Alexander Tong

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-… (see more)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 (preprint)

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-… (see more)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 (preprint)

Assessing Neural Network Representations During Training Using Noise-Resilient Diffusion Spectral Entropy

Danqi Liao

Chen Liu

Benjamin W Christensen

Guillaume Huguet

Guy Wolf

Maximilian Nickel

Ian Adelstein

Smita Krishnaswamy

Entropy and mutual information in neural networks provide rich information on the learning process, but they have proven difficult to comput… (see more)e reliably in high dimensions. Indeed, in noisy and high-dimensional data, traditional estimates in ambient dimensions approach a fixed entropy and are prohibitively hard to compute. To address these issues, we leverage data geometry to access the underlying manifold and reliably compute these information-theoretic measures. Specifically, we define diffusion spectral entropy (DSE) in neural representations of a dataset as well as diffusion spectral mutual information (DSMI) between different variables representing data. First, we show that they form noise-resistant measures of intrinsic dimensionality and relationship strength in high-dimensional simulated data that outperform classic Shannon entropy, nonparametric estimation, and mutual information neural estimation (MINE). We then study the evolution of representations in classification networks with supervised learning, self-supervision, or overfitting. We observe that (1) DSE of neural representations increases during training; (2) DSMI with the class label increases during generalizable learning but stays stagnant during overfitting; (3) DSMI with the input signal shows differing trends: on MNIST it increases, while on CIFAR-10 and STL-10 it decreases. Finally, we show that DSE can be used to guide better network initialization and that DSMI can be used to predict downstream classification accuracy across 962 models on ImageNet.

2024-01-01

CISS (published)

Learnable Filters for Geometric Scattering Modules

Frederik Wenkel

Dhananjay Bhaskar

Kincaid MacDonald

Jackson Grady

Michael Perlmutter

Smita Krishnaswamy

Guy Wolf

2024-01-01

IEEE Transactions on Signal Processing (published)

Metric Flow Matching for Smooth Interpolations on the Data Manifold

Kacper Kapusniak

Peter Potaptchik

Teodora Reu

Leo Zhang

Michael M. Bronstein

Joey Bose

Francesco Di Giovanni

Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source dist… (see more)ribution into a target distribution. Despite being a fundamental building block, conditional paths have been designed principally under the assumption of Euclidean geometry, resulting in straight interpolations. However, this can be particularly restrictive for tasks such as trajectory inference, where straight paths might lie outside the data manifold, thus failing to capture the underlying dynamics giving rise to the observed marginals. In this paper, we propose Metric Flow Matching (MFM), a novel simulation-free framework for conditional flow matching where interpolants are approximate geodesics learned by minimizing the kinetic energy of a data-induced Riemannian metric. This way, the generative model matches vector fields on the data manifold, which corresponds to lower uncertainty and more meaningful interpolations. We prescribe general metrics to instantiate MFM, independent of the task, and test it on a suite of challenging problems including LiDAR navigation, unpaired image translation, and modeling cellular dynamics. We observe that MFM outperforms the Euclidean baselines, particularly achieving SOTA on single-cell trajectory prediction.

2024-01-01

NeurIPS (published)

Sequence-Augmented SE(3)-Flow Matching For Conditional Protein Generation.

James Vuckovic

Eric Laufer

Cheng-Hao Liu

Michael M. Bronstein

2024-01-01

Neural Information Processing Systems (published)

dblp.uni-trier.de

Simulation-Free Schrödinger Bridges via Score and Flow Matching

Yanlei Zhang

We present simulation-free score and flow matching ([SF]…

2024-01-01

AISTATS (published)

Causal Discovery in Gene Regulatory Networks with GFlowNet: Towards Scalability in Large Systems

Trang Nguyen

Kanika Madan

Yoshua Bengio

Dianbo Liu

Understanding causal relationships within Gene Regulatory Networks (GRNs) is essential for unraveling the gene interactions in cellular proc… (see more)esses. However, causal discovery in GRNs is a challenging problem for multiple reasons including the existence of cyclic feedback loops and uncertainty that yields diverse possible causal structures. Previous works in this area either ignore cyclic dynamics (assume acyclic structure) or struggle with scalability. We introduce Swift-DynGFN as a novel framework that enhances causal structure learning in GRNs while addressing scalability concerns. Specifically, Swift-DynGFN exploits gene-wise independence to boost parallelization and to lower computational cost. Experiments on real single-cell RNA velocity and synthetic GRN datasets showcase the advancement in learning causal structure in GRNs and scalability in larger systems.

2023-10-27

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

Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms

Michael Perlmutter

Feng Gao

Guy Wolf

Matthew Hirn

The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. R… (see more)ecently, several works have introduced generalizations of the scattering transform for non-Euclidean settings such as graphs. Our work builds upon these constructions by introducing windowed and non-windowed geometric scattering transforms for graphs based upon a very general class of asymmetric wavelets. We show that these asymmetric graph scattering transforms have many of the same theoretical guarantees as their symmetric counterparts. As a result, the proposed construction unifies and extends known theoretical results for many of the existing graph scattering architectures. In doing so, this work helps bridge the gap between geometric scattering and other graph neural networks by introducing a large family of networks with provable stability and invariance guarantees. These results lay the groundwork for future deep learning architectures for graph-structured data that have learned filters and also provably have desirable theoretical properties.

2023-10-25

SIAM Journal on Mathematics of Data Science (published)

Causal Inference in Gene Regulatory Networks with GFlowNet: Towards Scalability in Large Systems

Trang Nguyen

Kanika Madan

Yoshua Bengio

Dianbo Liu

Understanding causal relationships within Gene Regulatory Networks (GRNs) is essential for unraveling the gene interactions in cellular proc… (see more)esses. However, causal discovery in GRNs is a challenging problem for multiple reasons including the existence of cyclic feedback loops and uncertainty that yields diverse possible causal structures. Previous works in this area either ignore cyclic dynamics (assume acyclic structure) or struggle with scalability. We introduce Swift-DynGFN as a novel framework that enhances causal structure learning in GRNs while addressing scalability concerns. Specifically, Swift-DynGFN exploits gene-wise independence to boost parallelization and to lower computational cost. Experiments on real single-cell RNA velocity and synthetic GRN datasets showcase the advancement in learning causal structure in GRNs and scalability in larger systems.

2023-10-05

ArXiv (preprint)

Causal Inference in Gene Regulatory Networks with GFlowNet: Towards Scalability in Large Systems

Trang Nguyen

Kanika Madan

Yoshua Bengio

Dianbo Liu

Understanding causal relationships within Gene Regulatory Networks (GRNs) is essential for unraveling the gene interactions in cellular proc… (see more)esses. However, causal discovery in GRNs is a challenging problem for multiple reasons including the existence of cyclic feedback loops and uncertainty that yields diverse possible causal structures. Previous works in this area either ignore cyclic dynamics (assume acyclic structure) or struggle with scalability. We introduce Swift-DynGFN as a novel framework that enhances causal structure learning in GRNs while addressing scalability concerns. Specifically, Swift-DynGFN exploits gene-wise independence to boost parallelization and to lower computational cost. Experiments on real single-cell RNA velocity and synthetic GRN datasets showcase the advancement in learning causal structure in GRNs and scalability in larger systems.

2023-10-05

ArXiv (preprint)