arXiv subjects

Mathilde Papillon

Publications and source records attributed to Mathilde Papillon.

18 recordsLinked to original sources

arXiv2026

TopoSHAP: Shapley for Explainable and Efficient Topological Deep Learning

Topological deep learning (TDL) extends learning on graphs, such as molecules or social networks, to higher-order structures, such as rings in a molecule or groups in a social network. Explaining which of these structures drive a model's predictions, and which architectural components matter most for its performance, remains challenging. We introduce TopoSHAP, an efficient and general explanation framework that addresses both questions across topological domains and model architectures. TopoSHAP-cell assigns Shapley values to topological data cells and extracts compact explanations. These explanations match or outperform graph-based counterparts on GraphXAI benchmark data while running up to 112$\times$ faster. They also reveal advantageous topological feature design, leading to measured improvements in explanation recovery and predictive accuracy. On the architecture side, TopoSHAP-neighbor explains how neighborhoods contribute to model performance, and turns these evaluations into a backward-elimination search that identifies smaller, competitive architectures early in training. This is up to $11.3\times$ cheaper than traditional TDL training sweeps.

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arXiv2026

MotionBench-XAI: Benchmarking What Shapes Shapley Explanations in Spatiotemporal Machine Learning

Predicting outcomes from spatiotemporal data, such as assessing Parkinson's severity from human motion, often requires explainability in addition to accuracy. Practitioners need to know what drove the prediction, whether it be spatial (a body joint), temporal (a specific window), or both. Shapley values are attributions computed by treating input features as players in a cooperative game and measuring how the model output changes as coalitions of players are removed. Computing them involves choosing what counts as players, how absent players are imputed, and how the game is evaluated. How these choices affect explanation quality is poorly understood for spatiotemporal data, and real data carries no ground-truth attributions to check against. We present MotionBench-XAI, a benchmark built on i) five synthetic spatiotemporal datasets with exact ground-truth Shapley values, ii) three real datasets across clinical gait, electrocardiogram, and audio, iii) ten attribution methods across three player sets, and iv) three trained architectures. We show that grouping features into players, across time, space, or both, matters more than the choice of imputer. Generative imputers improve explanations only when their conditional models are accurate. On real data, the standard proxy metrics select contradictory best methods. We distill these findings into practical insights and provide an open-source pipeline.

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arXiv2026

A Phenomenology of Neural Geometry in Vision-Language-Action Models

Robotic manipulation is inherently geometric, but what shape does the world take inside the policy that performs it? Prior work on vision-language-action (VLA) policies establishes that task-relevant variables are linearly readable from activations, yet readability certifies only that a variable is present and says nothing about the shape its values trace, which may be curved and multi-dimensional. Using controlled sweeps, natural rollouts, linear probes, and activation interventions, we build a taxonomy of seven task-relevant concepts in VLA models. We find that realized geometry is predominantly multi-dimensional and is shaped by the constraints under which the policy acts. Physical joint limits, for example, leave wrist orientation an open arc rather than a circle, and distance to the target, a single scalar, is realized in two orthogonal subspaces, a coarse ruler for the approach and a fine ruler for the grasp. The same geometries reappear in two further VLA models on real-world robot data, indicating that they are neither model-specific nor artifacts of simulation. We demonstrate how the findings are actionable by steering along the geometry a concept realizes. Overall, this work lays out an initial phenomenology of realized geometry in VLA policies and demonstrates that a concept's shape carries as much importance as its readability.

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arXiv2026

Causal Analysis of Robot Foundation Models Enables Efficiency Gains

Vision-language-action (VLA) models are a promising approach to general purpose robot manipulation. While the internal computation of vision-language models, which compose the backbone of VLAs, has been studied extensively, less is known about how their perceptual and semantic representations are transformed into action in VLA models. We study this question mechanistically in three frontier VLA models ($π_{0.5}$, MolmoAct2, and MolmoBot) by analyzing the causal pathways through which the input image and the instruction shape actions. Across the three models, activation patching shows that causally relevant information influences the action expert (AE) through a narrow band of mid-to-late cross-attention layers, which we term the action-conditioning interface. The content of this information changes with token and layer within the model. Early-to-mid layer representations of the target noun token determine which object is selected, whereas mid-to-late layers carry the spatial information in text tokens that redirects the movement when patched. Where spatial information is stored in prompt tokens various based on the architecture. In MolmoAct2 the model forms task-conditioned representations at the text positions that follow the instruction, whereas $π_{0.5}$ additionally stores this information at image token positions. We show that these findings can be translated directly into improving model efficiency. We find that restricting MolmoBot's action expert conditioning to only 3 out of 36 layers reduces inference FLOPs by up to $33\%$ while maintaining comparable task success with the default model across 3,000 evaluation episodes ($46.7\%$ vs. $46.9\%$), and the same principle carries over to real-robot deployment of $π_{0.5}$.

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arXiv2026

Multi-Dimensional Featurizers Yield Fine-Grained Steering and Data Shaping in Robot Foundation Models

Can better feature discovery improve control over robot behavior through internal interventions and training data? Recent work in vision and language models reveals multidimensional features, motivating block-sparse featurizers (BSFs), which represent each feature in a low-dimensional subspace. We investigate whether recovering this structure provides an interpretable interface for steering vision-language-action models and shaping the data from which they learn. We show that BSFs recover several multi-dimensional task-relevant features underlying the model's computation (e.g., perception, language, proprioceptive state, episode phase, and control variables). We causally validate these features through fine-grained steering: targeted changes in visual perception, semantic representation, and spatial localization produce predictable changes in downstream action prediction. Finally, we use feature-based data attribution to isolate where a specific behavior (failure recovery) arises in the training dataset, identifying fewer than $1.4\%$ of training tokens whose masking is sufficient to remove the targeted behavior. Overall, our results show how matching featurizers to representation geometry can provide more effective tools for understanding and changing robot behavior.

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arXiv2026

Look Before You Lift: Visual and Quantitative Diagnostics for Topological Deep Learning

Topological deep learning (TDL) methods rely on lifting raw data into higher-order discrete domains such as simplicial complexes, cell complexes, and hypergraphs. In practice, this lifting step is often treated as a black box: practitioners select a lifting and then tune architectures, with limited visibility into whether the induced higher-order connectivity is meaningful for the downstream task. To address this missing diagnostic layer, we propose a visualization technique called TopoExplorer that leverages the strictly augmented Hasse graph form of topological datasets for exploratory data analysis. For the first time, practitioners can easily visualize the incidence- and adjacency-based neighborhoods that define the lifted dataset, as well as read off key graph metrics that describe its structural and feature landscape. Via an extensive set of experiments across many datasets and liftings, we show that several of these metrics correlate with downstream model performance, suggesting they can help inform TDL preprocessing design. Our perspective reframes the TDL workflow from lift-train to lift-look-design-train, enabling more principled, interpretable, and efficient model development. TopoExplorer is hosted at https://topoexplorer.pagekite.me, and its source code is available at github.com/geometric-intelligence/topoexplorer.

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arXiv2026

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

While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems. In response to this, Topological Deep Learning (TDL) leverages more general combinatorial representations--such as simplicial or cellular complexes--to accommodate higher-order interactions. Existing TDL methods often extend GNNs through Higher-Order Message Passing (HOMP), but face critical scalability challenges due to the steep complexity overhead of propagating messages through combinatorial structures. To overcome this limitation, we propose HOPSE (Higher-Order Positional and Structural Encoder), a framework free of message passing layers that uses Hasse graph decompositions to derive efficient and expressive encodings over arbitrary higher-order domains. Notably, HOPSE scales linearly with the size of combinatorial representations while preserving the expressive power and permutation equivariance of the HOMP approaches. Experiments on molecular and topological benchmarks show that it matches or surpasses state-of-the-art performance while consistently achieving speedups over HOMP-based models, opening a new path for scalable TDL. The code is available at https://github.com/geometric-intelligence/topobench.git.

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arXiv2025

TopoTune : A Framework for Generalized Combinatorial Complex Neural Networks

Graph Neural Networks (GNNs) effectively learn from relational data by leveraging graph symmetries. However, many real-world systems -- such as biological or social networks -- feature multi-way interactions that GNNs fail to capture. Topological Deep Learning (TDL) addresses this by modeling and leveraging higher-order structures, with Combinatorial Complex Neural Networks (CCNNs) offering a general and expressive approach that has been shown to outperform GNNs. However, TDL lacks the principled and standardized frameworks that underpin GNN development, restricting its accessibility and applicability. To address this issue, we introduce Generalized CCNNs (GCCNs), a simple yet powerful family of TDL models that can be used to systematically transform any (graph) neural network into its TDL counterpart. We prove that GCCNs generalize and subsume CCNNs, while extensive experiments on a diverse class of GCCNs show that these architectures consistently match or outperform CCNNs, often with less model complexity. In an effort to accelerate and democratize TDL, we introduce TopoTune, a lightweight software for defining, building, and training GCCNs with unprecedented flexibility and ease.

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arXiv2025

TopoBench: A Framework for Benchmarking Topological Deep Learning

This work introduces TopoBench, an open-source library designed to standardize benchmarking and accelerate research in topological deep learning (TDL). TopoBench decomposes TDL into a sequence of independent modules for data generation, loading, transforming and processing, as well as model training, optimization and evaluation. This modular organization provides flexibility for modifications and facilitates the adaptation and optimization of various TDL pipelines. A key feature of TopoBench is its support for transformations and lifting across topological domains. Mapping the topology and features of a graph to higher-order topological domains, such as simplicial and cell complexes, enables richer data representations and more fine-grained analyses. The applicability of TopoBench is demonstrated by benchmarking several TDL architectures across diverse tasks and datasets.

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arXiv2025

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

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

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arXiv2025

Ordered Topological Deep Learning: a Network Modeling Case Study

Computer networks are the foundation of modern digital infrastructure, facilitating global communication and data exchange. As demand for reliable high-bandwidth connectivity grows, advanced network modeling techniques become increasingly essential to optimize performance and predict network behavior. Traditional modeling methods, such as packet-level simulators and queueing theory, have notable limitations --either being computationally expensive or relying on restrictive assumptions that reduce accuracy. In this context, the deep learning-based RouteNet family of models has recently redefined network modeling by showing an unprecedented cost-performance trade-off. In this work, we revisit RouteNet's sophisticated design and uncover its hidden connection to Topological Deep Learning (TDL), an emerging field that models higher-order interactions beyond standard graph-based methods. We demonstrate that, although originally formulated as a heterogeneous Graph Neural Network, RouteNet serves as the first instantiation of a new form of TDL. More specifically, this paper presents OrdGCCN, a novel TDL framework that introduces the notion of ordered neighbors in arbitrary discrete topological spaces, and shows that RouteNet's architecture can be naturally described as an ordered topological neural network. To the best of our knowledge, this marks the first successful real-world application of state-of-the-art TDL principles --which we confirm through extensive testbed experiments--, laying the foundation for the next generation of ordered TDL-driven applications.

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arXiv2024

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

We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes. TopoX consists of three packages: TopoNetX facilitates constructing and computing on these domains, including working with nodes, edges and higher-order cells; TopoEmbedX provides methods to embed topological domains into vector spaces, akin to popular graph-based embedding algorithms such as node2vec; TopoModelX is built on top of PyTorch and offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The extensively documented and unit-tested source code of TopoX is available under MIT license at https://pyt-team.github.io/}{https://pyt-team.github.io/.

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arXiv2024

ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain

This paper describes the 2nd edition of the ICML Topological Deep Learning Challenge that was hosted within the ICML 2024 ELLIS Workshop on Geometry-grounded Representation Learning and Generative Modeling (GRaM). The challenge focused on the problem of representing data in different discrete topological domains in order to bridge the gap between Topological Deep Learning (TDL) and other types of structured datasets (e.g. point clouds, graphs). Specifically, participants were asked to design and implement topological liftings, i.e. mappings between different data structures and topological domains --like hypergraphs, or simplicial/cell/combinatorial complexes. The challenge received 52 submissions satisfying all the requirements. This paper introduces the main scope of the challenge, and summarizes the main results and findings.

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arXiv2024

Attending to Topological Spaces: The Cellular Transformer

Topological Deep Learning seeks to enhance the predictive performance of neural network models by harnessing topological structures in input data. Topological neural networks operate on spaces such as cell complexes and hypergraphs, that can be seen as generalizations of graphs. In this work, we introduce the Cellular Transformer (CT), a novel architecture that generalizes graph-based transformers to cell complexes. First, we propose a new formulation of the usual self- and cross-attention mechanisms, tailored to leverage incidence relations in cell complexes, e.g., edge-face and node-edge relations. Additionally, we propose a set of topological positional encodings specifically designed for cell complexes. By transforming three graph datasets into cell complex datasets, our experiments reveal that CT not only achieves state-of-the-art performance, but it does so without the need for more complex enhancements such as virtual nodes, in-domain structural encodings, or graph rewiring.

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arXiv2024

Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks

The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to electrostatic interactions between atoms in a protein. Topological Deep Learning (TDL) provides a comprehensive framework to process and extract knowledge from data associated with these systems, such as predicting the social community to which an individual belongs or predicting whether a protein can be a reasonable target for drug development. TDL has demonstrated theoretical and practical advantages that hold the promise of breaking ground in the applied sciences and beyond. However, the rapid growth of the TDL literature for relational systems has also led to a lack of unification in notation and language across message-passing Topological Neural Network (TNN) architectures. This presents a real obstacle for building upon existing works and for deploying message-passing TNNs to new real-world problems. To address this issue, we provide an accessible introduction to TDL for relational systems, and compare the recently published message-passing TNNs using a unified mathematical and graphical notation. Through an intuitive and critical review of the emerging field of TDL, we extract valuable insights into current challenges and exciting opportunities for future development.

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arXiv2024

ICML 2023 Topological Deep Learning Challenge : Design and Results

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. This paper describes the design of the challenge and summarizes its main findings.

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arXiv2022

PirouNet: Creating Dance through Artist-Centric Deep Learning

Using Artificial Intelligence (AI) to create dance choreography with intention is still at an early stage. Methods that conditionally generate dance sequences remain limited in their ability to follow choreographer-specific creative direction, often relying on external prompts or supervised learning. In the same vein, fully annotated dance datasets are rare and labor intensive. To fill this gap and help leverage deep learning as a meaningful tool for choreographers, we propose "PirouNet", a semi-supervised conditional recurrent variational autoencoder together with a dance labeling web application. PirouNet allows dance professionals to annotate data with their own subjective creative labels and subsequently generate new bouts of choreography based on their aesthetic criteria. Thanks to the proposed semi-supervised approach, PirouNet only requires a small portion of the dataset to be labeled, typically on the order of 1%. We demonstrate PirouNet's capabilities as it generates original choreography based on the "Laban Time Effort", an established dance notion describing intention for a movement's time dynamics. We extensively evaluate PirouNet's dance creations through a series of qualitative and quantitative metrics, validating its applicability as a tool for choreographers.

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arXiv2022

Intentional Choreography with Semi-Supervised Recurrent VAEs

We summarize the model and results of PirouNet, a semi-supervised recurrent variational autoencoder. Given a small amount of dance sequences labeled with qualitative choreographic annotations, PirouNet conditionally generates dance sequences in the style of the choreographer.

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