Concept-based (CB) models provide interpretability and support test-time human intervention, while standard neural networks (NN) offer strong task performance but little transparency. Prior work has explored hybrid formulations that integrate concepts and additional representations to improve accuracy, often at the cost of human interventions. We introduce the \emph{Synergy Concept-Based Model (SynCB)} framework, that combines a CB branch with a complementary neural branch, and a trainable routing module that dynamically selects which branch to use for each input. Unlike prior models, which fuse residual and concept-based predictions, SynCB keeps the two branches distinct and coordinates them through the routing module. Moreover, both branches are learned jointly, allowing information sharing between the complementary neural branch and CB branches through their common backbone. To improve responsiveness to interventions, we further introduce a test-time intervention policy and a corresponding loss. Across five datasets and CB benchmarks, SynCB consistently achieves higher task accuracy while remaining more responsive to human interventions, surpassing the full neural baseline by up to 3.9 percentage points and exceeding the strongest competitor in intervention performance by up to 6.43 percentage points.
Concept Bottleneck Models (CBMs) have become a popular approach to enable interpretability in neural networks by constraining classifier inputs to a set of human-understandable concepts. While effective, current models embed concepts in flat Euclidean space, treating them as independent, orthogonal dimensions. Concepts, however, are highly structured and organized in semantic hierarchies. To resolve this mismatch, we propose Hyperbolic Concept Bottleneck Models (HypCBM), a post-hoc framework that grounds the bottleneck in this structure by reformulating concept activation as asymmetric geometric containment in hyperbolic space. Rather than treating entailment cones as a pre-training penalty, we show they encode a natural test-time activation signal: the margin of inclusion within a concept's entailment cone yields sparse, hierarchy-aware activations without any additional supervision or learned modules. We further introduce an adaptive scaling law for hierarchically faithful interventions, propagating user corrections coherently through the concept tree. Empirically, HypCBM rivals post-hoc Euclidean models trained on 20× more data in sparse regimes required for human interpretability, with stronger hierarchical consistency and improved robustness to input corruptions.
Daniel Uyterlinde, Swasti Shreya Mishra, Pascal Mettes
Concept Bottleneck Models (CBMs) are interpretable-by-design neural networks that detect human-understandable concepts from the input and use them to generate predictions. By allowing users to inspect the concepts underlying a prediction and explore how predictions change under alternative concept configurations, CBMs have emerged as one of the most prominent approaches to supporting human-AI collaboration. However, user studies investigating their actual effectiveness as decision-support systems remain limited. We present two large-scale user studies (N participants = 705, N observations = 6,959) evaluating how concept-based explanations and user interventions on the model's concepts affect the performance of the human-AI team in two distinct binary classification tasks. Our results show that CBMs, and particularly their interactive component, can improve human-AI team accuracy relative to both unaided human performance and performance with non-interpretable AI support. However, these benefits emerge only under certain conditions: classification tasks perceived as difficult, easily identifiable concepts, and active interaction with the model. We also discuss how inaccurate concept detection may undermine users' trust in the model. Overall, this work provides practical guidance for the deployment of CBMs as effective decision-support tools.
Neuro-Symbolic Concept-based Models (NeSy-CBMs) are a family of architectures that integrate neural networks with symbolic reasoning for enhanced reliability in high-stakes applications. They work by first extracting high-level concepts from the input and then inferring a task label from these compatibly with given logical constraints. Yet, their label and concept predictions can be overconfident, making it difficult for stakeholders to gauge when the model's decisions can be trusted. We address this issue by integrating ideas from Conformal Prediction (CP), a framework providing rigorous, distribution-free coverage guarantees. We formalize three desiderata -- consistency, coverage, and conciseness -- that any conformal method for NeSy-CBMs should satisfy, and show that existing approaches fall short of at least one. We then introduce COCOCO, a post-hoc framework that conformalizes concepts and labels jointly and reconciles them via a single deduction-abduction revision step. COCOCO satisfies all three desiderata, retains distribution-free coverage, is robust to imperfect knowledge and supports user-specified size budgets. Our experiments on 8 data sets highlight how COCOCO compares favorably against competitors and natural baselines in terms of performance and set size.
Samuele Bortolotti, Emanuele Marconato, Andrea Pugnana +2