Alexandre Duplessis

Quentin Bertrand, Avishek Joey Bose, Alexandre Duplessis et al.

Deep generative models have made tremendous progress in modeling complex data, often exhibiting generation quality that surpasses a typical human's ability to discern the authenticity of samples. Undeniably, a key driver of this success is enabled by the massive amounts of web-scale data consumed by these models. Due to these models' striking performance and ease of availability, the web will inevitably be increasingly populated with synthetic content. Such a fact directly implies that future iterations of generative models will be trained on both clean and artificially generated data from past models. In this paper, we develop a framework to rigorously study the impact of training generative models on mixed datasets -- from classical training on real data to self-consuming generative models trained on purely synthetic data. We first prove the stability of iterative training under the condition that the initial generative models approximate the data distribution well enough and the proportion of clean training data (w.r.t. synthetic data) is large enough. We empirically validate our theory on both synthetic and natural images by iteratively training normalizing flows and state-of-the-art diffusion models on CIFAR10 and FFHQ.

Adnan Ben Mansour, Gaia Carenini, Alexandre Duplessis et al.

Federated Learning has been recently proposed for distributed model training at the edge. The principle of this approach is to aggregate models learned on distributed clients to obtain a new more general "average" model (FedAvg). The resulting model is then redistributed to clients for further training. To date, the most popular federated learning algorithm uses coordinate-wise averaging of the model parameters for aggregation. In this paper, we carry out a complete general mathematical convergence analysis to evaluate aggregation strategies in a federated learning framework. From this, we derive novel aggregation algorithms which are able to modify their model architecture by differentiating client contributions according to the value of their losses. Moreover, we go beyond the assumptions introduced in theory, by evaluating the performance of these strategies and by comparing them with the one of FedAvg in classification tasks in both the IID and the Non-IID framework without additional hypothesis.

Adnan Ben Mansour, Gaia Carenini, Alexandre Duplessis et al.

To date, the most popular federated learning algorithms use coordinate-wise averaging of the model parameters. We depart from this approach by differentiating client contributions according to the performance of local learning and its evolution. The technique is inspired from control theory and its classification performance is evaluated extensively in IID framework and compared with FedAvg.

Alicja Maksymiuk, Alexandre Duplessis, Michael Bronstein et al.

Macrocycles are ring-shaped molecules that offer a promising alternative to small-molecule drugs due to their enhanced selectivity and binding affinity against difficult targets. Despite their chemical value, they remain underexplored in generative modeling, likely owing to their scarcity in public datasets and the challenges of enforcing topological constraints in standard deep generative models. We introduce MacroGuide: Topological Guidance for Macrocycle Generation, a diffusion guidance mechanism that uses Persistent Homology to steer the sampling of pretrained molecular generative models toward the generation of macrocycles, in both unconditional and conditional (protein pocket) settings. At each denoising step, MacroGuide constructs a Vietoris-Rips complex from atomic positions and promotes ring formation by optimizing persistent homology features. Empirically, applying MacroGuide to pretrained diffusion models increases macrocycle generation rates from 1% to 99%, while matching or exceeding state-of-the-art performance on key quality metrics such as chemical validity, diversity, and PoseBusters checks.

Abderrahim Bendahi, Alexandre Duplessis, Arnaud Fickinger

Persistence-based topological optimization deforms a point cloud $X \subset \mathbb{R}^d$ by minimizing objectives of the form $L(X) = \ell(\mathrm{Dgm}(X))$, where $\mathrm{Dgm}(X)$ is a persistence diagram. In practice, optimization is limited by two coupled issues: persistent homology is typically computed on subsamples, and the resulting topological gradients are highly sparse, with only a few anchor points receiving nonzero updates. Motivated by diffeomorphic interpolation, which extends sparse gradients to smooth ambient vector fields via Reproducing Kernel Hilbert Space (RKHS) interpolation, we propose a more scalable pipeline that improves both subsampling and gradient extension. We introduce subsampling via random slicing, a lightweight scheme that promotes iteration-wise geometric coverage and mitigates density bias. We further replace the costly kernel solve with a fast Nadaraya-Watson (NW) Gaussian convolution, producing a globally defined smooth update field at a fraction of the computational cost, while being more suited for topological optimization tasks. We provide theoretical guarantees for NW smoothing, including anchor approximation bounds and global Lipschitz estimates. Experiments in $2$D and $3$D show that combining random slicing with NW smoothing yields consistent speedups and improved objective values over other baselines on common persistence losses.

Adnan Ben Mansour, Gaia Carenini, Alexandre Duplessis

The future of machine learning lies in moving data collection along with training to the edge. Federated Learning, for short FL, has been recently proposed to achieve this goal. The principle of this approach is to aggregate models learned over a large number of distributed clients, i.e., resource-constrained mobile devices that collect data from their environment, to obtain a new more general model. The latter is subsequently redistributed to clients for further training. A key feature that distinguishes federated learning from data-center-based distributed training is the inherent heterogeneity. In this work, we introduce and analyse a novel aggregation framework that allows for formalizing and tackling computational heterogeneity in federated optimization, in terms of both heterogeneous data and local updates. Proposed aggregation algorithms are extensively analyzed from a theoretical, and an experimental prospective.