Organizations: UNC Chapel Hill · Rutgers University · Duke University
Abstract
In many machine learning problems, there may exist multiple models that achieve nearly identical predictive performance while relying on fundamentally different internal logic. However, standard training procedures produce a single model, offering no practical way to explore alternatives that may better suit downstream needs. The set of these equally accurate models is known as the Rashomon set. Exploring the Rashomon set is particularly challenging in large and complex hypothesis spaces, such as Concept Bottleneck Models (CBMs), which are widely used in computer vision to make predictions through intermediate, human-understandable concepts. In this paper, we provide a method for efficiently exploring the Rashomon set of CBMs. Our framework introduces a specialized parallel adapter-based construction, combined with a checkpointing scheme and a concept diversity objective, to generate multiple equally accurate CBMs from a single training process. Empirical results show that our method finds models with better diversity than baselines while using much less memory. We further demonstrate that access to these diverse yet accurate CBMs enables trustworthy model selection, resolution of inter-class confusion, and reliable abstention in decision-making.
Concept-bottleneck models (CBMs) are neural classifiers that compute predictions from high-level concepts extracted from the input. CBMs ensure stakeholders can understand the concepts -- and the predictions they entail -- by learning these from concept-level annotations, which are however seldom available. Recent CBM architectures work around this issue by obtaining annotations from Vision-Language Models (VLMs). While greatly broadening applicability, doing so can yield lower quality concepts and therefore less interpretable models. We strike for a middle ground by introducing Vision-plus-Human-guided CBM (VH-CBM), a hybrid approach that exploits both VLMs and a small amount of dense annotations. VH-CBM employs a Gaussian Process in the VLM's embedding space, which captures useful global information about the target domain, to propagate the expert's supervision to any target data point. Our empirical evaluation shows how VH-CBM predicts more accurate concepts than VLM-guided CBMs even when annotating as little as 1% of the data, while sporting better concept calibration and supporting active learning.
Concept Bottleneck Models (CBMs) provide an intrinsically interpretable alternative to post-hoc explanations. However, existing CBMs often rely on predefined concept vocabularies or supervised annotations, lack explicit concept grounding, and summarize each concept with a single image-level score -- discarding spatial recurrence and inter-concept dependencies. We propose a Graph-based Concept Bottleneck Model (G-CBM), an intrinsically interpretable framework that performs unsupervised concept discovery via Non-negative Matrix Factorization (NMF) and represents the discovered concepts as nodes in a per-image concept-graph representation. G-CBM matches region-level features to these concept nodes -- providing concept grounding and capturing concept recurrence across the image -- and applies a \emph{tunable concept filtering threshold} τ to suppress weak region-level features. A Graph Attention Network (GAT) then performs concept-level reasoning by modeling nonlinear dependencies across nodes. Across ImageNet, HAM10000, PH2, and Derm7pt, G-CBM achieves an average relative AUC improvement of 3.7% over a ResNet-50 baseline. Concept filtering frequently improves predictive performance while inducing selective concept use, achieving peak AUC of 0.96 on PH2 with only 2 of 10 concepts and 0.92 on HAM10000 with 3.8 of 9 concepts. On dermoscopy benchmarks, G-CBM is competitive with supervised approaches requiring external annotations. Deletion/insertion analyses with random ablation controls show that the learned concept ranking faithfully reflects model predictions.
Concept Bottleneck Models (CBMs) have emerged as a prominent paradigm for interpretable deep learning, learning by grounding predictions in human-understandable concepts. However, their practical deployment is hindered by the high cost of test-time intervention, as correcting model errors typically requires human experts to manually inspect and verify a large set of predicted concepts. Existing approaches suffer from a fundamental structural limitation: they either adopt a single static concept set, forcing experts to exhaustively annotate concepts and incurring prohibitive intervention costs, or train multiple models tailored to different concept budgets, resulting in substantial computational and maintenance overhead. To address this challenge, we propose the Matryoshka Concept Bottleneck Model (MCBM), a unified architecture that enables adaptive concept utilization within a single model. Inspired by Matryoshka Representation Learning, MCBM organizes concepts into a nested hierarchy based on maximum relevance and minimum redundancy, allowing inference at multiple levels of conceptual granularity without retraining. Theoretically, we show that MCBM reduces the expected intervention costs from linear to logarithmic order, O(logK), while guaranteeing monotonic performance improvement. Empirically, extensive experiments demonstrate that MCBM matches the performance of independently trained models while enabling dynamic and efficient expert interaction.