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Applications · Physics

Tailin Wu, Takashi Maruyama, Long Wei, Tao Zhang, Yilun Du, Gianluca Iaccarino, Jure Leskovec

Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem that arises across fields such as mechanical engineering to aerospace engineering. Inverse design is typically formulated as an optimization problem, with recent works leveraging optimization across learned dynamics models. However, as models are optimized they tend to fall into adversarial modes, preventing effective sampling. We illustrate that by instead optimizing over the learned energy function captured by the diffusion model, we can avoid such adversarial examples and significantly improve design performance. We further illustrate how such a design system is compositional, enabling us to combine multiple different diffusion models representing subcomponents of our desired system to design systems with every specified component. In an N-body interaction task and a challenging 2D multi-airfoil design task, we demonstrate that by composing the learned diffusion model at test time, our method allows us to design initial states and boundary shapes that are more complex than those in the training data. Our method generalizes to more objects for N-body dataset and discovers formation flying to minimize drag in the multi-airfoil design task. Project website and code can be found at https://github.com/AI4Science-WestlakeU/cindm.

Deep Learning · Generative Models and Autoencoders

Chenhao Li, Elijah Stanger-Jones, Steve Heim, Sang bae Kim

Motion trajectories offer reliable references for physics-based motion learning but suffer from sparsity, particularly in regions that lack sufficient data coverage. To address this challenge, we introduce a self-supervised, structured representation and generation method that extracts spatial-temporal relationships in periodic or quasi-periodic motions. The motion dynamics in a continuously parameterized latent space enable our method to enhance the interpolation and generalization capabilities of motion learning algorithms. The motion learning controller, informed by the motion parameterization, operates online tracking of a wide range of motions, including targets unseen during training. With a fallback mechanism, the controller dynamically adapts its tracking strategy and automatically resorts to safe action execution when a potentially risky target is proposed. By leveraging the identified spatial-temporal structure, our work opens new possibilities for future advancements in general motion representation and learning algorithms.

Applications · Physics

Ashutosh Singh, Ricardo Borsoi, Deniz Erdogmus, Tales Imbiriba

Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based solutions face important challenges when dealing with spatio-temporal PDEs over long time scales. Specifically, the current theory of NOs does not present a systematic framework to perform data assimilation and efficiently correct the evolution of PDE solutions over time based on sparsely sampled noisy measurements. In this paper, we propose a learning-based state-space approach to compute the solution operators to infinite-dimensional semilinear PDEs. Exploiting the structure of semilinear PDEs and the theory of nonlinear observers in function spaces, we develop a flexible recursive method that allows for both prediction and data assimilation by combining prediction and correction operations. The proposed framework is capable of producing fast and accurate predictions over long time horizons, dealing with irregularly sampled noisy measurements to correct the solution, and benefits from the decoupling between the spatial and temporal dynamics of this class of PDEs. We show through experiments on the Kuramoto-Sivashinsky, Navier-Stokes and Korteweg-de Vries equations that the proposed model is robust to noise and can leverage arbitrary amounts of measurements to correct its prediction over a long time horizon with little computational overhead.

Zhen Liu, Yao Feng, Yuliang Xiu, Weiyang Liu, Liam Paull, Michael J Black, Bernhard Schoelkopf

The creation of photorealistic virtual worlds requires the accurate modeling of 3D surface geometry for a wide range of objects. For this, meshes are appealing since they enable 1) fast physics-based rendering with realistic material and lighting, 2) physical simulation, and 3) are memory-efficient for modern graphics pipelines. Recent work on reconstructing and statistically modeling 3D shape, however, has critiqued meshes as being topologically inflexible. To capture a wide range of object shapes, any 3D representation must be able to model solid, watertight, shapes as well as thin, open, surfaces. Recent work has focused on the former, and methods for reconstructing open surfaces do not support fast reconstruction with material and lighting or unconditional generative modelling. Inspired by the observation that open surfaces can be seen as islands floating on watertight surfaces, we parametrize open surfaces by defining a manifold signed distance field on watertight templates. With this parametrization, we further develop a grid-based and differentiable representation that parametrizes both watertight and non-watertight meshes of arbitrary topology. Our new representation, called Ghost-on-the-Shell (G-Shell), enables two important applications: differentiable rasterization-based reconstruction from multiview images and generative modelling of non-watertight meshes. We empirically demonstrate that G-Shell achieves state-of-the-art performance on non-watertight mesh reconstruction and generation tasks, while also performing effectively for watertight meshes.

Optimization · Sampling and Optimization

Nick Richardson, Deniz Oktay, Yaniv Ovadia, James Bowden, Ryan P Adams

Integrals with discontinuous integrands are ubiquitous, arising from discrete structure in applications like topology optimization, graphics, and computational geometry. These integrals are often part of a forward model in an inverse problem where it is necessary to reason backwards about the parameters, ideally using gradient-based optimization. Monte Carlo methods are widely used to estimate the value of integrals, but this results in a non-differentiable approximation that is amenable to neither conventional automatic differentiation nor reparameterization-based gradient methods. This significantly disrupts efforts to integrate machine learning methods in areas that exhibit these discontinuities: physical simulation and robotics, design, graphics, and computational geometry. Although bespoke domain-specific techniques can handle special cases, a general methodology to wield automatic differentiation in these discrete contexts is wanting. We introduce a differentiable variant of the simple Monte Carlo estimator which samples line segments rather than points from the domain. We justify our estimator analytically as conditional Monte Carlo and demonstrate the diverse functionality of the method as applied to image stylization, topology optimization, and computational geometry.

Applications · Chemistry and Drug Discovery

Saba Ghaffari, Ehsan Saleh, Alex Schwing, Yu-Xiong Wang, Martin Burke, Saurabh Sinha

Protein design, a grand challenge of the day, involves optimization on a fitness landscape, and leading methods adopt a model-based approach where a model is trained on a training set (protein sequences and fitness) and proposes candidates to explore next. These methods are challenged by sparsity of high-fitness samples in the training set, a problem that has been in the literature. A less recognized but equally important problem stems from the distribution of training samples in the design space: leading methods are not designed for scenarios where the desired optimum is in a region that is not only poorly represented in training data, but also relatively far from the highly represented low-fitness regions. We show that this problem of “separation” in the design space is a significant bottleneck in existing model-based optimization tools and propose a new approach that uses a novel VAE as its search model to overcome the problem. We demonstrate its advantage over prior methods in robustly finding improved samples, regardless of the imbalance and separation between low- and high-fitness samples. Our comprehensive benchmark on real and semi-synthetic protein datasets as well as solution design for physics-informed neural networks, showcases the generality of our approach in discrete and continuous design spaces. Our implementation is available at https://github.com/sabagh1994/PGVAE.

Deep Learning · Other Representation Learning

Daniil Kirilenko, Vitaliy Vorobyov, Aleksey Kovalev, Aleksandr Panov

Object-centric architectures usually apply a differentiable module to the entire feature map to decompose it into sets of entity representations called slots. Some of these methods structurally resemble clustering algorithms, where the cluster's center in latent space serves as a slot representation. Slot Attention is an example of such a method, acting as a learnable analog of the soft k-means algorithm. Our work employs a learnable clustering method based on the Gaussian Mixture Model. Unlike other approaches, we represent slots not only as centers of clusters but also incorporate information about the distance between clusters and assigned vectors, leading to more expressive slot representations. Our experiments demonstrate that using this approach instead of Slot Attention improves performance in object-centric scenarios, achieving state-of-the-art results in the set property prediction task.

Wanru Zhao, Yihong Chen, Royson Lee, Xinchi Qiu, Yan Gao, Hongxiang Fan, Nic Lane

Pretrained large language models (LLMs) have emerged as a cornerstone in modern natural language processing, with their utility expanding to various applications and languages. However, the fine-tuning of multilingual LLMs, particularly for low-resource languages, is fraught with challenges steming from data-sharing restrictions (the physical border) and from the inherent linguistic differences (the linguistic border). These barriers hinder users of various languages, especially those in low-resource regions, from fully benefiting from the advantages of LLMs.To overcome these challenges, we propose the Federated Prompt Tuning Paradigm for Multilingual Scenarios, which leverages parameter-efficient fine-tuning in a manner that preserves user privacy. We have designed a comprehensive set of experiments and introduced the concept of "language distance" to highlight the several strengths of this paradigm. Even under computational constraints, our method not only bolsters data efficiency but also facilitates mutual enhancements across languages, particularly benefiting low-resource ones. Compared to traditional local crosslingual transfer tuning methods, our approach achieves a 6.9\% higher accuracy, reduces the training parameters by over 99\%, and demonstrates stronger cross-lingual generalization. Such findings underscore the potential of our approach to promote social equality, ensure user privacy, and champion linguistic diversity.

Deep Learning · Large Language Models

Sehyun Kwon, Jaden Park, Minkyu Kim, Jaewoong Cho, Ernest K Ryu, Kangwook Lee

Classical clustering methods do not provide users with direct control of the clustering results, and the clustering results may not be consistent with the relevant criterion that a user has in mind. In this work, we present a new methodology for performing image clustering based on user-specified criteria in the form of text by leveraging modern Vision-Language Models and Large Language Models. We call our method Image Clustering Conditioned on Text Criteria (IC$|$TC), and it represents a different paradigm of image clustering. IC$|$TC requires a minimal and practical degree of human intervention and grants the user significant control over the clustering results in return. Our experiments show that IC$|$TC can effectively cluster images with various criteria, such as human action, physical location, or the person's mood, significantly outperforming baselines.

Applications · Physics

Tatsunori Taniai, Ryo Igarashi, Yuta Suzuki, Naoya Chiba, Kotaro Saito, Yoshitaka Ushiku, Kanta Ono

Predicting physical properties of materials from their crystal structures is a fundamental problem in materials science. In peripheral areas such as the prediction of molecular properties, fully connected attention networks have been shown to be successful. However, unlike these finite atom arrangements, crystal structures are infinitely repeating, periodic arrangements of atoms, whose fully connected attention results in *infinitely connected attention*. In this work, we show that this infinitely connected attention can lead to a computationally tractable formulation, interpreted as *neural potential summation*, that performs infinite interatomic potential summations in a deeply learned feature space. We then propose a simple yet effective Transformer-based encoder architecture for crystal structures called *Crystalformer*. Compared to an existing Transformer-based model, the proposed model requires only 29.4% of the number of parameters, with minimal modifications to the original Transformer architecture. Despite the architectural simplicity, the proposed method outperforms state-of-the-art methods for various property regression tasks on the Materials Project and JARVIS-DFT datasets.

Deep Learning · Graph Neural Networks

Yunyang Li, Yusong Wang, Lin Huang, Han Yang, Xinran Wei, Jia Zhang, Tong Wang, Zun Wang, Bin Shao, Tie-Yan Liu

Computational simulation of chemical and biological systems using *ab initio* molecular dynamics has been a challenge over decades. Researchers have attempted to address the problem with machine learning and fragmentation-based methods. However, the two approaches fail to give a satisfactory description of long-range and many-body interactions, respectively. Inspired by fragmentation-based methods, we propose the Long-Short-Range Message-Passing (LSR-MP) framework as a generalization of the existing equivariant graph neural networks (EGNNs) with the intent to incorporate long-range interactions efficiently and effectively. We apply the LSR-MP framework to the recently proposed ViSNet and demonstrate the state-of-the-art results with up to 40% MAE reduction for molecules in MD22 and Chignolin datasets. Consistent improvements to various EGNNs will also be discussed to illustrate the general applicability and robustness of our LSR-MP framework. The code for our experiments and trained model weights could be found at https://github.com/liyy2/LSR-MP.

Deep Learning · Large Language Models

Huaixiu Steven Zheng, Swaroop Mishra, Xinyun Chen, Heng-Tze Cheng, Ed H. Chi, Quoc V Le, Denny Zhou

We present STEP-BACK PROMPTING, a simple prompting technique that enables LLMs to do abstractions to derive high-level concepts and first principles from instances containing specific details. Using the concepts and principles to guide reasoning, LLMs significantly improve their abilities in following a correct reasoning path towards the solution. We conduct experiments of STEP-BACK PROMPTING with PaLM-2L, GPT-4 and Llama2-70B models, and observe substantial performance gains on various challenging reasoning-intensive tasks including STEM, Knowledge QA, and Multi-Hop Reasoning. For instance, STEP-BACK PROMPTING improves PaLM-2L performance on MMLU (Physics and Chemistry) by 7% and 11% respectively, TimeQA by 27%, and MuSiQue by 7%.

Deep Learning · Generative Models and Autoencoders

Zhengyao Jiang, Yingchen Xu, Nolan Wagener, Yicheng Luo, Michael Janner, Edward Grefenstette, Tim Rocktaeschel, Yuandong Tian

Humanoid control is an important research challenge offering avenues for integration into human-centric infrastructures and enabling physics-driven humanoid animations.The daunting challenges in this field stem from the difficulty of optimizing in high-dimensional action spaces and the instability introduced by the bipedal morphology of humanoids. However, the extensive collection of human motion-captured data and the derived datasets of humanoid trajectories, such as MoCapAct, paves the way to tackle these challenges. In this context, we present Humanoid Generalist Autoencoding Planner (H-GAP), a state-action trajectory generative model trained on humanoid trajectories derived from human motion-captured data, capable of adeptly handling downstream control tasks with Model Predictive Control (MPC).For 56 degrees of freedom humanoid, we empirically demonstrate that H-GAP learns to represent and generate a wide range of motor behaviors. Further, without any learning from online interactions, it can also flexibly transfer these behaviours to solve novel downstream control tasks via planning. Notably, H-GAP excels established MPC baselines with access to the ground truth model, and is superior or comparable to offline RL methods trained for individual tasks.Finally, we do a series of empirical studies on the scaling properties of H-GAP, showing the potential for performance gains via additional data but not computing.

Applications · Physics

Juncai He, Xinliang Liu, Jinchao Xu

In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural operator as follows: the output of the $i$-th neuron in a nonlinear operator layer is defined by $\mathcal O_i(u) = \sigma\left( \sum_j \mathcal W_{ij} u + \mathcal B_{ij}\right)$. Here, $\mathcal W_{ij}$ denotes the bounded linear operator connecting $j$-th input neuron to $i$-th output neuron, and the bias $\mathcal B_{ij}$ takes the form of a function rather than a scalar. Given its new universal approximation property, the efficient parameterization of the bounded linear operators between two neurons (Banach spaces) plays a critical role. As a result, we introduce MgNO, utilizing multigrid structures to parameterize these linear operators between neurons. This approach offers both mathematical rigor and practical expressivity. Additionally, MgNO obviates the need for conventional lifting and projecting operators typically required in previous neural operators. Moreover, it seamlessly accommodates diverse boundary conditions. Our empirical observations reveal that MgNO exhibits superior ease of training compared to CNN-based models, while also displaying a reduced susceptibility to overfitting when contrasted with spectral-type neural operators. We demonstrate the efficiency and accuracy of our method with consistently state-of-the-art performance on different types of partial differential equations (PDEs).

Miscellaneous Aspects of Machine Learning · Representation Learning

Tao Yu, Toni Liu, Albert Tseng, Christopher De Sa

Hyperbolic space has proven to be well-suited for capturing hierarchical relations in data, such as trees and directed acyclic graphs. Prior work introduced the concept of entailment cones, which uses partial orders defined by nested cones in the Poincar\'e ball to model hierarchies. Here, we introduce the ``shadow cones" framework, a physics-inspired entailment cone construction. Specifically, we model partial orders as subset relations between shadows formed by a light source and opaque objects in hyperbolic space. The shadow cones framework generalizes entailment cones to a broad class of formulations and hyperbolic space models beyond the Poincar\'e ball. This results in clear advantages over existing constructions: for example, shadow cones possess better optimization properties over constructions limited to the Poincar\'e ball. Our experiments on datasets of various sizes and hierarchical structures show that shadow cones consistently and significantly outperform existing entailment cone constructions. These results indicate that shadow cones are an effective way to model partial orders in hyperbolic space, offering physically intuitive and novel insights about the nature of such structures.

Applications · Neuroscience, Cognitive Science

T. Anderson Keller, Lyle Muller, Terrence Sejnowski, Max Welling

Traveling waves of neural activity have been observed throughout the brain at a diversity of regions and scales; however, their precise computational role is still debated. One physically inspired hypothesis suggests that the cortical sheet may act like a wave-propagating system capable of invertibly storing a short-term memory of sequential stimuli through induced waves traveling across the cortical surface, and indeed many experimental results from neuroscience correlate wave activity with memory tasks. To date, however, the computational implications of this idea have remained hypothetical due to the lack of a simple recurrent neural network architecture capable of exhibiting such waves. In this work, we introduce a model to fill this gap, which we denote the Wave-RNN (wRNN), and demonstrate how such an architecture indeed efficiently encodes the recent past through a suite of synthetic memory tasks where wRNNs learn faster and reach significantly lower error than wave-free counterparts. We further explore the implications of this memory storage system on more complex sequence modeling tasks such as sequential image classification and find that wave-based models not only again outperform comparable wave-free RNNs while using significantly fewer parameters, but additionally perform comparably to more complex gated architectures such as LSTMs and GRUs.

Applications · Physics

Yeongwoo Song, Hawoong Jeong

Recent advances in deep learning for physics have focused on discovering shared representations of target systems by incorporating physics priors or inductive biases into neural networks. While effective, these methods are limited to the system domain, where the type of system remains consistent and thus cannot ensure the adaptation to new, or unseen physical systems governed by different laws. For instance, a neural network trained on a mass-spring system cannot guarantee accurate predictions for the behavior of a two-body system or any other system with different physical laws.In this work, we take a significant leap forward by targeting cross domain generalization within the field of Hamiltonian dynamics. We model our system with a graph neural network (GNN) and employ a meta learning algorithm to enable the model to gain experience over a distribution of systems and make it adapt to new physics. Our approach aims to learn a unified Hamiltonian representation that is generalizable across multiple system domains, thereby overcoming the limitations of system-specific models. We demonstrate that the meta-trained model captures the generalized Hamiltonian representation that is consistent across different physical domains.Overall, through the use of meta learning, we offer a framework that achieves cross domain generalization, providing a step towards a unified model for understanding a wide array of dynamical systems via deep learning.

Tim De Ryck, Florent Bonnet, Siddhartha Mishra, Emmanuel de Bézenac

In this paper, we investigate the behavior of gradient descent algorithms in physics-informed machine learning methods like PINNs, which minimize residuals connected to partial differential equations (PDEs). Our key result is that the difficulty in training these models is closely related to the conditioning of a specific differential operator. This operator, in turn, is associated to the Hermitian square of the differential operator of the underlying PDE. If this operator is ill-conditioned, it results in slow or infeasible training. Therefore, preconditioning this operator is crucial. We employ both rigorous mathematical analysis and empirical evaluations to investigate various strategies, explaining how they better condition this critical operator, and consequently improve training.

Optimization · Sampling and Optimization

Marien Renaud, Jiaming Liu, Valentin De Bortoli, Andres Almansa, Ulugbek Kamilov

Posterior sampling has been shown to be a powerful Bayesian approach for solving imaging inverse problems. The recent plug-and-play unadjusted Langevin algorithm (PnP-ULA) has emerged as a promising method for Monte Carlo sampling and minimum mean squared error (MMSE) estimation by combining physical measurement models with deep-learning priors specified using image denoisers. However, the intricate relationship between the sampling distribution of PnP-ULA and the mismatched data-fidelity and denoiser has not been theoretically analyzed. We address this gap by proposing a posterior-$L_2$ pseudometric and using it to quantify an explicit error bound for PnP-ULA under mismatched posterior distribution. We numerically validate our theory on several inverse problems such as sampling from Gaussian mixture models and image deblurring. Our results suggest that the sensitivity of the sampling distribution of PnP-ULA to a mismatch in the measurement model and the denoiser can be precisely characterized.

Applications · Robotics

Guillaume Bono, Leonid Antsfeld, Assem Sadek, Gianluca Monaci, Christian Wolf

Agents navigating in 3D environments require some form of memory, which should hold a compact and actionable representation of the history of observations useful for decision taking and planning. In most end-to-end learning approaches the representation is latent and usually does not have a clearly defined interpretation, whereas classical robotics addresses this with scene reconstruction resulting in some form of map, usually estimated with geometry and sensor models and/or learning. In this work we propose to learn an actionable representation of the scene independently of the targeted downstream task and without explicitly optimizing reconstruction. The learned representation is optimized by a blind auxiliary agent trained to navigate with it on multiple short sub episodes branching out from a waypoint and, most importantly, without any direct visual observation. We argue and show that the blindness property is important and forces the (trained) latent representation to be the only means for planning. With probing experiments we show that the learned representation optimizes navigability and not reconstruction. On downstream tasks we show that it is robust to changes in distribution, in particular the sim2real gap, which we evaluate with a real physical robot in a real office building, significantly improving performance.