Alexander Tong

Nikolay Malkin

Alexander Tong

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

2024-05-01

ICML.cc/2024/Conference (poster)

Improving and Generalizing Flow-Based Generative Models with Minibatch Optimal Transport

Alexander Tong

Nikolay Malkin

Guillaume Huguet

Yanlei Zhang

Jarrid Rector-Brooks

Kilian FATRAS

Continuous normalizing flows (CNFs) are an attractive generative modeling technique, but they have been held back by limitations in their si… (see more)mulation-based maximum likelihood training. We introduce the generalized \textit{conditional flow matching} (CFM) technique, a family of simulation-free training objectives for CNFs. CFM features a stable regression objective like that used to train the stochastic flow in diffusion models but enjoys the efficient inference of deterministic flow models. In contrast to both diffusion models and prior CNF training algorithms, CFM does not require the source distribution to be Gaussian or require evaluation of its density. A variant of our objective is optimal transport CFM (OT-CFM), which creates simpler flows that are more stable to train and lead to faster inference, as evaluated in our experiments. Furthermore, OT-CFM is the first method to compute dynamic OT in a simulation-free way. Training CNFs with CFM improves results on a variety of conditional and unconditional generation tasks, such as inferring single cell dynamics, unsupervised image translation, and Schrödinger bridge inference.

2024-03-11

TMLR (accepted)

Iterated Denoising Energy Matching for Sampling from Boltzmann Densities

Tara Akhound-Sadegh

Jarrid Rector-Brooks

Joey Bose

Sarthak Mittal

Pablo Lemos

Cheng-Hao Liu

Marcin Sendera

Siamak Ravanbakhsh

Gauthier Gidel

Nikolay Malkin

Alexander Tong

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)

arxiv.org

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

Danqi Liao

Chen Liu

Benjamin W Christensen

Alexander Tong

Guillaume Huguet

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)

Simulation-Free Schrödinger Bridges via Score and Flow Matching

Alexander Tong

Nikolay Malkin

Kilian FATRAS

Lazar Atanackovic

Yanlei Zhang

Guillaume Huguet

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

Alexander Tong

Kanika Madan

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

Alexander Tong

Feng Gao

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)

arxiv.org

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

Trang Nguyen

Alexander Tong

Kanika Madan

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)

arxiv.org

DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets

Lazar Atanackovic

Alexander Tong

Jason Hartford

Leo J Lee

Bo Wang

Neural FIM for learning Fisher information metrics from point cloud data

Oluwadamilola Fasina

Guillaume Huguet

Alexander Tong

Yanlei Zhang

Maximilian Nickel

Ian Adelstein

Smita Krishnaswamy

Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the under… (see more)lying intrinsic geometry of data, diffusion embeddings are inherently limited due to their discrete nature. To this end, we propose neural FIM, a method for computing the Fisher information metric (FIM) from point cloud data - allowing for a continuous manifold model for the data. Neural FIM creates an extensible metric space from discrete point cloud data such that information from the metric can inform us of manifold characteristics such as volume and geodesics. We demonstrate Neural FIM’s utility in selecting parameters for the PHATE visualization method as well as its ability to obtain information pertaining to local volume illuminating branching points and cluster centers embeddings of a toy dataset and two single-cell datasets of IPSC reprogramming and PBMCs (immune cells).

2023-07-03

Proceedings of the 40th International Conference on Machine Learning (published)

Simulation-Free Schrödinger Bridges via Score and Flow Matching

Alexander Tong

Nikolay Malkin

Kilian FATRAS

Lazar Atanackovic

Yanlei Zhang

Guillaume Huguet

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

2023-06-19

ICML.cc/2023/Workshop/Frontiers4LCD (published)

Graph Fourier MMD for Signals on Graphs

Samuel Leone

Aarthi Venkat

Guillaume Huguet

Alexander Tong

Smita Krishnaswamy

While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little at… (see more)tention has been given to computing such distances for distributions on graphs. However, there has been a marked increase in data that either lies on graph (such as protein interaction networks) or can be modeled as a graph (single cell data), particularly in the biomedical sciences. Thus, it becomes important to find ways to compare signals defined on such graphs. Here, we propose Graph Fourier MMD (GFMMD), a novel distance between distributions and signals on graphs. GFMMD is defined via an optimal witness function that is both smooth on the graph and maximizes the difference in expectation between the pair of distributions on the graph. We find an analytical solution to this optimization problem as well as an embedding of distributions that results from this method. We also prove several properties of this method including scale invariance and applicability to disconnected graphs. We showcase it on graph benchmark datasets as well on single cell RNA-sequencing data analysis. In the latter, we use the GFMMD-based gene embeddings to find meaningful gene clusters. We also propose a novel type of score for gene selection called gene localization score which helps select genes for cellular state space characterization.

2023-05-21

SampTA/2023/Conference (published)