Guy Wolf

Biographie

Guy Wolf est professeur titulaire au Département de mathématiques et de statistique (DMS) de l'Université de Montréal (UdeM), titulaire d'une chaire en IA Canada-CIFAR et membre académique principal de Mila (l'Institut québécois d'intelligence artificielle), chercheur associé au CRCHUM (Centre de recherche du Centre hospitalier de l'Université de Montréal) et chercheur principal participant au Laboratoire international Helmholtz pour la dynamique cellulaire causale.

En 2024, il a reçu une bourse de recherche Humboldt pour chercheurs expérimentés, dans le cadre de laquelle il a été professeur invité à l'Université de Heidelberg (2024) et à Helmholtz Munich (2024-2026) en Allemagne. Avant de joindre l'UdeM et Mila, il a été professeur adjoint Gibbs (2015-2018) au sein du programme de mathématiques appliquées, puis chercheur scientifique associé au Département de génétique (2018) de l'Université Yale (Connecticut, États-Unis). Auparavant, il a travaillé comme chercheur postdoctoral (2013-2015) au Département d'informatique de l'École normale supérieure à Paris (France). Il détient un doctorat en informatique de l'Université de Tel-Aviv (Israel) et possède cinq ans d'expérience préalable en conception et développement de logiciels informatiques pour l'analyse de données en contexte militaire.

Ses recherches actuelles portent sur l'apprentissage guidé de représentations pour l'exploration de données, notamment par des méthodes qui exploitent l'apprentissage de variétés (manifold learning) et l'apprentissage profond géométrique pour la réduction de dimensionnalité, la visualisation, le débruitage, l'augmentation de données et la modélisation à gros grains (coarse graining). Bien que ces approches s'appliquent à un large éventail de domaines, il s'intéresse particulièrement à l'intersection de l'IA et de la santé, notamment aux outils facilitant l'analyse exploratoire de données biomédicales, comme dans les domaines de la multiomique sur cellule unique (single-cell multiomics), de la découverte de médicaments et des neurosciences.

Étudiants actuels

Adrien Aumon

Doctorat - UdeM

adrien.aumon@mila.quebec

Semih Cantürk

Doctorat - UdeM

semihcanturk00@gmail.com

Joao Felipe Carneiro Barbosa Rocha

Collaborateur·rice de recherche - Yale University

Co-superviseur⋅e :

joaofelipe.rocha@mila.quebec

sebastian.damrich@mila.quebec

Sebastian Damrich

Collaborateur·rice de recherche - University of Tübingen

Maxine Dussault

Maîtrise recherche - UdeM

Co-superviseur⋅e :

Margarida Carvalho

maxine.dussault@mila.quebec

Stefan Horoi

Doctorat - UdeM

stefan.horoi@mila.quebec

Xiao Huang

Maîtrise recherche - Concordia

Superviseur⋅e principal⋅e :

xiaolong.huang@mila.quebec

Collaborateur·rice alumni - UdeM

guillaume.huguet@mila.quebec

Paul Janson

Doctorat - Concordia

Superviseur⋅e principal⋅e :

myriam.lizotte@mila.quebec

paul.janson@mila.quebec

Doctorat - UdeM

Gabriele Malagoli

Visiteur de recherche indépendant - Helmholtz Munich

gabriele.malagoli@mila.quebec

Philippe Martin

Doctorat - UdeM

Co-superviseur⋅e :

Paul François

philippe.martin@mila.quebec

Paria Mehrbod

Maîtrise recherche - Concordia

Superviseur⋅e principal⋅e :

paria.mehrbod@mila.quebec

Lydia Mezrag

Doctorat - UdeM

lydia.mezrag@mila.quebec

Kevin Moon

Collaborateur·rice de recherche

Sacha Morin

Doctorat - UdeM

Co-superviseur⋅e :

Liam Paull

sacha.morin@mila.quebec

Postdoctorat - Concordia

Superviseur⋅e principal⋅e :

geraldin.nanfack@mila.quebec

Shuang Ni

Doctorat - UdeM

shuang.ni@mila.quebec

Albert Orozco Camacho

Doctorat - Concordia

Superviseur⋅e principal⋅e :

Jake Rhodes

Collaborateur·rice de recherche - BYU

rhodes@stat.byu.edu

thomas.sabourin@mila.quebec

Thomas Sabourin

Maîtrise recherche - UdeM

johannes.schmidt@mila.quebec

Johannes Schmidt

Visiteur de recherche indépendant - University of Fribourg

Doctorat - UdeM

Superviseur⋅e principal⋅e :

Julie Hussin

matthew.scicluna@mila.quebec

francisco.jose.tellez@mila.quebec

Simeon Tchoffo

Doctorat - UdeM

simeontchoffo@gmail.com

Francisco Tellez

Maîtrise recherche - UdeM

Jesuino Vieira Filho

Maîtrise recherche - UdeM

Collaborateur·rice alumni - UdeM

Co-superviseur⋅e :

yanlei.zhang@mila.quebec

Analyser le paradoxe des interférons inhérent à la COVID-19 au moyen de la réduction de la dimensionnalité et du regroupement

Billets de blogue

Graph and representation of working methodology, and graph of data on deaths 60 days after onset of symptoms.

19 février 2025

par

Sacha Morin

Elsa Brunet-Ratnasingham

Guy Wolf

Lire l'article

Publications

Geometry Regularized Autoencoders

Andres F. Duque Correa

Sacha Morin

Kevin R. Moon

A fundamental task in data exploration is to extract low dimensional representations that capture intrinsic geometry in data, especially for… (voir plus) faithfully visualizing data in two or three dimensions. Common approaches use kernel methods for manifold learning. However, these methods typically only provide an embedding of the input data and cannot extend naturally to new data points. Autoencoders have also become popular for representation learning. While they naturally compute feature extractors that are extendable to new data and invertible (i.e., reconstructing original features from latent representation), they often fail at representing the intrinsic data geometry compared to kernel-based manifold learning. We present a new method for integrating both approaches by incorporating a geometric regularization term in the bottleneck of the autoencoder. This regularization encourages the learned latent representation to follow the intrinsic data geometry, similar to manifold learning algorithms, while still enabling faithful extension to new data and preserving invertibility. We compare our approach to autoencoder models for manifold learning to provide qualitative and quantitative evidence of our advantages in preserving intrinsic structure, out of sample extension, and reconstruction. Our method is easily implemented for big-data applications, whereas other methods are limited in this regard.

2023-05-31

IEEE Transactions on Pattern Analysis and Machine Intelligence (publié)

Identifying Critical Neurons in ANN Architectures using Mixed Integer Programming

Mostafa Elaraby

Margarida Carvalho

2023-05-22

Integration of Constraint Programming, Artificial Intelligence, and Operations Research (publié)

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

Abhinav Godavarthi

Yu Xing

Scott Gigante

Holly R. Steach

Jessie Huang

Janhavi Narain

Kisung You

George Mourgkos

Rahul M. Dhodapkar … (voir 5 de plus)

Matthew Hirn

Bastian Rieck

Brian P. Hafler

Due to commonalities in pathophysiology, age-related macular degeneration (AMD) represents a uniquely accessible model to investigate thera… (voir plus)pies for neurodegenerative diseases, leading us to examine whether pathways of disease progression are shared across neurodegenerative conditions. Here we use single-nucleus RNA sequencing to profile lesions from 11 postmortem human retinas with age-related macular degeneration and 6 control retinas with no history of retinal disease. We create a machine-learning pipeline based on recent advances in data geometry and topology and identify activated glial populations enriched in the early phase of disease. Examining single-cell data from Alzheimer’s disease and progressive multiple sclerosis with our pipeline, we find a similar glial activation profile enriched in the early phase of these neurodegenerative diseases. In late-stage age-related macular degeneration, we identify a microglia-to-astrocyte signaling axis mediated by interleukin-1β which drives angiogenesis characteristic of disease pathogenesis. We validated this mechanism using in vitro and in vivo assays in mouse, identifying a possible new therapeutic target for AMD and possibly other neurodegenerative conditions. Thus, due to shared glial states, the retina provides a potential system for investigating therapeutic approaches in neurodegenerative diseases.

2023-05-04

Nature Communications (publié)

Reliability of CKA as a Similarity Measure in Deep Learning

MohammadReza Davari

Comparing learned neural representations in neural networks is a challenging but important problem, which has been approached in different w… (voir plus)ays. The Centered Kernel Alignment (CKA) similarity metric, particularly its linear variant, has recently become a popular approach and has been widely used to compare representations of a network's different layers, of architecturally similar networks trained differently, or of models with different architectures trained on the same data. A wide variety of conclusions about similarity and dissimilarity of these various representations have been made using CKA. In this work we present analysis that formally characterizes CKA sensitivity to a large class of simple transformations, which can naturally occur in the context of modern machine learning. This provides a concrete explanation of CKA sensitivity to outliers, which has been observed in past works, and to transformations that preserve the linear separability of the data, an important generalization attribute. We empirically investigate several weaknesses of the CKA similarity metric, demonstrating situations in which it gives unexpected or counter-intuitive results. Finally we study approaches for modifying representations to maintain functional behaviour while changing the CKA value. Our results illustrate that, in many cases, the CKA value can be easily manipulated without substantial changes to the functional behaviour of the models, and call for caution when leveraging activation alignment metrics.

2023-04-30

International Conference on Learning Representations (Accept: poster)

Conditional Flow Matching: Simulation-Free Dynamic Optimal Transport

Nikolay Malkin

Yanlei Zhang

2022-12-31

arXiv.org (prépublication)

Geodesic Sinkhorn for Fast and Accurate Optimal Transport on Manifolds

María Ramos Zapatero

Christopher J. Tape

Efficient computation of optimal transport distance between distributions is of growing importance in data science. Sinkhorn-based methods a… (voir plus)re currently the state-of-the-art for such computations, but require

2022-12-31

2023 IEEE 33rd International Workshop on Machine Learning for Signal Processing (MLSP) (publié)

Multi-view manifold learning of human brain-state trajectories.

Erica L. Busch

Jessie Huang

Andrew Benz

Tom Wallenstein

Guillaume Lajoie

Nicholas B. Turk-Browne

The complexity of the human brain gives the illusion that brain activity is intrinsically high-dimensional. Nonlinear dimensionality-reducti… (voir plus)on methods such as uniform manifold approximation and t-distributed stochastic neighbor embedding have been used for high-throughput biomedical data. However, they have not been used extensively for brain activity data such as those from functional magnetic resonance imaging (fMRI), primarily due to their inability to maintain dynamic structure. Here we introduce a nonlinear manifold learning method for time-series data—including those from fMRI—called temporal potential of heat-diffusion for affinity-based transition embedding (T-PHATE). In addition to recovering a low-dimensional intrinsic manifold geometry from time-series data, T-PHATE exploits the data’s autocorrelative structure to faithfully denoise and unveil dynamic trajectories. We empirically validate T-PHATE on three fMRI datasets, showing that it greatly improves data visualization, classification, and segmentation of the data relative to several other state-of-the-art dimensionality-reduction benchmarks. These improvements suggest many potential applications of T-PHATE to other high-dimensional datasets of temporally diffuse processes.

2022-12-31

Nature Computational Science (publié)

Time-inhomogeneous diffusion geometry and topology

Bastian Rieck

Jessie Huang

Manik Kuchroo

Matthew Hirn

Diffusion condensation is a dynamic process that yields a sequence of multiscale data representations that aim to encode meaningful abstract… (voir plus)ions. It has proven effective for manifold learning, denoising, clustering, and visualization of high-dimensional data. Diffusion condensation is constructed as a time-inhomogeneous process where each step first computes and then applies a diffusion operator to the data. We theoretically analyze the convergence and evolution of this process from geometric, spectral, and topological perspectives. From a geometric perspective, we obtain convergence bounds based on the smallest transition probability and the radius of the data, whereas from a spectral perspective, our bounds are based on the eigenspectrum of the diffusion kernel. Our spectral results are of particular interest since most of the literature on data diffusion is focused on homogeneous processes. From a topological perspective, we show diffusion condensation generalizes centroid-based hierarchical clustering. We use this perspective to obtain a bound based on the number of data points, independent of their location. To understand the evolution of the data geometry beyond convergence, we use topological data analysis. We show that the condensation process itself defines an intrinsic condensation homology. We use this intrinsic topology as well as the ambient persistent homology of the condensation process to study how the data changes over diffusion time. We demonstrate both types of topological information in well-understood toy examples. Our work gives theoretical insights into the convergence of diffusion condensation, and shows that it provides a link between topological and geometric data analysis.

2022-12-31

SIAM Journal on Mathematics of Data Science (publié)

Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms

Michael Perlmutter

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… (voir plus)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.

2022-12-31

SIAM Journal on Mathematics of Data Science (publié)

Manifold Interpolating Optimal-Transport Flows for Trajectory Inference

D.S. Magruder

Oluwadamilola Fasina

Manik Kuchroo

We present a method called Manifold Interpolating Optimal-Transport Flow (MIOFlow) that learns stochastic, continuous population dynamics fr… (voir plus)om static snapshot samples taken at sporadic timepoints. MIOFlow combines dynamic models, manifold learning, and optimal transport by training neural ordinary differential equations (Neural ODE) to interpolate between static population snapshots as penalized by optimal transport with manifold ground distance. Further, we ensure that the flow follows the geometry by operating in the latent space of an autoencoder that we call a geodesic autoencoder (GAE). In GAE the latent space distance between points is regularized to match a novel multiscale geodesic distance on the data manifold that we define. We show that this method is superior to normalizing flows, Schrödinger bridges and other generative models that are designed to flow from noise to data in terms of interpolating between populations. Theoretically, we link these trajectories with dynamic optimal transport. We evaluate our method on simulated data with bifurcations and merges, as well as scRNA-seq data from embryoid body differentiation, and acute myeloid leukemia treatment.

2022-11-30

PubMed (inconnu)

Can Hybrid Geometric Scattering Networks Help Solve the Maximum Clique Problem?

Yimeng Min

Frederik Wenkel

Michael A. Perlmutter

We propose a geometric scattering-based graph neural network (GNN) for approximating solutions of the NP-hard maximum clique (MC) problem. W… (voir plus)e construct a loss function with two terms, one which encourages the network to find highly connected nodes and the other which acts as a surrogate for the constraint that the nodes form a clique. We then use this loss to train an efficient GNN architecture that outputs a vector representing the probability for each node to be part of the MC and apply a rule-based decoder to make our final prediction. The incorporation of the scattering transform alleviates the so-called oversmoothing problem that is often encountered in GNNs and would degrade the performance of our proposed setup. Our empirical results demonstrate that our method outperforms representative GNN baselines in terms of solution accuracy and inference speed as well as conventional solvers like Gurobi with limited time budgets. Furthermore, our scattering model is very parameter efficient with only

2022-11-28

Conference on Neural Information Processing Systems (Accept)

Long Range Graph Benchmark

Vijay Prakash Dwivedi

Anh Tuan Luu

Graph Neural Networks (GNNs) that are based on the message passing (MP) paradigm generally exchange information between 1-hop neighbors to b… (voir plus)uild node representations at each layer. In principle, such networks are not able to capture long-range interactions (LRI) that may be desired or necessary for learning a given task on graphs. Recently, there has been an increasing interest in development of Transformer-based methods for graphs that can consider full node connectivity beyond the original sparse structure, thus enabling the modeling of LRI. However, MP-GNNs that simply rely on 1-hop message passing often fare better in several existing graph benchmarks when combined with positional feature representations, among other innovations, hence limiting the perceived utility and ranking of Transformer-like architectures. Here, we present the Long Range Graph Benchmark (LRGB) with 5 graph learning datasets: PascalVOC-SP, COCO-SP, PCQM-Contact, Peptides-func and Peptides-struct that arguably require LRI reasoning to achieve strong performance in a given task. We benchmark both baseline GNNs and Graph Transformer networks to verify that the models which capture long-range dependencies perform significantly better on these tasks. Therefore, these datasets are suitable for benchmarking and exploration of MP-GNNs and Graph Transformer architectures that are intended to capture LRI.

2022-11-28

Neural Information Processing Systems (Accept)