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Alexander Tong

Postdoctorate - Université de Montréal
Supervisor

Publications

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.
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
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
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.
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.
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.
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.
DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets
Lazar Atanackovic
Alexander Tong
Jason Hartford
Leo J Lee
BO WANG
A Heat Diffusion Perspective on Geodesic Preserving Dimensionality Reduction
Guillaume Huguet
Alexander Tong
Edward De Brouwer
Yanlei Zhang
Ian Adelstein
Smita Krishnaswamy
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]…
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.
Single-cell analysis reveals inflammatory interactions driving macular degeneration
Manik Kuchroo
Marcello DiStasio
Eric Song
Eda Calapkulu
Le Zhang
Maryam Ige
Amar H. Sheth
Abdelilah Majdoubi
Madhvi Menon
Alexander Tong
Abhinav Godavarthi
Yu Xing
Scott Gigante
Holly Steach
Jessie Huang
Je-chun Huang
Guillaume Huguet
Janhavi Narain
Kisung You
George Mourgkos … (see 6 more)
Rahul M. Dhodapkar
Matthew Hirn
Bastian Rieck
Smita Krishnaswamy
Brian P. Hafler
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).