🤖 machine learning

Federated Concept-Based Models: Interpretable models with distributed supervision

This paper introduces Federated Concept-based Models (F-CMs), a novel framework that enables the training of interpretable deep learning models across distributed institutions by aggregating concept-level information and dynamically adapting architecture to evolving supervision sets while preserving data privacy.

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

Published 2026-05-12

📖 5 min read🧠 Deep dive

CC BY 4.0

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

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to teach a group of doctors from different hospitals how to diagnose a complex illness. Each doctor has seen different patients and knows different symptoms (concepts). However, there are two big problems:

Privacy: They cannot share their patient files with each other.
Incomplete Knowledge: No single doctor knows all the symptoms. One might know about "fever," another about "rash," and a third about "cough."

Usually, to build a smart AI that explains why it makes a diagnosis (an "interpretable" model), you need a massive list of all possible symptoms and how they relate to each other. But getting that list is expensive and hard to find in just one hospital.

This paper introduces a new method called Federated Concept-based Models (F-CMs). Think of it as a "Smart Team-Up" that solves the privacy and knowledge gaps without anyone ever seeing the raw patient data.

Here is how it works, using a simple analogy:

The Problem: The "Fixed Blueprint" Trap

Imagine the doctors are trying to build a giant, shared machine to diagnose patients.

Old Way (Standard Federated Learning): They agree on a fixed blueprint for the machine before they start. If a new doctor joins later who knows about a symptom the blueprint didn't include (like "swollen lymph nodes"), the machine can't learn it. It's like trying to add a new room to a house that was built with a rigid, unchangeable floor plan.
The Issue: In the real world, doctors (clients) join and leave, and they discover new symptoms over time. A fixed blueprint fails here.

The Solution: The "Lego" Machine (F-CMs)

The authors propose a machine built like Lego blocks. Instead of a fixed blueprint, the machine is made of interchangeable modules, where each block represents a specific symptom (concept) or the final diagnosis.

Here are the three magic steps the system takes every time a new doctor joins:

1. The "Consensus Map" (Graph Aggregation)

Every doctor draws a rough sketch of how the symptoms they know relate to each other. Some sketches might be messy or wrong because they only saw a few patients.

What happens: The central server (the "Team Leader") collects all these sketches. Instead of picking one, it looks for the most common connections. If 9 out of 10 doctors say "Fever leads to Rash," the server draws that line. If a doctor says "Fever leads to Rain," the server ignores it because no one else agrees.
Result: A single, high-quality "Master Map" of how symptoms connect, built from everyone's partial knowledge.

2. The "Modular Expansion" (Dynamic Architecture Adaptation)

This is the paper's biggest innovation.

Scenario: A new doctor joins who knows about a symptom called "Swollen Lymph Nodes" that no one else knew about.
Old Way: You would have to tear down the whole machine and rebuild it from scratch to add this new part. This is slow and wastes all the knowledge you already learned.
F-CM Way: The system looks at the Master Map, sees the new "Swollen Lymph Nodes" block, and snaps a new Lego block onto the machine. It only builds the specific part needed for that new symptom. The rest of the machine (the parts for "Fever" and "Rash") stays exactly as it was, preserving all the previous learning.
Benefit: The machine grows organically without needing a total reboot.

3. The "Specialized Training" (Module-Specific Optimization)

Now, the doctors start training the machine.

The Rule: A doctor only gets to touch the Lego blocks they understand. If a doctor knows about "Fever" but not "Swollen Lymph Nodes," they can only update the "Fever" block. The "Swollen Lymph Nodes" block stays frozen (unchanged) for that doctor.
Result: The server collects updates only for the blocks that were touched. It averages them out to make that specific block smarter. This ensures that doctors don't accidentally "break" parts of the machine they don't understand.

Why This Matters (The Results)

The authors tested this on medical imaging (like X-rays) and simulated medical data. They found:

It's as accurate as having all the data in one place: Even though the data was split up and private, the final machine performed just as well as if they had pooled all the data together.
It handles new information: When new doctors with new symptoms joined, the F-CM system adapted quickly and kept learning. The old "fixed blueprint" systems got stuck and performed poorly.
It's efficient: Because it only updates the specific blocks that need changing, it saves a massive amount of computing power compared to rebuilding the whole model every time.
It works on "invisible" concepts: Even if a specific hospital never saw a certain symptom, the system can still make predictions about it because it learned the concept from other hospitals.

In a Nutshell

F-CMs is like a living, breathing team of experts that builds a shared knowledge base. Instead of forcing everyone to agree on a rigid plan before starting, it allows the plan to evolve. As new experts join with new ideas, the system simply adds new pieces to the puzzle, keeping the old pieces intact, all while keeping everyone's private data locked in their own safes.

Technical Summary: Federated Concept-Based Models (F-CMs)

Problem Statement

Concept-Based Models (CMs) enhance deep learning interpretability by grounding predictions in human-understandable concepts. However, their practical deployment is hindered by the high cost and scarcity of concept annotations within single data sources. While Federated Learning (FL) offers a paradigm for collaborative training across distributed data owners without sharing raw data, existing FL frameworks are ill-suited for CMs. Standard FL assumes a fixed, shared model architecture, whereas CMs rely on an architecture explicitly tied to a specific set of concepts and their dependencies. In realistic FL settings characterized by statistical heterogeneity and temporal non-stationarity (e.g., clients joining/leaving or data drift), the set of available concepts and their structural relationships can evolve. This creates a fundamental mismatch: standard FL cannot accommodate the architectural adaptations required when new concepts or dependencies emerge, leading to a loss of interpretability or the need for costly full retraining.

Methodology: Federated Concept-Based Models (F-CMs)

The authors propose Federated Concept-Based Models (F-CMs), a framework designed to deploy CMs in evolving federated settings. F-CMs address the mismatch between static FL assumptions and dynamic concept spaces through three core mechanisms:

Graph Aggregation:
Instead of assuming a pre-defined global structure, the server aggregates structural information (Directed Acyclic Graphs or DAGs) provided by clients. Each client $k$ submits a weighted adjacency matrix $A^{(k)}$ representing its local confidence in edges between supervised variables. The server constructs a shared global DAG $G_t$ by summing these confidences and applying a maximum-consensus rule to determine edge existence and direction. This process handles noisy or conflicting local structures and ensures the global model reflects the collective knowledge of the federation.
Dynamic Architecture Adaptation:
The shared CM is decomposed into modular components: a latent encoder, concept-specific encoders, and a task decoder. As new clients join or data distributions shift, introducing previously unseen concepts or dependencies, the architecture adapts modularly:
- Expansion: New modules are instantiated for new concepts.
- Rewiring: If dependencies change (e.g., a new edge $C_i \to C_j$ ), the input to the corresponding module is updated.
- Warm-Start: Existing parameters for unaffected modules are preserved, while new parameters are initialized (e.g., zero-initialized or randomly). This avoids full retraining and retains previously learned knowledge.
Module-Specific Optimization and Aggregation:
To handle partial supervision (where a client may only annotate a subset of concepts), F-CMs employ a masked optimization strategy. During local training, clients freeze modules for variables they do not supervise. Consequently, updates are generated only for supervised components. The server then performs module-wise aggregation, averaging parameters for each specific module only over the subset of clients that provided supervision for that variable. This ensures that the global model integrates heterogeneous supervision without forcing clients to optimize for concepts they cannot observe.

Key Contributions

The paper introduces F-CMs as the first methodology to address evolving concept spaces under temporal non-stationarity in FL by adapting model structure rather than assuming a fixed architecture. The specific contributions are:

Novel Methodology: A systematic approach to deploying concept-based architectures in realistic federated settings, handling heterogeneous, partial concept supervision and temporal non-stationarity.
Architectural Flexibility: Moving beyond the fixed-architecture assumption of standard FL, F-CMs allow the shared model structure to adapt during training, enabling the incorporation of architectural interpretability.
Privacy-Preserving Knowledge Sharing: Reducing the annotation burden at individual institutions by enabling the aggregation of concept knowledge across entities without sharing raw data.
Empirical Validation: Instantiation of F-CMs with four distinct CM architectures (CBM, CEM, CGM, C2BM) and validation on synthetic Bayesian network benchmarks and two real-world medical imaging datasets (SIIM-Pneumothorax and CheXpert).

Experimental Results

The authors evaluated F-CMs against centralized upper bounds, localized training, static federated variants (S-F-CMs), and state-of-the-art federated concept-learning baselines (FedCBM, FCL).

Accuracy and Coverage: F-CMs achieved task accuracy and concept coverage comparable to centralized training with full concept supervision. In contrast, static federated baselines and localized models suffered significant performance drops and failed to cover concepts introduced by late-arriving clients.
Intervention Effectiveness: F-CMs enabled interpretable inference and effective interventions on concepts that were locally unannotated at specific institutions. When ground-truth concepts were intervened upon, F-CMs maintained high label accuracy, demonstrating that the model successfully leverages pooled supervision to reason about concepts it did not directly observe during local training.
Efficiency under Non-Stationarity: In scenarios where new clients introduced unseen concepts, F-CMs converged faster and to lower loss than static baselines. Crucially, F-CMs required updating only a small fraction of parameters (e.g., 8%–61% depending on the setting) compared to 100% for a full retraining baseline (S-F-CMs Reinit), demonstrating high adaptation efficiency.
Robustness: The framework showed robustness to inter-client semantic disagreement and graph perturbations (noise in client-provided DAGs). The proposed graph aggregation strategy effectively denoised inconsistent local proposals.
Multimodal Extension: A proof-of-concept extension demonstrated that F-CMs can handle heterogeneous input modalities (e.g., images and text) while sharing a common semantic concept space.

Significance and Claims

The paper claims that F-CMs represent a significant step toward scaling interpretable models while adhering to real-world constraints such as data privacy, annotation scarcity, and dynamic deployment environments. By bridging the gap between the static nature of standard FL and the structural requirements of CMs, F-CMs enable:

Interpretable Inference on Unseen Concepts: The ability to perform interpretable predictions on concepts that are not annotated at a specific client, a capability not present in existing static federated approaches.
Sustainable Federation Growth: A mechanism to integrate new data sources and supervision types without discarding previously learned knowledge or incurring the computational cost of full retraining.
Privacy-Preserving Interpretability: A pathway to aggregate high-level semantic knowledge across institutions, reducing the need for expensive, centralized concept annotation efforts.

The authors acknowledge limitations, noting that current CM architectures were not originally designed for evolving spaces, and future work could focus on developing federation-aware CMs with greater modularity. They also highlight the need for further privacy analysis regarding potential attack surfaces specific to concept-based federated models.