Rémi VAUCHER (Halias Technology)

Signatures, and Quiver Representations: don't be afraid to use Algebra in Causality

Understanding and testing causal relationships is a central challenge in modern artificial intelligence. In this talk, we introduce a mathematical perspective on causality based on two theoretical tools: path signatures and quiver representations. Signatures provide a hierarchical and universal description of temporal data, enabling the detection of differential causality. Quiver representations then offer an algebraic framework in which these relations can be encoded and tested in a structured and interpretable way. This approach bridges algebra, geometry and machine learning, suggesting new avenues for causal inference in dynamic settings. We will present the core mathematical ideas and illustrate their potential through examples. The Quiver Representations part is a joint work with Antoine Caradot.

Manal BENHAMZA (CentraleSupélec)

Counterfactual Robustness: a framework to analyze the robustness of Causal Generative Models across interventions

Data generation using generative models is one of the most impressive growing field of artificial intelligence. However, such models are black boxes trained on huge datasets lacking interpretability properties. Causality is a natural framework to include expert knowledge into deep generative models. Other expected beneficial properties of causal generative models are fairness, transparency and robustness of the generation process. Up to our best knowledge, while many works have analyzed general generative models’ robustness, surprisingly none have focused on their causal counterpart even if their robustness is a common claim. In the present paper, we introduce the fundamental concept of counterfactual robustness, which evaluates how sensitive causal generative models are to interventions with respect to distribution shifts. Through a series of experiments on synthetic and real-life datasets, we demonstrate that all the studied causal generative models are not equal with respect to counterfactual robustness. More surprisingly, we show that all causal interventions are also not equally robust. We provide a simple explanation based on the causal mechanisms between the variables, that is theoretically grounded in the case of an extended CausalVAE. Our in-depth analysis also yields an efficient way to identify the most robust intervention based on prior knowledge on the causal graph.

Ali AGHABABAEI (Université Grenoble Alpes)

Unified Framework for Pre-trained Neural Network Compression via Decomposition and Optimized Rank Selection

Modern deep neural networks often contain millions of parameters, making them impractical for deployment on resource-constrained devices. In this talk, I present RENE (Rank adapt tENsor dEcomposition), a unified framework that combines tensor decomposition with automatic rank selection to efficiently compress pre-trained neural networks. Unlike traditional approaches that rely on manually chosen or grid-searched ranks, RENE performs continuous rank optimization through a multi-step search strategy, exploring large rank spaces while keeping memory and computation manageable. The method identifies layer-wise optimal ranks without requiring training data and subsequently fine-tunes the decomposed model through a lightweight distillation process. Experiments on benchmark datasets, covering both convolutional and transformer architectures, demonstrate superior compression rates with strong accuracy preservation.

12:45 - 1:45pm | Lunch Break

2:45 - 3:30pm | Sweet Break

Sonia MAZELET (Polytechnique)

Unsupervised Learning for Optimal Transport plan prediction between unbalanced graphs

Optimal transport between graphs, based on Gromov-Wasserstein and other extensions, is a powerful tool for comparing and aligning graph structures.  However, solving the associated non-convex optimization problems is computationally expensive, which limits the scalability of these methods to large graphs. In this work, we present Unbalanced Learning of Optimal Transport (ULOT), a deep learning method that predicts optimal transport plans between two graphs. Our method is trained by minimizing the fused unbalanced Gromov-Wasserstein (FUGW) loss. We propose a novel neural architecture with cross-attention that is conditioned on the FUGW tradeoff hyperparameters. We evaluate ULOT on synthetic stochastic block model (SBM) graphs and on real cortical surface data obtained from fMRI. ULOT predicts transport plans with competitive loss up to two orders of magnitude faster than classical solvers.  Furthermore, the predicted plan can be used as a warm start for classical solvers to accelerate their convergence. Finally, the predicted transport plan is fully differentiable with respect to the graph inputs and FUGW hyperparameters, enabling the optimization of functionals of the ULOT plan.

Alexandre Chaussard (LPSM, Sorbonne Université)

Identifiability of AVEs

When studying ecosystems, hierarchical trees are often used to organize entities based on proximity criteria, such as the taxonomy in microbiology, social classes in geography, or product types in retail businesses, offering valuable insights into entity relationships. Despite their significance, current count-data models do not leverage this structured information. In particular, the widely used Poisson log-normal (PLN) model, known for its ability to model interactions between entities from count data, lacks the possibility to incorporate such hierarchical tree structures, limiting its applicability in domains characterized by such complexities. To address this matter, we introduce the PLN-Tree model as an extension of the PLN model, specifically designed for modeling hierarchical count data. By integrating structured deep variational inference techniques, we propose an adapted training procedure and establish identifiability results in the Poisson Log-Normal framework, enhancing both theoretical foundations and practical interpretability. Additionally, we present a proof-of-concept implication of identifiability by illustrating the practical benefits of using identifiable features for classification tasks.

Chuong LUONG (Université de Lorraine)

New Conditions for the Identifiability of Block-Term Tensor Decompositions

Tensor decompositions have become an important tool in machine learning and data analysis, as they can exploit the multidimensional structure of data. In particular, identifiability guarantees provide essential theoretical support to various latent variable modelling and source separation (e.g., unmixing) methods. However, for decompositions in block terms - which enjoy increased flexibility compared to the classical canonical polyadic decomposition, since each component is a block of multilinear ranks (L_r, M_r, N_r) -fewer results are available. In this ongoing work, we study the identifiability of general block-term decompositions of three-dimensional tensors from an algebraic-geometric viewpoint. Our current results provide new sufficient conditions for the identifiability of generic tensors based on the tensor dimensions, the shape of each block, and the number of components in the model (i.e., the tensor rank). Compared to previous results available in the literature, our conditions show that identifiability can hold for a larger number of components in certain regimes.

Mélissa ABIDER (Université Paris-Saclay)

Between identifiability and explainability: a mathematical and empirical exploration of variational models

Deep generative models, such as variational autoencoders (VAEs), learn to represent complex data in a hidden latent space. However, this representation is not always unique: several internal structures can produce the same observed results. This identifiability problem raises fundamental questions about the understanding and interpretation of AI models. In this presentation, I will offer both a theoretical and visual exploration of this phenomenon. I will briefly review the probabilistic framework of VAEs, before showing, through a small experiment, how regularization (β) and data noise influence the shape and stability of the latent space. These observations illustrate the trade-off between model fidelity and clarity of internal representation. This work aims to link the mathematical aspects of identifiability to the challenges of explainability in AI, and to open the discussion on how these properties could guide the design of more interpretable models.