Siamak Ravanbakhsh

Iterated Denoising Energy Matching for Sampling from Boltzmann Densities

Cheng-Hao Liu

Efficiently generating statistically independent samples from an unnormalized probability distribution, such as equilibrium samples of many-… (voir plus)body systems, is a foundational problem in science. In this paper, we propose Iterated Denoising Energy Matching (iDEM), an iterative algorithm that uses a novel stochastic score matching objective leveraging solely the energy function and its gradient -- and no data samples -- to train a diffusion-based sampler. Specifically, iDEM alternates between (I) sampling regions of high model density from a diffusion-based sampler and (II) using these samples in our stochastic matching objective to further improve the sampler. iDEM is scalable to high dimensions as the inner matching objective, is simulation-free, and requires no MCMC samples. Moreover, by leveraging the fast mode mixing behavior of diffusion, iDEM smooths out the energy landscape enabling efficient exploration and learning of an amortized sampler. We evaluate iDEM on a suite of tasks ranging from standard synthetic energy functions to invariant

2024-02-09

ArXiv (prépublication)

Iterated Denoising Energy Matching for Sampling from Boltzmann Densities

Cheng-Hao Liu

Efficiently generating statistically independent samples from an unnormalized probability distribution, such as equilibrium samples of many-… (voir plus)body systems, is a foundational problem in science. In this paper, we propose Iterated Denoising Energy Matching (iDEM), an iterative algorithm that uses a novel stochastic score matching objective leveraging solely the energy function and its gradient -- and no data samples -- to train a diffusion-based sampler. Specifically, iDEM alternates between (I) sampling regions of high model density from a diffusion-based sampler and (II) using these samples in our stochastic matching objective to further improve the sampler. iDEM is scalable to high dimensions as the inner matching objective, is simulation-free, and requires no MCMC samples. Moreover, by leveraging the fast mode mixing behavior of diffusion, iDEM smooths out the energy landscape enabling efficient exploration and learning of an amortized sampler. We evaluate iDEM on a suite of tasks ranging from standard synthetic energy functions to invariant

2024-02-09

ArXiv (prépublication)

Iterated Denoising Energy Matching for Sampling from Boltzmann Densities

Cheng-Hao Liu

Efficiently generating statistically independent samples from an unnormalized probability distribution, such as equilibrium samples of many-… (voir plus)body systems, is a foundational problem in science. In this paper, we propose Iterated Denoising Energy Matching (iDEM), an iterative algorithm that uses a novel stochastic score matching objective leveraging solely the energy function and its gradient -- and no data samples -- to train a diffusion-based sampler. Specifically, iDEM alternates between (I) sampling regions of high model density from a diffusion-based sampler and (II) using these samples in our stochastic matching objective to further improve the sampler. iDEM is scalable to high dimensions as the inner matching objective, is simulation-free, and requires no MCMC samples. Moreover, by leveraging the fast mode mixing behavior of diffusion, iDEM smooths out the energy landscape enabling efficient exploration and learning of an amortized sampler. We evaluate iDEM on a suite of tasks ranging from standard synthetic energy functions to invariant

2024-02-09

ArXiv (prépublication)

Iterated Denoising Energy Matching for Sampling from Boltzmann Densities

Cheng-Hao Liu

Efficiently generating statistically independent samples from an unnormalized probability distribution, such as equilibrium samples of many-… (voir plus)body systems, is a foundational problem in science. In this paper, we propose Iterated Denoising Energy Matching (iDEM), an iterative algorithm that uses a novel stochastic score matching objective leveraging solely the energy function and its gradient -- and no data samples -- to train a diffusion-based sampler. Specifically, iDEM alternates between (I) sampling regions of high model density from a diffusion-based sampler and (II) using these samples in our stochastic matching objective to further improve the sampler. iDEM is scalable to high dimensions as the inner matching objective, is simulation-free, and requires no MCMC samples. Moreover, by leveraging the fast mode mixing behavior of diffusion, iDEM smooths out the energy landscape enabling efficient exploration and learning of an amortized sampler. We evaluate iDEM on a suite of tasks ranging from standard synthetic energy functions to invariant

2024-02-09

ArXiv (prépublication)

E(3)-Equivariant Mesh Neural Networks

Thuan N.a. Trang

Nhat-Khang Ngô

Daniel Levy

Thieu N. Vo

Truong Son Hy

Triangular meshes are widely used to represent three-dimensional objects. As a result, many recent works have address the need for geometric… (voir plus) deep learning on 3D mesh. However, we observe that the complexities in many of these architectures does not translate to practical performance, and simple deep models for geometric graphs are competitive in practice. Motivated by this observation, we minimally extend the update equations of E(n)-Equivariant Graph Neural Networks (EGNNs) (Satorras et al., 2021) to incorporate mesh face information, and further improve it to account for long-range interactions through hierarchy. The resulting architecture, Equivariant Mesh Neural Network (EMNN), outperforms other, more complicated equivariant methods on mesh tasks, with a fast run-time and no expensive pre-processing. Our implementation is available at https://github.com/HySonLab/EquiMesh

2024-02-07

ArXiv (prépublication)

On Diffusion Modeling for Anomaly Detection

Known for their impressive performance in generative modeling, diffusion models are attractive candidates for density-based anomaly detectio… (voir plus)n. This paper investigates different variations of diffusion modeling for unsupervised and semi-supervised anomaly detection. In particular, we find that Denoising Diffusion Probability Models (DDPM) are performant on anomaly detection benchmarks yet computationally expensive. By simplifying DDPM in application to anomaly detection, we are naturally led to an alternative approach called Diffusion Time Estimation (DTE). DTE estimates the distribution over diffusion time for a given input and uses the mode or mean of this distribution as the anomaly score. We derive an analytical form for this density and leverage a deep neural network to improve inference efficiency. Through empirical evaluations on the ADBench benchmark, we demonstrate that all diffusion-based anomaly detection methods perform competitively for both semi-supervised and unsupervised settings. Notably, DTE achieves orders of magnitude faster inference time than DDPM, while outperforming it on this benchmark. These results establish diffusion-based anomaly detection as a scalable alternative to traditional methods and recent deep-learning techniques for standard unsupervised and semi-supervised anomaly detection settings.

2024-01-16

ICLR.cc/2024/Conference (spotlight)

Efficient Dynamics Modeling in Interactive Environments with Koopman Theory

Arnab Kumar Mondal

Siba Smarak Panigrahi

Sai Rajeswar

Kaleem Siddiqi

The accurate modeling of dynamics in interactive environments is critical for successful long-range prediction. Such a capability could adva… (voir plus)nce Reinforcement Learning (RL) and Planning algorithms, but achieving it is challenging. Inaccuracies in model estimates can compound, resulting in increased errors over long horizons. We approach this problem from the lens of Koopman theory, where the nonlinear dynamics of the environment can be linearized in a high-dimensional latent space. This allows us to efficiently parallelize the sequential problem of long-range prediction using convolution while accounting for the agent’s action at every time step. Our approach also enables stability analysis and better control over gradients through time. Taken together, these advantages result in significant improvement over the existing approaches, both in the efficiency and the accuracy of modeling dynamics over extended horizons. We also show that this model can be easily incorporated into dynamics modeling for model-based planning and model-free RL and report promising experimental results.

2024-01-16

ICLR.cc/2024/Conference (poster)

E(3)-Equivariant Mesh Neural Networks

Thuan Nguyen Anh Trang

Khang Nhat Ngo

Daniel Levy

Thieu Vo

Truong Son Hy

Triangular meshes are widely used to represent three-dimensional objects. As a result, many recent works have addressed the need for geometr… (voir plus)ic deep learning on 3D meshes. However, we observe that the complexities in many of these architectures do not translate to practical performance, and simple deep models for geometric graphs are competitive in practice. Motivated by this observation, we minimally extend the update equations of E(n)-Equivariant Graph Neural Networks (EGNNs) (Satorras et al., 2021) to incorporate mesh face information and further improve it to account for long-range interactions through a hierarchy. The resulting architecture, Equivariant Mesh Neural Network (EMNN), outperforms other, more complicated equivariant methods on mesh tasks, with a fast run-time and no expensive preprocessing. Our implementation is available at https://github.com/HySonLab/EquiMesh.

2024-01-01

AISTATS (publié)

Symmetry Breaking and Equivariant Neural Networks

Sékou-Oumar Kaba

Using symmetry as an inductive bias in deep learning has been proven to be a principled approach for sample-efficient model design. However,… (voir plus) the relationship between symmetry and the imperative for equivariance in neural networks is not always obvious. Here, we analyze a key limitation that arises in equivariant functions: their incapacity to break symmetry at the level of individual data samples. In response, we introduce a novel notion of 'relaxed equivariance' that circumvents this limitation. We further demonstrate how to incorporate this relaxation into equivariant multilayer perceptrons (E-MLPs), offering an alternative to the noise-injection method. The relevance of symmetry breaking is then discussed in various application domains: physics, graph representation learning, combinatorial optimization and equivariant decoding.

2023-12-14

ArXiv (prépublication)

Symmetry Breaking and Equivariant Neural Networks

Sékou-Oumar Kaba

Using symmetry as an inductive bias in deep learning has been proven to be a principled approach for sample-efficient model design. However,… (voir plus) the relationship between symmetry and the imperative for equivariance in neural networks is not always obvious. Here, we analyze a key limitation that arises in equivariant functions: their incapacity to break symmetry at the level of individual data samples. In response, we introduce a novel notion of 'relaxed equivariance' that circumvents this limitation. We further demonstrate how to incorporate this relaxation into equivariant multilayer perceptrons (E-MLPs), offering an alternative to the noise-injection method. The relevance of symmetry breaking is then discussed in various application domains: physics, graph representation learning, combinatorial optimization and equivariant decoding.

2023-11-28

NeurIPS.cc/2023/Workshop/NeurReps (présentation orale)

Physics-Informed Transformer Networks

Fabricio Dos Santos

F. Dos

Tara Akhound-Sadegh

Physics-informed neural networks (PINNs) have been recognized as a viable alternative to conventional numerical solvers for Partial Differen… (voir plus)tial Equations (PDEs). The main appeal of PINNs is that since they directly enforce the PDE equation, one does not require access to costly ground truth solutions for training the model. However, a key challenge is their limited generalization across varied initial conditions. Addressing this, our study presents a novel Physics-Informed Transformer (PIT) model for learning the solution operator for PDEs. Using the attention mechanism, PIT learns to leverage the relationships between its initial condition and query points, resulting in a significant improvement in generalization. Moreover, in contrast to existing physics-informed networks, our model is invariant to the discretization of the input domain, providing great flexibility in problem specification and training. We validated our proposed method on the 1D Burgers’ and the 2D Heat equations, demonstrating notable improvement over standard PINN models for operator learning with negligible computational overhead.

2023-10-31

NeurIPS.cc/2023/Workshop/DLDE (poster)