Guy Wolf

Biography

Guy Wolf is a Full Professor in the Department of Mathematics and Statistics (DMS) at the Université de Montréal (UdeM), a Canada CIFAR AI Chair & Core Academic Member at Mila (the Quebec AI institute), an Associate Researcher with CRCHUM (the Montreal university hospital research center), and a participating PI in the Helmholtz International Lab for Causal Cell Dynamics.

In 2024 he has been awarded a Humboldt Experienced Research Fellowship, as part of which he was a visiting professor at Heidelberg University (2024) and Helmholtz Munich (2024-2026) in Germany. Prior to joining UdeM and Mila, he was a Gibbs Assistant Professor (2015-2018) in the Applied Math Program and an Associate Research Scientist in the Department of Genetics (2018) at Yale University (CT, USA). Previously, he was a Postdoctoral Researcher (2013-2015) in the Department of Computer Science at École Normale Supérieure in Paris (France). He holds a Ph.D. in Computer Science from Tel Aviv University (Israel), and has five years of prior experience in IT software design & development for data analysis in military settings.

His current research focuses on guided representation learning for data exploration, including methods that leverage manifold learning and geometric deep learning for dimensionality reduction, visualization, denoising, data augmentation, and coarse graining. While relevant for a wide range of applications, he is particularly interested in the intersection of AI & health, including tools supporting exploratory analysis of biomedical data, e.g., in single-cell multiomics, drug discovery, and neuroscience.

Current Students

Adrien Aumon

PhD - Université de Montréal

adrien.aumon@mila.quebec

Semih Cantürk

PhD - Université de Montréal

semihcanturk00@gmail.com

Joao Felipe Carneiro Barbosa Rocha

Collaborating researcher - Yale University

Co-supervisor :

joaofelipe.rocha@mila.quebec

sebastian.damrich@mila.quebec

Sebastian Damrich

Collaborating researcher - University of Tübingen

Maxine Dussault

Master's Research - Université de Montréal

Co-supervisor :

Margarida Carvalho

maxine.dussault@mila.quebec

Stefan Horoi

PhD - Université de Montréal

stefan.horoi@mila.quebec

Master's Research - Concordia University

Principal supervisor :

xiaolong.huang@mila.quebec

Collaborating Alumni - Université de Montréal

guillaume.huguet@mila.quebec

Paul Janson

PhD - Concordia University

Principal supervisor :

myriam.lizotte@mila.quebec

paul.janson@mila.quebec

PhD - Université de Montréal

Gabriele Malagoli

Independent visiting researcher - Helmholtz Munich

gabriele.malagoli@mila.quebec

Philippe Martin

PhD - Université de Montréal

Co-supervisor :

Paul François

philippe.martin@mila.quebec

Paria Mehrbod

Master's Research - Concordia University

Principal supervisor :

paria.mehrbod@mila.quebec

Lydia Mezrag

PhD - Université de Montréal

lydia.mezrag@mila.quebec

Kevin Moon

Collaborating researcher

Sacha Morin

PhD - Université de Montréal

Co-supervisor :

Liam Paull

sacha.morin@mila.quebec

Postdoctorate - Concordia University

Principal supervisor :

geraldin.nanfack@mila.quebec

Shuang Ni

PhD - Université de Montréal

shuang.ni@mila.quebec

Albert Orozco Camacho

PhD - Concordia University

Principal supervisor :

Jake Rhodes

Collaborating researcher - BYU

rhodes@stat.byu.edu

thomas.sabourin@mila.quebec

Thomas Sabourin

PhD - Université de Montréal

johannes.schmidt@mila.quebec

Johannes Schmidt

Independent visiting researcher - University of Fribourg

PhD - Université de Montréal

Principal supervisor :

Julie Hussin

matthew.scicluna@mila.quebec

Ammar Sherif

PhD - Concordia University

Principal supervisor :

francisco.jose.tellez@mila.quebec

ammar.sherif@mila.quebec

Simeon Tchoffo

PhD - Université de Montréal

simeontchoffo@gmail.com

Francisco Tellez

Master's Research - Université de Montréal

Jesuino Vieira Filho

Master's Research - Université de Montréal

Collaborating Alumni - Université de Montréal

Co-supervisor :

yanlei.zhang@mila.quebec

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

GeoSinkhorn Flow: Geometry-Aware Flow Matching for Perturbation-Conditioned Dynamics in Single cell Data Phenoscapes

Ke Xu

Alistair Wilkinson

Ni Shuang

Guillaume Huguet

Gerstein Mark

Christopher J. Tape

Single-cell technologies increasingly enable large-scale profiling of complex biological systems across many experimental perturbations, but… (see more) understanding how a system reorganizes across an entire space of conditions is difficult to interpret from single-cell embeddings alone. Phenoscapes address this by embedding entire cell-state distributions, rather than individual cells, as points in a data-driven landscape. Thus, a single dot represents one experimental condition rather than one cell, yielding a map of the perturbation or patient landscape that reveals how phenotype varies continuously across conditions. Phenoscapes remain a comparatively new and underexplored representation and existing static phenoscapes position experimental conditions relative to one another without specifying trajectories that describe how a cellular population moves from one condition to another. Flow- and trajectory-based models for single-cell data are numerous, but existing approaches operate at the level of individual cells, are not built to respect the geometry of a phenoscape, and typically cannot generalize their predicted flows to conditions not seen during training. Here we introduce GeoSinkhorn Flow, a perturbation-conditioned, geometry-aware flow-matching framework specialized designed to convert a static phenoscape into a dynamic phenoscape, in which each condition-level point is additionally connected by geodesic, condition-aware transport trajectories that are consistent with the phenoscape's underlying geometry. GeoSinkhorn Flow can also model transitions directly between time points without constructing a phenoscape. GeoSinkhorn Flow uses heat-diffusion geometry to define manifold-aware transport costs and trains a geometric autoencoder whose latent Euclidean distances stay aligned with the static phenoscape geometry while extending it to unseen cells. By explicitly conditioning the learned transport dynamics on perturbation-specific gene or drug embeddings, GeoSinkhorn Flow generalizes its trajectories to new measurement conditions, produces intermediate progression states along a trajectory, and extends predictions to unseen cells and held-out perturbations. An unbalanced optimal transport variant further learns growth or transition weights, so that changes in relative cell-state abundance or transition propensity are modeled together with state movement. Across synthetic manifolds, patient-derived organoid drug responses, Perturb-seq knockdowns, and time-resolved CyTOF signaling, GeoSinkhorn Flow recovered intrinsic manifold geometry, inferred biologically coherent response trajectories, and generalized to held-out drug combinations, perturbation genes, and time points. Together, these results establish GeoSinkhorn Flow as a perturbation-conditioned, phenoscape-consistent dynamical framework, distinct from standard flow-matching approaches, for converting static phenoscapes into dynamic ones that generalize across experimental conditions.

2026-10-21

bioRxiv (accepted)

Path Laplacian Encodings for Directed Graphs

Lydia Mezrag

Semih Cantürk

Michael Perlmutter

Bastian Rieck

Directed graphs naturally model many real-world systems in which interactions are asymmetric, such as citation networks, web graphs, and inf… (see more)ormation-flow networks. However, graph learning methods commonly rely on message passing with symmetrized graph representations or positional encodings that only partially exploit edge directionality. We introduce PathLapPE, a novel spectral positional encoding (PE) derived from the path Laplacian on directed graphs. PathLapPE provides node- and edge-level features that encode directional higher-order structure and can be incorporated into standard graph learning architectures. Empirical results on node- and graph-level benchmark tasks show that PathLapPE yields consistent improvements across several architectures, especially when combined with direction-aware message passing. Compared with magnetic Laplacian positional encodings, a widely studied spectral positional encoding for directed graphs, PathLapPE does not require additional fine-tuning of directionality hyperparameters while offering competitive runtime and performance.

2026-10-02

arXiv (preprint)

A Closed Form Depth-Width Law for Neural Collapse in Deep Linear Networks

Pankhil Gawade

Kirsten Fischer

Ewa Szczurek

How depth and width of neural networks shape learned representations is usually studied only after training. We show that, in a tractable fe… (see more)ature-learning setting, this dependence can instead be obtained in closed form. Using neural collapse as a probe of representation geometry, we express NC1--NC3 directly in terms of the learned feature kernel, extending an identity known for NC1 to the angular part of NC2 and to NC3 under a ridge readout. For deep linear networks with exchangeable class structure, the resulting kernel equations yield a geometric law, exact within the theory, for the layerwise evolution of within-class variability. At large width, the accumulated compression becomes a function of the depth-to-width ratio

2026-09-28

AXIOM @ Neural Information Processing Systems (poster)

Circuit Discovery Helps Detect LLM Jailbreaking: A Mechanistic Interpretability Study

Despite extensive safety alignment, large language models (LLMs) remain vulnerable to jailbreak attacks that bypass safeguards to elicit har… (see more)mful content. While prior work attributes this vulnerability to safety training limitations, the internal mechanisms by which LLMs process adversarial prompts remain poorly understood. We present a mechanistic analysis of the jailbreaking behavior in a large-scale, safety-aligned LLM, focusing on LLaMA-2-7B-chat-hf. Leveraging edge attribution patching and subnetwork probing, we systematically identify computational circuits responsible for generating affirmative responses to jailbreak prompts. Ablating these circuits during the first token prediction can reduce attack success rates by up to 80\%, demonstrating its critical role in safety bypass. Our analysis uncovers key attention heads and MLP pathways that mediate adversarial prompt exploitation, revealing how important tokens propagate through these components to override safety constraints. These findings advance the understanding of adversarial vulnerabilities in aligned LLMs and pave the way for targeted, interpretable defense mechanisms based on mechanistic interpretability.

2026-08-26

arXiv (preprint)

Mapping Alzheimer’s neuropathology signatures to the whole brain transcriptome using machine learning data-fusion

L. M. Hodgson

David A Bennett

Elisabeth B. Binder

Danilo Bzdok

Abstract In Alzheimer’s disease (AD), misfolded proteins emerge across the entire brain in structured, yet not rigid, spatiotemporal patte… (see more)rns. Yet, a systematic bias of single-cell genomics toward sampling mostly cortical tissue limits our understanding of the whole-brain transcriptomic vulnerability to AD. Here, we develop a machine learning method to extrapolate local AD neuropathology signatures to the whole brain. By analyzing gene expression profiles of over two million cortical cells from 427 humans spanning the AD-pathology spectrum, we derive transcriptomic estimators of AD neuropathology. After extensive validations on datasets with known ground truth, we apply this framework to three million cells from 108 brain regions in the Siletti whole human brain atlas and derive an anticipated brain map of transcriptomic signatures indexing AD neuropathology. This interrogation of regions spanning the cortical, subcortical, and brainstem structures uncovers transcriptomic signatures associated with hyperphosphorylated tau in the medulla oblongata, dorsal raphe nucleus, and the tuberal and mammillary regions of the hypothalamus. At the cellular level, assessments of these signatures across 31 cell populations identify VGLUT1/2 expressing neurons, astrocytes, and microglia as key neuropathology-resembling populations. Within the hippocampus, pathology signatures surface in the rostral cornu ammonis (CA) subfields, particularly in the CA1 pyramidal neurons and dentate granule cells. β-amyloid-like signatures localize to the neocortex with laminar selectivity — most prominently in upper layer somatostatin+ intratelencephalic neurons (L2-L3), but also in deep layer intratelencephalic and corticothalamic neurons (L5-L6). Neocortical astrocytes and microglia exhibiting disease associated signatures similarly demonstrate a unique laminar preference. Together, this study provides the first whole human brain map of AD pathology-associated transcriptomic signals, and exposes cell type, region, and cortex layer specific vulnerabilities.

2026-08-23

bioRxiv (accepted)

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

Pankhil Gawade

Adam Izdebski

Myriam Lizotte

Kevin R. Moon

Jake Slater Rhodes

Ewa Szczurek

Pretrained transformers provide general-purpose molecular embeddings for downstream tasks. While these embeddings provide task-agnostic stru… (see more)ctural patterns, they lack task-specific alignment, limiting downstream performance. Here, we introduce Freeze, Diffuse, Decode (FDD), a diffusion-based framework that adapts pretrained transformer embeddings to downstream tasks by building a task supervised diffusion geometry over the frozen embeddings, without any backbone training. Applied to antimicrobial peptide design, FDD yields low-dimensional, predictive, and interpretable representations that support property prediction, retrieval, and latent-space interpolation.

2026-07-15

Topology, Algebra, and Geometry in Data Science (oral)

César Miguel Valdez Cordova

Towards Distilling the Representational Geometry of Language Models

Andrew J Steindl

Dhananjay Bhaskar

Ian Adelstein

Large neural networks are increasingly combined through weight-space merging and distilled into smaller models, but weights and activations … (see more)are not canonical coordinates: two networks can implement similar functions while differing by permutations, rescalings, or basis changes. We ask whether these operations can instead be guided by the geometry of a model's representation space. For each model, we summarize the relationships among probe examples using a diffusion operator built from internal activations. We then test a simple distillation procedure in which a student is trained to match a fixed diffusion-geometry target derived from a teacher. Across Pythia, BERT, and DeBERTa-v3, this target does not generally make the student inherit the teacher's specific representation geometry. Instead, distilled students usually remain closer to matched task-only controls, and the objective has little effect on held-out performance. These results suggest that representation-geometry objectives must be evaluated against the geometry a student would learn from ordinary training alone.

2026-07-15

Topology, Algebra, and Geometry in Data Science (poster)

Can Model Merging Improve Aggregation in DiLoCo?

Model merging techniques, which aggregate independently finetuned models into one to combine their capabilities, have become a topic of sign… (see more)ificant interest in recent years, with a broad array of methods having been proposed to tackle this problem. Simultaneously, an emerging trend in distributed learning has been the use of methods such as local SGD and DiLoCo, which greatly reduce communication costs by periodically aggregating the independently trained local models. However, these communication-efficient methods have been shown to degrade in performance relative to the FLOP-matched data-parallel gold standard as the number of independent local models grows and as the number of local training steps before global communication is increased. In this work, we draw an explicit analogy between the pseudo-gradient aggregation step in local SGD/DiLoCo and task arithmetic-based model merging, establishing a straightforward way to utilize merging methods in the context of distributed optimization. We then evaluate multiple state-of-the-art model merging methods in this setting and identify one method in particular, Iso-C, as a promising approach for improving DiLoCo. We find that DiLoCo SGD with Iso-C aggregation outperforms not only simple pseudo-gradient averaging but even the momentum-based DiLoCo, despite lacking a momentum mechanism itself. Building on this finding, we propose IsoLoCo, which adapts Iso-C for distributed training by equipping it with Nesterov momentum. Our empirical evaluations on language model pre-training across varying numbers of local workers show that IsoLoCo significantly outperforms DiLoCo, with the gap between them widening as the number of workers increases. This advantage remains present across model sizes and inner step counts, confirming that merging-inspired aggregation is an effective strategy for low-communication distributed training.

2026-07-02

arXiv (preprint)

Gaining Biological Insights through Supervised Data Visualization

Jake S. Rhodes

Adrien Aumon

Sacha Morin

Marc Girard

Catherine Larochelle

Boaz Lahav

Elsa Brunet-Ratnasingham

Wei Zhang

Adele Cutler

Anhong Zhou

Daniel E. Kaufmann

Stephanie Zandee

Alexandre Prat

Kevin R. Moon

Dimensionality reduction-based data visualization is pivotal in comprehending complex biological data. The most common methods, such as PHAT… (see more)E, t-SNE, and UMAP, are unsupervised and therefore reflect the dominant structure in the data, which may be independent of expert-provided labels. Here we introduce a supervised data visualization method called RF-PHATE, which integrates expert knowledge for further exploration of the data. RF-PHATE leverages random forests to capture intricate featurelabel relationships. Extracting information from the forest, RF-PHATE generates low-dimensional visualizations that highlight relevant data relationships while disregarding extraneous features. This approach scales to large datasets and applies to classification and regression. We illustrate RF-PHATE’s prowess through three case studies. In a multiple sclerosis study using longitudinal clinical and imaging data, RF-PHATE unveils a sub-group of patients with non-benign relapsingremitting Multiple Sclerosis, demonstrating its aptitude for time-series data. In the context of Raman spectral data, RF-PHATE effectively showcases the impact of antioxidants on diesel exhaust-exposed lung cells, highlighting its proficiency in noisy environments. Furthermore, RF-PHATE aligns established geometric structures with COVID-19 patient outcomes, enriching interpretability in a hierarchical manner. RF-PHATE bridges expert insights and visualizations, promising knowledge generation. Its adaptability, scalability, and noise tolerance underscore its potential for widespread adoption.

2026-06-29

Nature Computational Science (published)

Path-independent Flow Matching for Multi-parameter Generative Dynamics

Sina Sanjari

Yanlei Zhang

Flow Matching is a powerful framework for learning transport maps between probability distributions. Yet its standard single-parameter formu… (see more)lation is not designed to capture multi-parameter variations where the resulting transport should be path-independent. Path independence is crucial because it ensures that transformations depend only on the initial and target distributions, not on the specific path. In this work, we introduce Path-independent Flow Matching (PiFM), a method for learning vector fields whose induced flows yield path-independent transport between distributions. We show that PiFM generalizes Flow Matching to higher-dimensional parameter domains while enforcing structural conditions that ensure consistency of composed transformations. In addition, we show that, under suitable assumptions, PiFM approximates the Wasserstein barycenter, linking the framework to a notion of distributional interpolation. To enable practical training, we propose a tractable, simulation-free objective that regresses onto multi-parameter conditional probability paths. We showcase empirically that PiFM outperforms other approaches on both synthetic and real world data in interpolating path-independent trajectories and generating desired out of distribution samples.

2026-05-29

SPIGM @ International Conference on Machine Learning (poster)

Meta-Merging by Checkpoint Nowcasting

Albert Manuel Orozco Camacho

Boris Knyazev

Model merging---the direct combination of parameters from independently fine-tuned networks---offers a way to compose task-specific capabili… (see more)ties without retraining or ensemble inference. Existing merge methods are often built from hand-crafted arithmetic or sparsification heuristics, leaving open whether general learned weight-space operators can be repurposed for merging directly. We study this question with NiNo, a pre-trained checkpoint-nowcasting meta-network originally designed to predict near-future training states from short checkpoint histories. We show that pre-trained NiNo can be reused as a data-free pairwise meta-merge operator for independently fine-tuned models. On an 8-task CLIP ViT-B/16 benchmark, NiNo is competitive with strong arithmetic baselines and consistently lands in the same functional region as weight averaging, Task Arithmetic, and TIES. Moreover, NiNo is best on HumanEval in a Qwen3 language extension among the compared merge methods, while extending meta-merge beyond pairs remains an open challenge. These results position learned checkpoint nowcasting as a practical starting point for data-free model merging and motivate future weight-space learners trained for merging explicitly.

2026-05-23

WSS @ International Conference on Machine Learning (poster)

César Miguel Valdez Cordova

scShapeBench: Discovering geometry from high dimensional scRNAseq data

Andrew J. Steindl

João Felipe Rocha

Brian Tshilengi Di Bassinga

Zachary Warren

Matthew Scicluna

Shabarni Gupta

Leire Torices

Daniel Neumann

Timothy J. Mann

Ihuan Gunawan

Dhananjay Bhaskar

John G. Lock

Christine L. Chaffer

High-dimensional point cloud data arise across many scientific domains, especially single-cell biology. The shapes or topologies of these da… (see more)tasets determine the types of information that can be extracted. For example, clustered data supports cell-type identification, trajectory structures support transition analysis, and archetypal structures capture continua of cellular behaviors. Existing analysis pipelines often assume a specific shape. The standard Seurat pipeline combines UMAP visualization with Louvain clustering and therefore assumes clustered data, while tools such as Monocle and SPADE assume tree-like structures, and flow-based models such as MIOFlow and Conditional Flow Matching target trajectories. Choosing which pipeline to apply is therefore often left to bioinformaticians who visually inspect datasets before selecting an analysis strategy. With the rise of agentic AI scientists, automating shape detection is increasingly important for selecting downstream analysis pipelines. To address this problem, we introduce scShapeBench, a benchmark dataset for shape detection containing both synthetic and expert-annotated single-cell datasets. Synthetic datasets are sampled from ground-truth skeleton graphs with controlled variance. Real single-cell datasets are curated from diverse sources and annotated by experts into four categories: clusters, single trajectory, multi-branching, and archetypal. We additionally introduce scReebTower, a baseline method that uses diffusion geometry to extract Reeb graphs and connect visualization with pipeline selection. We provide topology-aware evaluation metrics and compare scReebTower against PAGA and Mapper on synthetic and real data. Our results indicate that scReebTower outperforms existing baselines. Overall, our contributions span benchmarks, evaluation metrics, and a baseline for automated shape detection in single-cell data.

2026-05-11

arXiv (preprint)