Guy Wolf

Biography

Guy Wolf is an associate professor in the Department of Mathematics and Statistics at Université de Montréal.

His research interests lie at the intersection of machine learning, data science and applied mathematics. He is particularly interested in data mining methods that use manifold learning and deep geometric learning, as well as applications for the exploratory analysis of biomedical data.

Wolf’s research focuses on exploratory data analysis and its applications in bioinformatics. His approaches are multidisciplinary and bring together machine learning, signal processing and applied math tools. His recent work has used a combination of diffusion geometries and deep learning to find emergent patterns, dynamics, and structure in big high dimensional- data (e.g., in single-cell genomics and proteomics).

Current Students

Adrien Aumon

PhD - Université de Montréal

Semih Cantürk

PhD - Université de Montréal

Joao Felipe Carneiro Barbosa Rocha

Collaborating researcher - Yale University

Collaborating Alumni

PhD - Université de Montréal

Xiao Huang

Master's Research - Concordia University

Principal supervisor :

PhD - Université de Montréal

Paul Janson

PhD - Concordia University

Principal supervisor :

PhD - Université de Montréal

Philippe Martin

PhD - Université de Montréal

Co-supervisor :

Paul François

Paria Mehrbod

Master's Research - Concordia University

Principal supervisor :

Eugene Belilovsky

Lydia Mezrag

PhD - Université de Montréal

Kevin Moon

Collaborating researcher

Sacha Morin

PhD - Université de Montréal

Co-supervisor :

Postdoctorate - Concordia University

Principal supervisor :

Shuang Ni

PhD - Université de Montréal

Albert Orozco Camacho

PhD - Concordia University

Principal supervisor :

Master's Research - Université de Montréal

Matthew Scicluna

PhD - Université de Montréal

Principal supervisor :

PhD - Université de Montréal

Francisco Tellez

Master's Research - Université de Montréal

Jesuino Vieira Filho

Master's Research - Université de Montréal

Postdoctorate - Université de Montréal

Co-supervisor :

Collaborating researcher - McGill University (assistant professor)

Exploring the COVID-19 Interferon Paradox with Dimensionality Reduction and Clustering

Blog Posts

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

February 19, 2025

Sacha Morin

Elsa Brunet-Ratnasingham

Guy Wolf

Read the article

Publications

Active search generation for nanophotonic design in the small data regime

Vincent Létourneau

Yuri Grinberg

Dan Kushnir

Yanlei Zhang

Dan-Xia Xu

2026-04-09

Machine Learning in Photonics (published)

MIOFlow 2.0: A unified framework for inferring cellular stochastic dynamics from single cell and spatial transcriptomics data

Xingzhi Sun

João Felipe Rocha

Brett Phelan

Dhananjay Bhaskar

Guillaume Huguet

Yanlei Zhang

D. S. Magruder

Alexander Tong

Ke Xu

Oluwadamilola Fasina

Mark Gerstein

Natalia Ivanova

Christine L. Chaffer

Smita Krishnaswamy

Understanding cellular trajectories via time-resolved single-cell transcriptomics is vital for studying development, regeneration, and disea… (see more)se. A key challenge is inferring continuous trajectories from discrete snapshots. Biological complexity stems from stochastic cell fate decisions, temporal proliferation changes, and spatial environmental influences. Current methods often use deterministic interpolations treating cells in isolation, failing to capture the probabilistic branching, population shifts, and niche-dependent signaling driving real biological processes. We introduce Manifold Interpolating Optimal-Transport Flow (MIOFlow) 2.0. This framework learns biologically informed cellular trajectories by integrating manifold learning, optimal transport, and neural differential equations. It models three core processes: (1) stochasticity and branching via Neural Stochastic Differential Equations; (2) non-conservative population changes using a learned growth-rate model initialized with unbalanced optimal transport; and (3) environmental influence through a joint latent space unifying gene expression with spatial features like local cell type composition and signaling. By operating in a PHATE-distance matching autoencoder latent space, MIOFlow 2.0 ensures trajectories respect the data's intrinsic geometry. Empirical comparisons show expressive trajectory learning via neural differential equations outperforms existing generative models, including simulation-free flow matching. Validated on synthetic datasets, embryoid body differentiation, and spatially resolved axolotl brain regeneration, MIOFlow 2.0 improves trajectory accuracy and reveals hidden drivers of cellular transitions, like specific signaling niches. MIOFlow 2.0 thus bridges single-cell and spatial transcriptomics to uncover tissue-scale trajectories.

2026-03-22

arXiv (preprint)

Multimodal Manifold Learning for Clonally Constrained Trajectory Inference

Irene Bonafonte Pardàs

Myriam Lizotte

Benjamin Schubert

A central goal of single-cell transcriptomics is to reconstruct dynamic cellular processes from static scRNA-seq snapshots, yet most traject… (see more)ory inference methods rely on transcriptomic similarity as a proxy for developmental linkage — an assumption that frequently fails. While lineage tracing overcomes this limitation, it requires genetic perturbations and specialized longitudinal designs. In adaptive immune cells, T and B cell receptors (AIRs) naturally encode clonal ancestry and are routinely sequenced alongside the transcriptome, providing lineage information in standard snapshot datasets, but existing trajectory methods are not adapted to exploit this signal. Here, we lay the foundation for incorporating AIR-encoded lineage information into trajectory inference by biasing RNA-based diffusion maps toward AIR-consistent paths, thereby integrating lineage constraints into learned cell-state representations. Across simulations of increasing complexity, our multimodal approach recovers more biologically plausible trajectories than RNA-only baselines. While optimized for lymphocyte differentiation, the framework generalizes to other endogenous lineage barcodes, such as mitochondrial mutations.

2026-03-03

LMRL @ International Conference on Learning Representations (poster)

openreview.net

Can Computational Reducibility Lead to Transferable Models for Graph Combinatorial Optimization?

Michael Perlmutter

A key challenge in deriving unified neural solvers for combinatorial optimization (CO) is efficient generalization of models between a given… (see more) set of tasks to new tasks not used during the initial training process. To address it, we first establish a new model, which uses a GCON module as a form of expressive message passing together with energy-based unsupervised loss functions. This model achieves high performance (often comparable with state-of-the-art results) across multiple CO tasks when trained individually on each task. We then leverage knowledge from the computational reducibility literature to propose pretraining and fine-tuning strategies that transfer effectively (a) between MVC, MIS and MaxClique, and (b) in a multi-task learning setting that additionally incorporates MaxCut, MDS and graph coloring. Additionally, in a leave-one-out, multi-task learning setting, we observe that pretraining on all but one task almost always leads to faster convergence on the remaining task when fine-tuning while avoiding negative transfer. Our findings indicate that learning common representations across multiple graph CO problems is viable through the use of expressive message passing coupled with pretraining strategies that are informed by the polynomial reduction literature, thereby taking an important step towards enabling the development of foundational models for neural CO. We provide an open-source implementation of our work at https://github.com/semihcanturk/COPT-MT .

2026-03-01

arXiv (preprint)

Position: Message-passing and spectral GNNs are two sides of the same coin

Antonis Vasileiou

Juan Cervino

Pascal Frossard

Charilaos I. Kanatsoulis

Christopher Morris

Michael T. Schaub

Pierre Vandergheynst

Zhiyang Wang

Ron Levie

Graph neural networks (GNNs) are commonly divided into message-passing neural networks (MPNNs) and spectral graph neural networks, reflectin… (see more)g two largely separate research traditions in machine learning and signal processing. This paper argues that this divide is mostly artificial, hindering progress in the field. We propose a viewpoint in which both MPNNs and spectral GNNs are understood as different parametrizations of permutation-equivariant operators acting on graph signals. From this perspective, many popular architectures are equivalent in expressive power, while genuine gaps arise only in specific regimes. We further argue that MPNNs and spectral GNNs offer complementary strengths. That is, MPNNs provide a natural language for discrete structure and expressivity analysis using tools from logic and graph isomorphism research, while the spectral perspective provides principled tools for understanding smoothing, bottlenecks, stability, and community structure. Overall, we posit that progress in graph learning will be accelerated by clearly understanding the key similarities and differences between these two types of GNNs, and by working towards unifying these perspectives within a common theoretical and conceptual framework rather than treating them as competing paradigms.

2026-02-09

arXiv (preprint)

Forest-Guided Semantic Transport for Label-Supervised Manifold Alignment

Adrien Aumon

Myriam Lizotte

Kevin R. Moon

Jake S. Rhodes

2026-01-31

ArXiv (preprint)

GraIP: A Benchmarking Framework For Neural Graph Inverse Problems

Semih Cantürk

Andrei Manolache

Arman Mielke

Chendi Qian

Antoine Siraudin

Christopher Morris

Mathias Niepert

A wide range of graph learning tasks, such as structure discovery, temporal graph analysis, and combinatorial optimization, focus on inferri… (see more)ng graph structures from data, rather than making predictions on given graphs. However, the respective methods to solve such problems are often developed in an isolated, task-specific manner and thus lack a unifying theoretical foundation. Here, we provide a stepping stone towards the formation of such a foundation and further development by introducing the Neural Graph Inverse Problem (GraIP) conceptual framework, which formalizes and reframes a broad class of graph learning tasks as inverse problems. Unlike discriminative approaches that directly predict target variables from given graph inputs, the GraIP paradigm addresses inverse problems, i.e., it relies on observational data and aims to recover the underlying graph structure by reversing the forward process, such as message passing or network dynamics, that produced the observed outputs. We demonstrate the versatility of GraIP across various graph learning tasks, including rewiring, causal discovery, and neural relational inference. We also propose benchmark datasets and metrics for each GraIP domain considered, and characterize and empirically evaluate existing baseline methods used to solve them. Overall, our unifying perspective bridges seemingly disparate applications and provides a principled approach to structural learning in constrained and combinatorial settings while encouraging cross-pollination of existing methods across graph inverse problems.

2026-01-25

ArXiv (preprint)

Scalable Tree Ensemble Proximities in Python

Adrien Aumon

Kevin R. Moon

Jake S. Rhodes

2025-12-31

arXiv (published)

Geometry-Aware Edge Pooling for Graph Neural Networks

Katharina Limbeck

Lydia Mezrag

Bastian Rieck

Graph Neural Networks (GNNs) have shown significant success for graph-based tasks. Motivated by the prevalence of large datasets in real-wor… (see more)ld applications, pooling layers are crucial components of GNNs. By reducing the size of input graphs, pooling enables faster training and potentially better generalisation. However, existing pooling operations often optimise for the learning task at the expense of discarding fundamental graph structures, thus reducing interpretability. This leads to unreliable performance across dataset types, downstream tasks and pooling ratios. Addressing these concerns, we propose novel graph pooling layers for structure-aware pooling via edge collapses. Our methods leverage diffusion geometry and iteratively reduce a graph's size while preserving both its metric structure and its structural diversity. We guide pooling using magnitude, an isometry-invariant diversity measure, which permits us to control the fidelity of the pooling process. Further, we use the spread of a metric space as a faster and more stable alternative ensuring computational efficiency. Empirical results demonstrate that our methods (i) achieve top performance compared to alternative pooling layers across a range of diverse graph classification tasks, (ii) preserve key spectral properties of the input graphs, and (iii) retain high accuracy across varying pooling ratios.

2025-12-02

Conference on Neural Information Processing Systems (Accept (poster))

openreview.net

Freeze, Diffuse, Decode: Geometry-Aware Adaptation of Pretrained Transformer Embeddings for Antimicrobial Peptide Design

Pankhil Gawade

Adam Izdebski

Myriam Lizotte

Kevin R. Moon

Jake S. Rhodes