Publications

bispectrum: Selective G-Bispectra Made Practical | NeurIPS 2026

Mathe, J., Myers, A., Mataigne, S., Miolane, N.

The authors introduce bispectrum, an open-source PyTorch library that overcomes previous computational bottlenecks by efficiently implementing selective G-bispectra for various group actions. Empirical evaluations demonstrate that using these differentiable modules as pooling layers yields sub-millisecond GPU performance and consistently outperforms alternative methods in low-data, moderate-capacity deep learning regimes.

OgBench: A Framework for Evaluating Graph Neural Networks on Omics Data | NeurIPS 2026

Cornelis, L., Mathe, J., Van Langendonck, L., Bernárdez, G., Miolane, N.

Most graph neural network benchmarks study many small graphs, but omics data has the opposite shape: few patient samples and very large graphs of genes, transcripts, or proteins. OgBench is the first benchmarking platform for this regime, and its results show that widely used GNNs often do not outperform simple MLPs and classical baselines, prompting a reassessment of how graph structure is used for biological data.

HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations | NeurIPS 2026

Bernárdez, G.*, Montagna, M.*, Van Langendonck, L.*, Carrasco, M., Akbari, A., Cornelis, L., Papillon, M., Barlet-Ros, P., Telyatnikov, L.**, Miolane, N.**

Graph Neural Networks (GNNs) model pairwise relations well but struggle with the higher-order interactions present in many real-world systems. Topological Deep Learning (TDL) extends GNNs using higher-order message passing (HOMP) on simplicial or cellular complexes, but suffers from combinatorial blowup and high complexity. To address this, HOPSE (Higher-Order Positional and Structural Encoder) avoids message passing entirely, instead using Hasse graph decompositions for efficient, expressive encodings. HOPSE scales linearly with data size, maintains expressive power and permutation equivariance, and achieves state-of-the-art accuracy with up to 7× speedups over HOMP-based models across molecular, expressivity, and topological benchmarks—opening a scalable path for TDL.

Synaptic Strength Controls Trainability and Structural Stability in Rank-Deficient RNNs | NeurIPS 2026

Dinc, F.*, de Ponnat, E.*, Weyer, H., Guerra, Y., Miolane, N.

Real-world networks, from brains to ecosystems, are low-rank yet keep learning. This paper introduces rank-deficient RNNs, which separate rank from synaptic strength, and shows that synaptic strength, not rank, governs learning: strong synapses enable rapid training that matches full-rank speed, while weak synapses spread computation across the network, making learned solutions robust to neuron loss.

Selective Disk Bispectrum: A Complete and Rotation Invariant Image Descriptor | NeurIPS 2026

Myers Lantow, A., Miolane, N.

Hand-crafted rotation-invariant descriptors are fast and interpretable but lose descriptive power, while learned representations are expressive but costly and opaque. This paper introduces the selective disk bispectrum (SDB), a complex-valued rotation-invariant image descriptor that preserves all information about an image except its orientation. The authors prove its invertibility, derive its reduced spatial and computational complexity and its behavior under noise, and validate it on noisy rotated-image classification and multi-reference alignment.

Sequential Group Composition: A Window into the Mechanics of Deep Learning | ICML 2026

Luca Marchetti, G., Kunin, D., Myers, A., Acosta, F., Miolane, N.

We introduce the sequential group composition task to study how networks learn structured computation, showing that two-layer networks can solve it but require width exponential in sequence length, while deeper architectures avoid this cost by exploiting associativity to scale linearly (RNNs) or logarithmically (multilayer networks) instead.

GraphUniverse: Enabling Systematic Evaluation of Inductive Generalization | ICLR 2026

Van Langendonck, L., Bernárdez, G., Miolane, N., Barlet-Ros, P.

When Machine Learning Gets Personal: Evaluating Prediction and Explanation | ICLR 2026

Cornelis, L., Bernardez, G., Jeong, H., & Miolane, N.

Alternating Gradient Flows: A Theory of Feature Learning in Two-layer Neural Networks | NeurIPS 2025

Kunin, D., Luca Marchetti, G., Chen, F., Karkada, D., B. Simon, J., R. DeWeese, M., Ganguli, S., Miolane, N.

This paper introduces Alternating Gradient Flows (AGF), a framework that models feature learning in two-layer networks trained from small initialization as an alternating process of neuron activation and loss minimization. AGF explains the timing and structure of loss drops during training, unifying prior analyses and revealing that networks learn features like principal components or Fourier modes in a predictable order.

TopoTune : A Framework for Generalized Combinatorial Complex Neural Networks | ICML 2025

Papillon, M., Bernárdez, G., Battiloro, C., Miolane, N.

We introduce Generalized Combinatorial Complex Neural Networks (GCCNs), a simple yet powerful family of Topological Deep Learning (TDL) models that generalize CCNNs, systematically extend graph neural networks to higher-order domains, and, through the TopoTune framework, enable flexible and accessible development of expressive TDL architectures.

Dynamical Phases of Short-Term Memory Mechanisms in RNNs | ICML 2025

Kurtkaya, B., Dinc, F., Yuksekgonul, M., Blanco-Pozo, M., Cirakman, E., Schnitzer, M., Yemez, Y., Tanaka, H., Yuan, P., & Miolane, N.

We uncover two distinct mechanisms—slow-point manifolds and limit cycles—that support short-term memory in recurrent networks, derive theoretical scaling laws governing their emergence, and validate these findings across 35,000 RNNs, offering new insights and testable predictions for neuroscience.

Learning Riemannian Metrics for Interpolating Animations | GSI (oral) 2025

Kushner, S., Modi, V., Miolane, N.

We present a method for upsampling low frame rate animations by interpolating character bone orientations along geodesics from a family of invariant Riemannian metrics on SO(3) products. An optimization step selects the best-fitting metric for compression, yielding results that outperform existing techniques.

On the Approximation of the Riemannian Barycenter | GSI (oral) 2025

Mataigne, S., Absil, P.-A., Miolane, N.

We present a method to compute an approximate Riemannian barycenter of a collection of points lying on a Riemannian manifold. Our approach relies on the use of theoretically proven under- and overapproximations of the Riemannian distance function. We compare it to the exact computation of the Riemannian barycenter and to an approach that approximates the Riemannian logarithm using lifting maps. Experiments are conducted on the Stiefel manifold.

Global Distortions from Local Rewards: Neural Coding Strategies in Path-Integrating Neural Systems | NeurIPS 2024

Acosta, F., Dinc, F., Redman, W., Madhav, M., Klindt, D., Miolane, N.

Grid cells, traditionally understood to encode physical location, exhibit globally distorted firing patterns in response to rewarded landmarks; by training path-integrating recurrent neural networks, this study reveals how spatial and reward information integrate in grid-like codes, offering a framework that bridges computational modeling with biologically grounded spatial navigation.

Not So griddy: Internal Representations of RNNs Path Integrating More Than One Agent | NeurIPS 2024

Redman W., Acosta, F., Acosta-Mendoza, S., Miolane, N.

We show that RNNs trained to path integrate multiple agents develop distinct unit- and population-level representations - such as weaker grid cells, stronger border cells, and relative position tuning - highlighting how multi-agent navigation shapes spatial coding and neural dynamics.

The Selective G-Bispectrum and its Inversion: Applications to G-Invariant Networks | NeurIPS 2024

Mataigne, S., Mathe, J., Sanborn, S., Hillar, C., Miolane, N.

We present the selective G-Bispectrum, a computationally efficient alternative to the full G-Bispectrum with O(|G|) complexity, which retains key invariance properties for group actions and enhances neural network performance in terms of accuracy, robustness, and speed.

Position: Topological Deep Learning is the New Frontier for Relational Learning | ICML 2024

Papamarkou, T., Birdal, T., Bronstein, M., Carlsson, G., Curry, J., Gao, Y., Hajij, M., Kwitt, R., Liò, P., Di Lorenzo, P., Maroulas, V., Miolane, N., Nasrin, F., Natesan Ramamurthy, K., Rieck, B., Scardapane, S., T. Schaub, M., Veličković, P., Wang, B., Wang, Y.,  Wei, G., Zamzmi, G.

This paper explores topological deep learning as a complementary approach to graph and geometric learning, outlining key open problems, potential solutions, and future research directions in the field.

A General Framework for Robust G-Invariance in G-Equivariant Networks | NeurIPS 2023

Sanborn, S., Miolane, N.

We introduce a general method for achieving robust group-invariance in group-equivariant convolutional neural networks (G-CNNs), which we call the G-triple-correlation (G-TC) layer. The approach leverages the theory of the triple-correlation on groups, which is the unique, lowest-degree polynomial invariant map that is also complete. Many commonly used invariant maps - such as the max - are incomplete: they remove both group and signal structure. A complete invariant, by contrast, removes only the variation due to the actions of the group, while preserving all information about the structure of the signal.

Equivariant Sparse Coding | Geometric Science of Information 2023

Shewmake, C., Miolane, N., Olshausen, B. Geometric Science of Information. (Oral)

We describe a sparse coding model of visual cortex that encodes image transformations in an equivariant manner. We present results on time-varying visual scenes.

Using an Elastic Metric for Statistical Analysis of Tumor Cell Shape Heterogeneity | Geometric Science of Information 2023

Li, W., Prasad, A., Miolane, N., Dao Duc, K. Geometric Science of Information (GSI): Session Biological Shape Analysis. (Oral)

We propose a methodology grounded in geometric statistics to study and compare cellular morphologies from the contours they form on planar surfaces. We present findings on a dataset of images from osteocarcoma cells that includes different cancer treatments known to affect the cell morphology.

CryoAI: Amortized Inference of Poses for Ab Initio Reconstruction of 3D Molecular Volumes from Real Cryo-EM Images | ECCV 2022

Levy, A., Poitevin, F., Martel, J., Nashed, Y., Peck, A., Miolane, N., Ratner, D., Dunne, M., Wetzstein, G.

4th International Symposium on Cryo-3D Image Analysis (Best Poster Award).

ECCV European Conference on Computer Vision.

Cryo-electron microscopy (cryo-EM) has become a tool of fundamental importance in structural biology. The algorithmic challenge of cryo-EM is to jointly estimate the unknown 3D poses and the 3D electron scattering potential of a biomolecule from millions of extremely noisy 2D images. Existing reconstruction algorithms, however, cannot easily keep pace with the rapidly growing size of cryo-EM datasets due to their high computational and memory cost. We introduce cryoAI, an ab initio reconstruction algorithm for homogeneous conformations that uses direct gradient-based optimization of particle poses and the electron scattering potential from single-particle cryo-EM data. [Code].

Learning Weighted Submanifolds With Riemannian Variational Autoencoders | CVPR 2020

Miolane, N., Holmes, S.

CVPR Conference of Computer Vision and Pattern Recognition.

Manifold-valued data naturally arises in medical imaging. One of the challenges that naturally arises consists of finding a lower-dimensional subspace for representing such manifold-valued data. Traditional techniques, like principal component analysis, are ill-adapted to tackle non-Euclidean spaces. We introduce Riemannian Variational Autoencoders to perform weighted submanifold learning powered by amortized variational inference.

A Unifying Framework from Neural Superposition to Sparse Interpretable Codes | Nature Machine Intelligence 2026

Klindt, D., O’Neill, C., Reizinger, P., Maurer, H., Miolane, N. 

Neural networks compress many concepts into fewer neurons than expected. This paper proposes that these scrambled features can be recovered and made interpretable through a three-step framework: identifiability theory, sparse coding, and behavioral testing. Linking questions about neural coding in the brain with efforts to make AI systems transparent.

Unsupervised Cell Segmentation by Fast Gaussian Processes | The New England Journal of Statistics in Data Science 2026

Baracaldo, L., King, B., Yan, H., Lin, Y., Miolane, N., Gu, N.

Bounds on the geodesic distances on the Stiefel manifold for a family of Riemannian metrics | Journal of Linear Algebra and its Applications 2026

Mataigne, S., Absil, P.A., Miolane, N.

The work enhances geodesic computation on the Stiefel manifold by analyzing a family of Riemannian metrics with distances equivalent to the Frobenius norm and introducing SkewLinearAlgebra.jl, a Julia package for efficient skew-symmetric matrix operations.

TopoBench: A Framework for Benchmarking Topological Deep Learning | DMLR 2025

Telyatnikov, L., Bernardez, G., Montagna, M., Vasylenko, P., Zamzmi, G., Hajij, M., Schaub, M., Miolane, N., Scardapane, S.,  Papamarkou, T.

TopoBenchmarkX is a modular open-source library that standardizes and accelerates research in Topological Deep Learning by enabling flexible benchmarking, transformation across topological domains, and evaluation of diverse TDL architectures.

Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures | MLST 2025

Papillon, M., Sanborn, A., Mathe, J., Cornelis, L., Bertics, A., Buracas, D., Lillemark, H., Shewmake, C., Dinc, F., Pennec, X., Miolane, N.

The emerging field of non-Euclidean machine learning generalizes classical methods to data with complex geometric, topological, and algebraic structures, offering a unified graphical taxonomy of recent advances along with insights into key challenges and future opportunities.

Learning from Landmarks, Curves, Surfaces, and Shapes in Geomstats | TOMS 2025

Pereira, L., Le Brigant, A., Myers, A., Hartman, E., Khan, A., Tuerkoen, M., Dold, T., Gu, M., Suárez-Serrato, P., Miolane, N.

We introduce the shape module of the Geomstats Python package, which provides tools for analyzing shape data—landmarks, curves, and surfaces—via implemented shape spaces, Riemannian geometry, and abstract mathematical structures, enabling statistical and machine learning tasks through a modular, object-oriented design with illustrative examples.

TopoX: A Suite of Python Packages for Machine Learning on Topological Domains | JMLR 2024

Hajij, M., Papillon, M., Frantzen, F., Agerberg, J., AlJabea, I., Ballester, R., Battiloro, C., Bernárdez, G., Birdal, T., Brent, A., Chin, P., Escalera, S., Fiorellino, S., Hoff Gardaa, O., Gopalakrishnan, G., Govil, D., Hoppe, J., Reddy Karri, M., Khouja, J., Lecha, M., Livesay, N., Meißner, J., Mukherjee, S., Nikitin, A., Papamarkou, T., Prílepok, J., Natesan Ramamurthy, K., Rosen, P., Guzmán-Sáenz, A., Salatiello, A., N. Samaga, S., Scardapane, S., T. Schaub, M., Scofano, L., Spinelli, I., Telyatnikov, L., Truong, Q., Walters, R., Yang, M., Zaghen, O., Zamzmi, G., Zia, A., Miolane, N.

TopoX is a Python suite for computing and machine learning on advanced topological domains, featuring tools for construction (TopoNetX), embedding (TopoEmbedX), and neural modeling (TopoModelX), with open-source code under the MIT license.

An Efficient Algorithm for the Riemannian Logarithm on the Stiefel Manifold for a Family of Riemannian Metrics | SIAM Journal on Matrix Analysis and Applications (SIMAX) 2024

Mataigne, S., Zimmermann, R., Miolane, N.

An efficient matrix-algebraic method is introduced to compute the Riemannian Log across a one-parameter family of metrics on the Stiefel manifold, unifying and extending prior approaches.

Parametric Information Geometry with the Package Geomstats | Transactions of Mathematical Software (TOMS) 2023

Le Brigant, A., Deschamps, J., Collas, A., Miolane, N.

We introduce the information geometry module of the Python package Geomstats. The module first implements Fisher-Rao Riemannian manifolds of widely used parametric families of probability distributions, such as normal, gamma, beta, Dirichlet distributions, and more. The module further gives the Fisher-Rao Riemannian geometry of any parametric family of distributions of interest, given a parameterized probability density function as input.  [Code].

Differentially Private Fréchet Mean on the Manifold of Symmetric Positive Definite (SPD) Matrices | TMLR 2023

Utpala, S., Vepakomma, P., Miolane, N.

Transactions of Machine Learning Research (TMLR).

We introduce the Tangent Gaussian mechanism for computing a differentially private Fréchet mean on the SPD manifold, achieving quadratic utility improvement in data dimension, eliminating the need for Markov Chain Monte Carlo MCMC sampling, and significantly boosting computational efficiency.

Introduction to Riemannian Geometry and Geometric Statistics: from theory to implementation with Geomstats | JFTML 2023

Guigui, N., Miolane, N., Pennec, X. 

Journal of Foundations and Trends in Machine Learning.

This work provides an accessible introduction to Riemannian geometry, including its implementation in Geomstats for statistical and machine learning applications on manifolds, emphasizing computational examples and ease of use akin to scikit-learn.

Geomstats: A Python Package for Riemannian Geometry in Machine Learning | JMLR 2020

Miolane, N., Guigui, N., Le Brigant, A., Mathe, J., Hou, B., Thanwerdas, Y., Heyder, S., Peltre, O., Koep, N., Cabanes, Y., Chauchat, P., Zaatiti, H., Hajri, H., Gerald, T. , Shewmake, C., Brooks, D., Kainz, B., Donnat, C., Holmes, S., Pennec, X.

Journal of Machine Learning Research.

We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more. [Code].

Topologically Constrained Template Estimation | SIAGA 2018

Miolane, N., Holmes, S., Pennec, X.

SIAM Journal on Applied Algebra and Geometry.

In most neuroimaging studies, one builds a brain template that serves as a reference for normalizing the measurements of each individual subject into a common space. Such a template should be representative of the population under study, thus avoiding bias in subsequent statistical analyses. The template is often computed by iteratively registering all images to the current template and then averaging the intensities of the registered images. Geometrically, the procedure can be summarized as the computation of the template as the “Fréchet mean” of the images projected in a quotient space. It has been argued recently that this type of algorithm could actually be asymptotically biased and therefore inconsistent. In other words, even with an infinite number of brain images in the database, the template estimate may not converge to the brain anatomy it is meant to estimate. Our paper investigates this phenomenon. We present a methodology that spatially quantifies the brain template's asymptotic bias. We identify the main variables that influence inconsistency. This leads us to investigate the topology of the template's intensity level sets, represented by its Morse--Smale (MS) complex. We propose a topologically constrained adaptation of the template computation that constructs a hierarchical template with bounded bias. We apply our method to the analysis of a brain template of 136 T1 weighted MR images from the Open Access Series of Imaging Studies (OASIS) database.

Template Shape Estimation in Computational Anatomy | SIIMS 2017

Miolane, N., Holmes, S., Pennec, X.

SIAM Journal of Imaging Science.

We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of the bias with respect to a parameter σ describing the measurement error on the data. We propose two bootstrap procedures that quantify the bias and correct it, if needed. They are applicable for any type of shape data. We give a rule of thumb to provide intuition on whether the bias has to be corrected. This exhibits the parameters that control the bias’ magnitude. We illustrate our results on simulated and real shape data.

Computing Bi-Invariant Pseudo-Metrics on Lie Groups | Entropy 2015

Miolane, N., Pennec, X.

Journal Entropy. [Code].

In computational anatomy, organ’s shapes are often modeled as deformations of a reference shape, i.e., as elements of a Lie group. To analyze the variability of the human anatomy in this framework, we need to perform statistics on Lie groups. A Lie group is a manifold with a consistent group structure. Statistics on Riemannian manifolds have been well studied, but to use the statistical Riemannian framework on Lie groups, one needs to define a Riemannian metric compatible with the group structure: a bi-invariant metric. However, it is known that Lie groups, which are not a direct product of compact and abelian groups, have no bi-invariant metric. However, what about bi-invariant pseudo-metrics? In other words: could we remove the assumption of the positivity of the metric and obtain consistent statistics on Lie groups through the pseudo-Riemannian framework? Our contribution is two-fold. First, we present an algorithm that constructs bi-invariant pseudo-metrics on a given Lie group, in the case of existence. Then, by running the algorithm on commonly-used Lie groups, we show that most of them do not admit any bi-invariant (pseudo-) metric. We thus conclude that the (pseudo-) Riemannian setting is too limited for the definition of consistent statistics on general Lie groups.

Flow Tree: A Model for Navigator Dynamics and Environmental Complexity | Journal of the Royal Society Interface (in press) 2026

Bertics, A., Chrastil, E., Miolane, N., & Carlson, J.

We introduce the Flow Tree, a novel data structure adapted from the Reeb graph, to capture and analyze dynamic navigation behaviors across multiple trajectories, enabling improved prediction of path difficulty and individual navigation success. Applied to VR maze data from 100 participants, Flow Trees outperform static metrics and reveal distinct strategies used by good versus poor navigators.

Towards Interpretable Cryo-EM: Disentangling Latent Spaces of Molecular Conformations | Frontiers in Molecular Biosciences 2024

A. Klindt, D., Hyvärinen, A., Levy, A., Miolane, N., Poitevin, F.

Interpreting cryo-EM latent spaces as a nonlinear ICA problem enables the discovery of identifiable, disentangled molecular conformations with broad implications for structural biology and AI-driven scientific discovery.

Unveiling Cellular Morphology: Statistical Analysis Using a Riemannian Elastic Metric in Cancer Cell Image Datasets | Information Geometry 2024

Li, W., Prasad, A., Miolane, N., Dao Duc, K.

The Square Root Velocity (SRV) metric offers improved characterization of cell shape heterogeneity and enhances classification of cancer-treated cells, outperforming linear metrics in both interpretability and accuracy.

Septins Regulate Border Cell Surface Geometry, Shape, and Motility Downstream of Rho in Drosophila | Journal Developmental Cell 2023

Gabbert, A., Mondo, J., Campanale, J., Mitchell, N., Myers, A., Streichan, S., Miolane, N., Montell, D.

Septins self-assemble into polymers that bind and deform membranes in vitro and regulate diverse cell behaviors in vivo. How their in vitro properties relate to their in vivo functions is under active investigation. Here we uncover requirements for septins in detachment and motility of border cell clusters in the Drosophila ovary.

Orthogonal Outlier Detection and Dimension Estimation for Improved MDS Embedding of Biological Datasets | Frontiers in Bioinformatics 2023

Li, W., Mirone, J., Prasad, A., Miolane, N., Legrand, C. and Dao Duc, K.

Conventional dimensionality reduction methods are sensitive to orthogonal outliers, which yield significant defects in the embedding. We introduce a robust method to address this problem for cell morphology and human microbiomes datasets.

Deep Generative Modeling for Volume Reconstruction in Cryo-Electron Microscopy | Journal of Structural Biology 2022

Donnat, C., Levy, A., Poitevin, F., Zhong, E., Miolane, N.

Journal of Structural Biology.

This review examines recent advances in deep generative modeling for cryo-EM reconstruction, highlighting opportunities and challenges in leveraging unsupervised deep learning techniques for high-resolution biomolecular imaging.