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Federated Concept-Based Models: Interpretable models with distributed supervision

Dario Fenoglio, Arianna Casanova, Francesco De Santis, Mohan Li, Gabriele Dominici, Johannes Schneider, Martin Gjoreski, Marc Langheinrich, Pietro Barbiero, Giovanni De Felice

TL;DR

Federated Concept-based Models address the need for interpretable predictions in privacy-sensitive, cross-institutional settings by grounding outputs in human-understandable concepts. F-CMs aggregate distributed concept supervision across clients and dynamically expand the shared concept space $\mathcal{M}_t$ and dependency graph $\mathcal{G}_t$, updating only affected modules to handle temporal non-stationarity. Four CM instantiations are evaluated on five synthetic Bayesian networks and a real SIIM-Pneumothorax dataset, showing that F-CMs preserve task accuracy and concept coverage close to centralized training while enabling interpretable inference for concepts unseen at individual sites. The framework also demonstrates efficient adaptation with limited parameter changes and supports privacy via module-wise FL updates and optional differential privacy mechanisms.

Abstract

Concept-based models (CMs) enhance interpretability in deep learning by grounding predictions in human-understandable concepts. However, concept annotations are expensive to obtain and rarely available at scale within a single data source. Federated learning (FL) could alleviate this limitation by enabling cross-institutional training that leverages concept annotations distributed across multiple data owners. Yet, FL lacks interpretable modeling paradigms. Integrating CMs with FL is non-trivial: CMs assume a fixed concept space and a predefined model architecture, whereas real-world FL is heterogeneous and non-stationary, with institutions joining over time and bringing new supervision. In this work, we propose Federated Concept-based Models (F-CMs), a new methodology for deploying CMs in evolving FL settings. F-CMs aggregate concept-level information across institutions and efficiently adapt the model architecture in response to changes in the available concept supervision, while preserving institutional privacy. Empirically, F-CMs preserve the accuracy and intervention effectiveness of training settings with full concept supervision, while outperforming non-adaptive federated baselines. Notably, F-CMs enable interpretable inference on concepts not available to a given institution, a key novelty with respect to existing approaches.

Federated Concept-Based Models: Interpretable models with distributed supervision

TL;DR

Federated Concept-based Models address the need for interpretable predictions in privacy-sensitive, cross-institutional settings by grounding outputs in human-understandable concepts. F-CMs aggregate distributed concept supervision across clients and dynamically expand the shared concept space and dependency graph , updating only affected modules to handle temporal non-stationarity. Four CM instantiations are evaluated on five synthetic Bayesian networks and a real SIIM-Pneumothorax dataset, showing that F-CMs preserve task accuracy and concept coverage close to centralized training while enabling interpretable inference for concepts unseen at individual sites. The framework also demonstrates efficient adaptation with limited parameter changes and supports privacy via module-wise FL updates and optional differential privacy mechanisms.

Abstract

Concept-based models (CMs) enhance interpretability in deep learning by grounding predictions in human-understandable concepts. However, concept annotations are expensive to obtain and rarely available at scale within a single data source. Federated learning (FL) could alleviate this limitation by enabling cross-institutional training that leverages concept annotations distributed across multiple data owners. Yet, FL lacks interpretable modeling paradigms. Integrating CMs with FL is non-trivial: CMs assume a fixed concept space and a predefined model architecture, whereas real-world FL is heterogeneous and non-stationary, with institutions joining over time and bringing new supervision. In this work, we propose Federated Concept-based Models (F-CMs), a new methodology for deploying CMs in evolving FL settings. F-CMs aggregate concept-level information across institutions and efficiently adapt the model architecture in response to changes in the available concept supervision, while preserving institutional privacy. Empirically, F-CMs preserve the accuracy and intervention effectiveness of training settings with full concept supervision, while outperforming non-adaptive federated baselines. Notably, F-CMs enable interpretable inference on concepts not available to a given institution, a key novelty with respect to existing approaches.
Paper Structure (58 sections, 19 equations, 9 figures, 8 tables, 1 algorithm)

This paper contains 58 sections, 19 equations, 9 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Concept-based models (CMs)
  4. Bipartite CMs
  5. Graph-Based CMs
  6. Federated Learning (FL)
  7. Statistical heterogeneity and temporal non-stationarity.
  8. Problem Setting
  9. Method
  10. F-CM Shared Model
  11. F-CM Training Pipeline
  12. Graph Aggregation
  13. Dynamic Architecture Adaptation
  14. Warm-start initialization.
  15. Module-Specific Training and Module-Wise Aggregation
  16. ...and 43 more sections

Figures (9)

  • Figure 1: F-CMs overview. At each round $t$, F-CMs performs three steps. (1) Graph aggregation: the server combines the concept graphs provided by participating clients into a shared graph $\mathcal{G}_t$. (2) Architecture update: the shared CM is updated to reflect $\mathcal{G}_t$ and/or the concepts known at round $t$ (only newly introduced or rewired modules are changed). (3) Training: the server broadcasts the model; each client trains only modules for concepts (and task) it supervises (dark grey), leaving the others frozen (light grey), and the server aggregates the corresponding module updates. The figure shows two consecutive rounds, where newly arriving clients introduce new concepts.
  • Figure 2: Label accuracy (%) on downstream variables (including the task) following interventions on concepts at deeper levels of the ground-truth graph hierarchy. Dashed lines denote interventions that are not possible for a given modality due to the absence of predictions for the corresponding concept.
  • Figure 3: Convergence under temporal non-stationarity. Average validation task loss across rounds for C$^2$BM and CEM, where new clients introduce unseen concepts. F-CMs (ours) adapt the architecture modularly and converge faster and to lower loss than S-F-CMs (no adaptation) and S-F-CMs Reinit (full retraining). The legend reports the fraction of modified parameters.
  • Figure 4: Task accuracy (%) following interventions on concepts at increasing depths of the ground-truth graph hierarchy. Dashed lines denote interventions that are not possible for a given modality due to the absence of predictions for the corresponding concept.
  • Figure 5: Label accuracy (%) following interventions on concepts at increasing depths of the ground-truth graph hierarchy across CMs instantiations.
  • ...and 4 more figures