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Applications/Physics

Yuting Hu, Jiajie Li, Florian Klemme, Gi-Joon Nam, Tengfei Ma, Hussam Amrouch, Jinjun Xiong

Nowadays integrated circuits (ICs) are underpinning all major information technology innovations including the current trends of artificial intelligence (AI). Modern IC designs often involve analyses of complex phenomena (such as timing, noise, and power etc.) for tens of billions of electronic components, like resistance (R), capacitance (C), transistors and gates, interconnected in various complex structures. Those analyses often need to strike a balance between accuracy and speed as those analyses need to be carried out many times throughout the entire IC design cycles. With the advancement of AI, researchers also start to explore news ways in leveraging AI to improve those analyses. This paper focuses on one of the most important analyses, timing analysis for interconnects. Since IC interconnects can be represented as an RC-tree, a specialized graph as tree, we design a novel tree-based graph neural network, SyncTREE, to speed up the timing analysis by incorporating both the structural and physical properties of electronic circuits. Our major innovations include (1) a two-pass message-passing (bottom-up and top-down) for graph embedding, (2) a tree contrastive loss to guide learning, and (3) a closed formular-based approach to conduct fast timing. Our experiments show that, compared to conventional GNN models, SyncTREE achieves the best timing prediction in terms of both delays and slews, all in reference to the industry golden numerical analyses results on real IC design data.

Applications/Computer Vision

Tushar Nagarajan, Santhosh Kumar Ramakrishnan, Ruta Desai, James Hillis, Kristen Grauman

First-person video highlights a camera-wearer's activities in the context of their persistent environment. However, current video understanding approaches reason over visual features from short video clips that are detached from the underlying physical space and capture only what is immediately visible. To facilitate human-centric environment understanding, we present an approach that links egocentric video and the environment by learning representations that are predictive of the camera-wearer's (potentially unseen) local surroundings. We train such models using videos from agents in simulated 3D environments where the environment is fully observable, and test them on human-captured real-world videos from unseen environments. On two human-centric video tasks, we show that models equipped with our environment-aware features consistently outperform their counterparts with traditional clip features. Moreover, despite being trained exclusively on simulated videos, our approach successfully handles real-world videos from HouseTours and Ego4D, and achieves state-of-the-art results on the Ego4D NLQ challenge.

Applications/Computer Vision

Yining Hong, Haoyu Zhen, Peihao Chen, Shuhong Zheng, Yilun Du, Zhenfang Chen, Chuang Gan

Large language models (LLMs) and Vision-Language Models (VLMs) have been proved to excel at multiple tasks, such as commonsense reasoning. Powerful as these models can be, they are not grounded in the 3D physical world, which involves richer concepts such as spatial relationships, affordances, physics, layout, and so on. In this work, we propose to inject the 3D world into large language models, and introduce a whole new family of 3D-LLMs. Specifically, 3D-LLMs can take 3D point clouds and their features as input and perform a diverse set of 3D-related tasks, including captioning, dense captioning, 3D question answering, task decomposition, 3Dgrounding, 3D-assisted dialog, navigation, and so on. Using three types of prompting mechanisms that we design, we are able to collect over 300k 3D-language data covering these tasks. To efficiently train 3D-LLMs, we first utilize a 3D feature extractor that obtains 3D features from rendered multi-view images. Then, we use 2D VLMs as our backbones to train our 3D-LLMs. By introducing a 3D localization mechanism, 3D-LLMs could better capture 3D spatial information. Experiments on ScanQA show that our model outperforms state-of-the-art baselines by a large margin (\textit{e.g.}, the BLEU-1 score surpasses state-of-the-art score by 9\%). Furthermore, experiments on our held-in datasets for 3D captioning, task composition, and 3D-assisted dialogue show that our model outperforms 2D VLMs. Qualitative examples also show that our model could perform more tasks beyond the scope of existing LLMs and VLMs. Our model and data will be publicly available.

Miscellaneous Aspects of Machine Learning/Online Learning, Active Learning and Bandits

Juan M. Cardenas, Ben Adcock, Nick Dexter

We introduce a general framework for active learning in regression problems. Our framework extends the standard setup by allowing for general types of data, rather than merely pointwise samples of the target function. This generalization covers many cases of practical interest, such as data acquired in transform domains (e.g., Fourier data), vector-valued data (e.g., gradient-augmented data), data acquired along continuous curves, and, multimodal data (i.e., combinations of different types of measurements). Our framework considers random sampling according to a finite number of sampling measures and arbitrary nonlinear approximation spaces (model classes). We introduce the concept of \textit{generalized Christoffel functions} and show how these can be used to optimize the sampling measures. We prove that this leads to near-optimal sample complexity in various important cases. This paper focuses on applications in scientific computing, where active learning is often desirable, since it is usually expensive to generate data. We demonstrate the efficacy of our framework for gradient-augmented learning with polynomials, Magnetic Resonance Imaging (MRI) using generative models and adaptive sampling for solving PDEs using Physics-Informed Neural Networks (PINNs).

Theory/Reinforcement Learning and Planning

Blake Bordelon, Paul Masset, Henry Kuo, Cengiz Pehlevan

Reinforcement learning has been successful across several applications in which agents have to learn to act in environments with sparse feedback. However, despite this empirical success there is still a lack of theoretical understanding of how the parameters of reinforcement learning models and the features used to represent states interact to control the dynamics of learning. In this work, we use concepts from statistical physics, to study the typical case learning curves for temporal difference learning of a value function with linear function approximators. Our theory is derived under a Gaussian equivalence hypothesis where averages over the random trajectories are replaced with temporally correlated Gaussian feature averages and we validate our assumptions on small scale Markov Decision Processes. We find that the stochastic semi-gradient noise due to subsampling the space of possible episodes leads to significant plateaus in the value error, unlike in traditional gradient descent dynamics. We study how learning dynamics and plateaus depend on feature structure, learning rate, discount factor, and reward function. We then analyze how strategies like learning rate annealing and reward shaping can favorably alter learning dynamics and plateaus. To conclude, our work introduces new tools to open a new direction towards developing a theory of learning dynamics in reinforcement learning.

Applications/Physics

Francesca Bartolucci, Emmanuel de Bézenac, Bogdan Raonic, Roberto Molinaro, Siddhartha Mishra, Rima Alaifari

Recently, operator learning, or learning mappings between infinite-dimensional function spaces, has garnered significant attention, notably in relation to learning partial differential equations from data. Conceptually clear when outlined on paper, neural operators necessitate discretization in the transition to computer implementations. This step can compromise their integrity, often causing them to deviate from the underlying operators. This research offers a fresh take on neural operators with a framework Representation equivalent Neural Operators (ReNO) designed to address these issues. At its core is the concept of operator aliasing, which measures inconsistency between neural operators and their discrete representations. We explore this for widely-used operator learning techniques. Our findings detail how aliasing introduces errors when handling different discretizations and grids and loss of crucial continuous structures. More generally, this framework not only sheds light on existing challenges but, given its constructive and broad nature, also potentially offers tools for developing new neural operators.

Applications/Physics

Niklas Freymuth, Philipp Dahlinger, Tobias Würth, Simon Reisch, Luise Kärger, Gerhard Neumann

The Finite Element Method, an important technique in engineering, is aided by Adaptive Mesh Refinement (AMR), which dynamically refines mesh regions to allow for a favorable trade-off between computational speed and simulation accuracy. Classical methods for AMR depend on task-specific heuristics or expensive error estimators, hindering their use for complex simulations. Recent learned AMR methods tackle these problems, but so far scale only to simple toy examples. We formulate AMR as a novel Adaptive Swarm Markov Decision Process in which a mesh is modeled as a system of simple collaborating agents that may split into multiple new agents. This framework allows for a spatial reward formulation that simplifies the credit assignment problem, which we combine with Message Passing Networks to propagate information between neighboring mesh elements. We experimentally validate the effectiveness of our approach, Adaptive Swarm Mesh Refinement (ASMR), showing that it learns reliable, scalable, and efficient refinement strategies on a set of challenging problems. Our approach significantly speeds up computation, achieving up to 30-fold improvement compared to uniform refinements in complex simulations. Additionally, we outperform learned baselines and achieve a refinement quality that is on par with a traditional error-based AMR strategy without expensive oracle information about the error signal.

Deep Learning/Generative Models and Autoencoders

George Stein, Jesse Cresswell, Rasa Hosseinzadeh, Yi Sui, Brendan Ross, Valentin Villecroze, Zhaoyan Liu, Anthony Caterini, Eric Taylor, Gabriel Loaiza-Ganem

We systematically study a wide variety of generative models spanning semantically-diverse image datasets to understand and improve the feature extractors and metrics used to evaluate them.Using best practices in psychophysics, we measure human perception of image realism for generated samples by conducting the largest experiment evaluating generative models to date, and find that no existing metric strongly correlates with human evaluations.Comparing to 17 modern metrics for evaluating the overall performance, fidelity, diversity, rarity, and memorization of generative models, we find that the state-of-the-art perceptual realism of diffusion models as judged by humans is not reflected in commonly reported metrics such as FID. This discrepancy is not explained by diversity in generated samples, though one cause is over-reliance on Inception-V3.We address these flaws through a study of alternative self-supervised feature extractors, find that the semantic information encoded by individual networks strongly depends on their training procedure, and show that DINOv2-ViT-L/14 allows for much richer evaluation of generative models. Next, we investigate data memorization, and find that generative models do memorize training examples on simple, smaller datasets like CIFAR10, but not necessarily on more complex datasets like ImageNet. However, our experiments show that current metrics do not properly detect memorization: none in the literature is able to separate memorization from other phenomena such as underfitting or mode shrinkage. To facilitate further development of generative models and their evaluation we release all generated image datasets, human evaluation data, and a modular library to compute 17 common metrics for 9 different encoders at https://github.com/layer6ai-labs/dgm-eval.

Applications/Physics

Lingbing Guo, Weiqing Wang, Zhuo Chen, Ningyu Zhang, Zequn Sun, Yixuan Lai, Qiang Zhang, Huajun Chen

Reasoning system dynamics is one of the most important analytical approaches for many scientific studies. With the initial state of a system as input, the recent graph neural networks (GNNs)-based methods are capable of predicting the future state distant in time with high accuracy. Although these methods have diverse designs in modeling the coordinates and interacting forces of the system, we show that they actually share a common paradigm that learns the integration of the velocity over the interval between the initial and terminal coordinates. However, their integrand is constant w.r.t. time. Inspired by this observation, we propose a new approach to predict the integration based on several velocity estimations with Newton–Cotes formulas and prove its effectiveness theoretically. Extensive experiments on several benchmarks empirically demonstrate consistent and significant improvement compared with the state-of-the-art methods.

Applications/Computer Vision

Changsheng Lv, Shuai Zhang, Yapeng Tian, Mengshi Qi, Huadong Ma

In this paper, we propose a Disentangled Counterfactual Learning (DCL) approach for physical audiovisual commonsense reasoning. The task aims to infer objects’ physics commonsense based on both video and audio input, with the main challenge is how to imitate the reasoning ability of humans. Most of the current methods fail to take full advantage of different characteristics in multi-modal data, and lacking causal reasoning ability in models impedes the progress of implicit physical knowledge inferring. To address these issues, our proposed DCL method decouples videos into static (time-invariant) and dynamic (time-varying) factors in the latent space by the disentangled sequential encoder, which adopts a variational autoencoder (VAE) to maximize the mutual information with a contrastive loss function. Furthermore, we introduce a counterfactual learning module to augment the model’s reasoning ability by modeling physical knowledge relationships among different objects under counterfactual intervention. Our proposed method is a plug-and-play module that can be incorporated into any baseline. In experiments, we show that our proposed method improves baseline methods and achieves state-of-the-art performance. Our source code is available at https://github.com/Andy20178/DCL.

Theory/Learning Theory

Samuel Lanthaler, T. Konstantin Rusch, Siddhartha Mishra

Coupled oscillators are being increasingly used as the basis of machine learning (ML) architectures, for instance in sequence modeling, graph representation learning and in physical neural networks that are used in analog ML devices. We introduce an abstract class of *neural oscillators* that encompasses these architectures and prove that neural oscillators are universal, i.e, they can approximate any continuous and casual operator mapping between time-varying functions, to desired accuracy. This universality result provides theoretical justification for the use of oscillator based ML systems. The proof builds on a fundamental result of independent interest, which shows that a combination of forced harmonic oscillators with a nonlinear read-out suffices to approximate the underlying operators.

Deep Learning/Attention Mechanisms

Wenchong He, Zhe Jiang, Tingsong Xiao, Zelin Xu, Shigang Chen, Ronald Fick, MILES MEDINA, Christine Angelini

Transformers are widely used deep learning architectures. Existing transformers are mostly designed for sequences (texts or time series), images or videos, and graphs. This paper proposes a novel transformer model for massive (up to a million) point samples in continuous space. Such data are ubiquitous in environment sciences (e.g., sensor observations), numerical simulations (e.g., particle-laden flow, astrophysics), and location-based services (e.g., POIs and trajectories). However, designing a transformer for massive spatial points is non-trivial due to several challenges, including implicit long-range and multi-scale dependency on irregular points in continuous space, a non-uniform point distribution, the potential high computational costs of calculating all-pair attention across massive points, and the risks of over-confident predictions due to varying point density. To address these challenges, we propose a new hierarchical spatial transformer model, which includes multi-resolution representation learning within a quad-tree hierarchy and efficient spatial attention via coarse approximation. We also design an uncertainty quantification branch to estimate prediction confidence related to input feature noise and point sparsity. We provide a theoretical analysis of computational time complexity and memory costs. Extensive experiments on both real-world and synthetic datasets show that our method outperforms multiple baselines in prediction accuracy and our model can scale up to one million points on one NVIDIA A100 GPU. The code is available at https://github.com/spatialdatasciencegroup/HST

Applications/Physics

Woojin Cho, Kookjin Lee, Donsub Rim, Noseong Park

In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design parameters) and solvers are required to perform rapid execution. In this study, we suggest a path that potentially opens up a possibility for physics-informed neural networks (PINNs), emerging deep-learning-based solvers, to be considered as one such solver. Although PINNs have pioneered a proper integration of deep-learning and scientific computing, they require repetitive time-consuming training of neural networks, which is not suitable for many-query scenarios. To address this issue, we propose a lightweight low-rank PINNs containing only hundreds of model parameters and an associated hypernetwork-based meta-learning algorithm, which allows efficient approximation of solutions of PDEs for varying ranges of PDE input parameters. Moreover, we show that the proposed method is effective in overcoming a challenging issue, known as "failure modes" of PINNs.

Reinforcement Learning/Continuous Action

Xuanle Zhao, Duzhen Zhang, Han Liyuan, Tielin Zhang, Bo Xu

Neural ordinary differential equations (ODEs) are widely recognized as the standard for modeling physical mechanisms, which help to perform approximate inference in unknown physical or biological environments. In partially observable (PO) environments, how to infer unseen information from raw observations puzzled the agents. By using a recurrent policy with a compact context, context-based reinforcement learning provides a flexible way to extract unobservable information from historical transitions. To help the agent extract more dynamics-related information, we present a novel ODE-based recurrent model combines with model-free reinforcement learning (RL) framework to solve partially observable Markov decision processes (POMDPs). We experimentally demonstrate the efficacy of our methods across various PO continuous control and meta-RL tasks. Furthermore, our experiments illustrate that our method is robust against irregular observations, owing to the ability of ODEs to model irregularly-sampled time series.

Applications/Physics

Qianli Shen, Wai Hoh Tang, Zhun Deng, Apostolos Psaros, Kenji Kawaguchi

Standard approaches for uncertainty quantification in deep learning and physics-informed learning have persistent limitations. Indicatively, strong assumptions regarding the data likelihood are required, the performance highly depends on the selection of priors, and the posterior can be sampled only approximately, which leads to poor approximations because of the associated computational cost.This paper introduces and studies confidence interval (CI) estimation for deterministic partial differential equations as a novel problem.That is, to propagate confidence, in the form of CIs, from data locations to the entire domain with probabilistic guarantees.We propose a method, termed Physics-Informed Confidence Propagation (PICProp), based on bi-level optimization to compute a valid CI without making heavy assumptions.We provide a theorem regarding the validity of our method, and computational experiments, where the focus is on physics-informed learning. Code is available at https://github.com/ShenQianli/PICProp.

Deep Learning/Sequential Models, Time series

Joon-Hyuk Ko, Hankyul Koh, Nojun Park, Wonho Jhe

Neural Ordinary Differential Equations (NeuralODEs) present an attractive way to extract dynamical laws from time series data, as they bridge neural networks with the differential equation-based modeling paradigm of the physical sciences. However, these models often display long training times and suboptimal results, especially for longer duration data. While a common strategy in the literature imposes strong constraints to the NeuralODE architecture to inherently promote stable model dynamics, such methods are ill-suited for dynamics discovery as the unknown governing equation is not guaranteed to satisfy the assumed constraints. In this paper, we develop a new training method for NeuralODEs, based on synchronization and homotopy optimization, that does not require changes to the model architecture. We show that synchronizing the model dynamics and the training data tames the originally irregular loss landscape, which homotopy optimization can then leverage to enhance training. Through benchmark experiments, we demonstrate our method achieves competitive or better training loss while often requiring less than half the number of training epochs compared to other model-agnostic techniques. Furthermore, models trained with our method display better extrapolation capabilities, highlighting the effectiveness of our method.

Applications/Robotics

Wenlong Huang, Fei Xia, Dhruv Shah, Danny Driess, Andy Zeng, Yao Lu, Pete Florence, Igor Mordatch, Sergey Levine, Karol Hausman 等

Recent progress in large language models (LLMs) has demonstrated the ability to learn and leverage Internet-scale knowledge through pre-training with autoregressive models. Unfortunately, applying such models to settings with embodied agents, such as robots, is challenging due to their lack of experience with the physical world, inability to parse non-language observations, and ignorance of rewards or safety constraints that robots may require. On the other hand, language-conditioned robotic policies that learn from interaction data can provide the necessary grounding that allows the agent to be correctly situated in the real world, but such policies are limited by the lack of high-level semantic understanding due to the limited breadth of the interaction data available for training them. Thus, if we want to make use of the semantic knowledge in a language model while still situating it in an embodied setting, we must construct an action sequence that is both likely according to the language model and also realizable according to grounded models of the environment. We frame this as a problem similar to probabilistic filtering: decode a sequence that both has high probability under the language model and high probability under a set of grounded model objectives. We demonstrate how such grounded models can be obtained across three simulation and real-world domains, and that the proposed decoding strategy is able to solve complex, long-horizon embodiment tasks in a robotic setting by leveraging the knowledge of both models.

Deep Learning

Ilyes Batatia, Mario Geiger, Jose Munoz, Tess Smidt, Lior Silberman, Christoph Ortner

Reductive Lie Groups, such as the orthogonal groups, the Lorentz group, or the unitary groups, play essential roles across scientific fields as diverse as high energy physics, quantum mechanics, quantum chromodynamics, molecular dynamics, computer vision, and imaging. In this paper, we present a general Equivariant Neural Network architecture capable of respecting the symmetries of the finite-dimensional representations of any reductive Lie Group. Our approach generalizes the successful ACE and MACE architectures for atomistic point clouds to any data equivariant to a reductive Lie group action. We also introduce the lie-nn software library, which provides all the necessary tools to develop and implement such general G-equivariant neural networks. It implements routines for the reduction of generic tensor products of representations into irreducible representations, making it easy to apply our architecture to a wide range of problems and groups. The generality and performance of our approach are demonstrated by applying it to the tasks of top quark decay tagging (Lorentz group) and shape recognition (orthogonal group).

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

wonje choi, Woo Kyung Kim, SeungHyun Kim, Honguk Woo

For embodied reinforcement learning (RL) agents interacting with the environment, it is desirable to have rapid policy adaptation to unseen visual observations, but achieving zero-shot adaptation capability is considered as a challenging problem in the RL context. To address the problem, we present a novel contrastive prompt ensemble (ConPE) framework which utilizes a pretrained vision-language model and a set of visual prompts, thus enables efficient policy learning and adaptation upon a wide range of environmental and physical changes encountered by embodied agents. Specifically, we devise a guided-attention-based ensemble approach with multiple visual prompts on the vision-language model to construct robust state representations. Each prompt is contrastively learned in terms of an individual domain factors that significantly affects the agent's egocentric perception and observation. For a given task, the attention-based ensemble and policy are jointly learned so that the resulting state representations not only generalize to various domains but are also optimized for learning the task. Through experiments, we show that ConPE outperforms other state-of-the-art algorithms for several embodied agent tasks including navigation in AI2THOR, manipulation in Metaworld, and autonomous driving in CARLA, while also improving the sample efficiency of policy learning and adaptation.

Applications/Physics

Fabien Casenave, Brian Staber, Xavier Roynard

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often involve the absence of shape parametrization during the inference stage, leaving us with only mesh discretizations as available data. Learning simulations from such mesh-based representations poses significant challenges, with recent advances relying heavily on deep graph neural networks to overcome the limitations of conventional machine learning approaches. Despite their promising results, graph neural networks exhibit certain drawbacks, including their dependency on extensive datasets and limitations in providing built-in predictive uncertainties or handling large meshes. In this work, we propose a machine learning method that do not rely on graph neural networks. Complex geometrical shapes and variations with fixed topology are dealt with using well-known mesh morphing onto a common support, combined with classical dimensionality reduction techniques and Gaussian processes. The proposed methodology can easily deal with large meshes without the need for explicit shape parameterization and provides crucial predictive uncertainties, which are essential for informed decision-making. In the considered numerical experiments, the proposed method is competitive with respect to existing graph neural networks, regarding training efficiency and accuracy of the predictions.