learned dynamics, and does not need access to optimal couplings. We showcase the versatility of the proposed framework by outperforming previous approaches for the single-cell trajectory inference, where incorporating prior knowledge into the dynamics is crucial for correct predictions.

Applications · Neuroscience, Cognitive Science

Tingting Dan, Ziquan Wei, Won Hwa Kim, Guorong Wu

The human brain is a complex inter-wired system that emerges spontaneous functional fluctuations. In spite of tremendous success in the experimental neuroscience field, a system-level understanding of how brain anatomy supports various neural activities remains elusive. Capitalizing on the unprecedented amount of neuroimaging data, we present a physics-informed deep model to uncover the coupling mechanism between brain structure and function through the lens of data geometry that is rooted in the widespread wiring topology of connections between distant brain regions. Since deciphering the puzzle of self-organized patterns in functional fluctuations is the gateway to understanding the emergence of cognition and behavior, we devise a geometric deep model to uncover manifold mapping functions that characterize the intrinsic feature representations of evolving functional fluctuations on the Riemannian manifold. In lieu of learning unconstrained mapping functions, we introduce a set of graph-harmonic scattering transforms to impose the brain-wide geometry on top of manifold mapping functions, which allows us to cast the manifold-based deep learning into a reminiscent of *MLP-Mixer* architecture (in computer vision) for Riemannian manifold. As a proof-of-concept approach, we explore a neural-manifold perspective to understand the relationship between (static) brain structure and (dynamic) function, challenging the prevailing notion in cognitive neuroscience by proposing that neural activities are essentially excited by brain-wide oscillation waves living on the geometry of human connectomes, instead of being confined to focal areas.

Applications · Robotics

Haoyu Zhen, Xiaowen Qiu, Peihao Chen, Jincheng Yang, Xin Yan, Yilun Du, Yining Hong, Chuang Gan

Recent vision-language-action (VLA) models rely on 2D inputs, lacking integration with the broader realm of the 3D physical world. Furthermore, they perform action prediction by learning a direct mapping from perception to action, neglecting the vast dynamics of the world and the relations between actions and dynamics. In contrast, human beings are endowed with world models that depict imagination about future scenarios to plan action accordingly. To this end, we propose 3D-VLA by introducing a new family of embodied foundation models that seamlessly link 3D perception, reasoning, and action through a generative world model. Specifically, 3D-VLA is built on top of a 3D-based large language model (LLM) and a set of action tokens is introduced to engage with the embodied environment. Furthermore, to inject generation abilities into the model, we train the embodied diffusion models and align them into the LLM for predicting the goal image and point cloud. To train our 3D-VLA, we curate a large-scale 3D embodied instruction dataset by extracting vast 3D-related information from existing robotics datasets. Our experiments on held-in datasets demonstrate that 3D-VLA significantly improves the reasoning, multimodality generation and planning capabilities in embodied environments, showcasing its potential in real-world applications.

Applications · Computer Vision

Zhicheng Zheng, Xin Yan, Zhenfang Chen, Jingzhou Wang, Qin Zhi Eddie Lim, Josh Tenenbaum, Chuang Gan

We introduce the Continuum Physical Dataset (ContPhy), a novel benchmark for assessing machine physical commonsense. ContPhy complements existing physical reasoning benchmarks by encompassing the inference of diverse physical properties, such as mass and density, across various scenarios and predicting corresponding dynamics. We evaluated a range of AI models and found that they still struggle to achieve satisfactory performance on ContPhy, which shows that current AI models still lack physical commonsense for the continuum, especially soft-bodies, and illustrates the value of the proposed dataset. We also introduce an oracle model (ContPRO) that marries the particle-based physical dynamic models with the recent large language models, which enjoy the advantages of both models, precise dynamic predictions, and interpretable reasoning. ContPhy aims to spur progress in perception and reasoning within diverse physical settings, narrowing the divide between human and machine intelligence in understanding the physical world.

Applications · Physics

Langwen Huang, Lukas Gianinazzi, Yuejiang Yu, Peter Dueben, Torsten Hoefler

The generation of initial conditions via accurate data assimilation is crucial for weather forecasting and climate modeling. We propose DiffDA as a denoising diffusion model capable of assimilating atmospheric variables using predicted states and sparse observations. Acknowledging the similarity between a weather forecast model and a denoising diffusion model dedicated to weather applications, we adapt the pretrained GraphCast neural network as the backbone of the diffusion model. Through experiments based on simulated observations from the ERA5 reanalysis dataset, our method can produce assimilated global atmospheric data consistent with observations at 0.25$^\circ$ ($\approx$30km) resolution globally. This marks the highest resolution achieved by ML data assimilation models. The experiments also show that the initial conditions assimilated from sparse observations (less than 0.96% of gridded data) and 48-hour forecast can be used for forecast models with a loss of lead time of at most 24 hours compared to initial conditions from state-of-the-art data assimilation in ERA5. This enables the application of the method to real-world applications, such as creating reanalysis datasets with autoregressive data assimilation.