Alexander Tong

proceedings.mlr.press

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

Yanlei Zhang

Continuous normalizing flows (CNFs) are an attractive generative modeling technique, but they have been held back by limitations in their si… (voir plus)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.

2024-03-10

TMLR (accepté)

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… (voir plus)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.

2023-12-31

CISS (publié)

Learnable Filters for Geometric Scattering Modules

Frederik Wenkel

Dhananjay Bhaskar

Kincaid MacDonald

Jackson Grady

Michael Perlmutter

Smita Krishnaswamy

Guy Wolf

2023-12-31

IEEE Transactions on Signal Processing (publié)

arxiv.org

Metric Flow Matching for Smooth Interpolations on the Data Manifold

Kacper Kapuśniak

Peter Potaptchik

Teodora Reu

Leo Zhang

Michael Bronstein

Avishek 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… (voir plus)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.

2023-12-31

NeurIPS (publié)

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

Guillaume Huguet

James Vuckovic

Kilian Fatras

Éric Thibodeau-Laufer

Cheng-Hao Liu

Michael Bronstein

Avishek Joey Bose

2023-12-31

Advances in Neural Information Processing Systems 37 (publié)

Simulation-Free Schrödinger Bridges via Score and Flow Matching

Yanlei Zhang

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

2023-12-31

AISTATS (publié)

proceedings.mlr.press

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… (voir plus)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.

2023-10-26

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

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… (voir plus)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.

2023-10-04

ArXiv (prépublication)

arxiv.org

DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets

Lazar Atanackovic

Jason Hartford

Leo J. Lee

Bo Wang

Yoshua Bengio

One of the grand challenges of cell biology is inferring the gene regulatory network (GRN) which describes interactions between genes and th… (voir plus)eir products that control gene expression and cellular function. We can treat this as a causal discovery problem but with two non-standard challenges: (1) regulatory networks are inherently cyclic so we should not model a GRN as a directed acyclic graph (DAG), and (2) observations have significant measurement noise, so for typical sample sizes there will always be a large equivalence class of graphs that are likely given the data, and we want methods that capture this uncertainty. Existing methods either focus on challenge (1), identifying cyclic structure from dynamics, or on challenge (2) learning complex Bayesian posteriors over DAGs, but not both. In this paper we leverage the fact that it is possible to estimate the "velocity" of gene expression with RNA velocity techniques to develop an approach that addresses both challenges. Because we have access to velocity information, we can treat the Bayesian structure learning problem as a problem of sparse identification of a dynamical system, capturing cyclic feedback loops through time. Since our objective is to model uncertainty over discrete structures, we leverage Generative Flow Networks (GFlowNets) to estimate the posterior distribution over the combinatorial space of possible sparse dependencies. Our results indicate that our method learns posteriors that better encapsulate the distributions of cyclic structures compared to counterpart state-of-the-art Bayesian structure learning approaches.

2023-09-20

NeurIPS.cc/2023/Conference (poster)

Neural FIM for learning Fisher information metrics from point cloud data

Oluwadamilola Fasina

Guillaume Huguet

Yanlei Zhang

Guy Wolf

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… (voir plus)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).

2023-07-02

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

proceedings.mlr.press

Graph Fourier MMD for Signals on Graphs

Samuel Leone

Aarthi Venkat

While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little at… (voir plus)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 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.

2023-05-20

SampTA/2023/Conference (publié)