# Quantifying the Accuracy-Interpretability Trade-Off in Concept-Based Sidechannel Models

arXiv: https://arxiv.org/abs/2510.05670 · HTML: https://mlsanity.com/paper/2510.05670/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 32 references that are in the map.
- First posted on arXiv 7 Oct 2025.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Label-Free Concept Bottleneck Models](https://mlsanity.com/paper/2304.06129/) (2023)
- [Promises and Pitfalls of Black-Box Concept Learning Models](https://mlsanity.com/paper/2106.13314/) (2021)
- [Concept-based Explainable Artificial Intelligence: A Survey](https://mlsanity.com/paper/2312.12936/) (2023)
- [Concept Bottleneck Model with Additional Unsupervised Concepts](https://mlsanity.com/paper/2202.01459/) (2022)
- [GlanceNets: Interpretabile, Leak-proof Concept-based Models](https://mlsanity.com/paper/2205.15612/) (2022)
- [Interpretable Neural-Symbolic Concept Reasoning](https://mlsanity.com/paper/2304.14068/) (2023)
- [Stochastic Concept Bottleneck Models](https://mlsanity.com/paper/2406.19272/) (2024)
- [Incremental Residual Concept Bottleneck Models](https://mlsanity.com/paper/2404.08978/) (2024)
- [Learning to Receive Help: Intervention-Aware Concept Embedding Models](https://mlsanity.com/paper/2309.16928/) (2023)
- [Causal Concept Graph Models: Beyond Causal Opacity in Deep Learning](https://mlsanity.com/paper/2405.16507/) (2024)
- [Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learning](https://mlsanity.com/paper/2309.07742/) (2023)
- [Interpretable Concept-Based Memory Reasoning](https://mlsanity.com/paper/2407.15527/) (2024)
- [Relational Concept Bottleneck Models](https://mlsanity.com/paper/2308.11991/) (2023)
- [If Concept Bottlenecks are the Question, are Foundation Models the Answer?](https://mlsanity.com/paper/2504.19774/) (2025)
- [Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lens](https://mlsanity.com/paper/2502.11245/) (2025)
- [Avoiding Leakage Poisoning: Concept Interventions Under Distribution Shifts](https://mlsanity.com/paper/2504.17921/) (2025)
- [Deferring Concept Bottleneck Models: Learning to Defer Interventions to Inaccurate Experts](https://mlsanity.com/paper/2503.16199/) (2025)
- [Benchmarking and Enhancing Disentanglement in Concept-Residual Models](https://mlsanity.com/paper/2312.00192/) (2023)
- [Linearly-Interpretable Concept Embedding Models for Text Analysis](https://mlsanity.com/paper/2406.14335/) (2024)
- [Towards Reasonable Concept Bottleneck Models](https://mlsanity.com/paper/2506.05014/) (2025)
- [Interpretable Hierarchical Concept Reasoning through Attention-Guided Graph Learning](https://mlsanity.com/paper/2506.21102/) (2025)
- [Neural Interpretable Reasoning](https://mlsanity.com/paper/2502.11639/) (2025)

## Built on by (most cited first, 3 of 3)

- [Rethinking Concept Bottleneck Models: From Pitfalls to Solutions](https://mlsanity.com/paper/2603.05629/) (2026)
- [Prototype-Grounded Concept Models for Verifiable Concept Alignment](https://mlsanity.com/paper/2604.16076/) (2026)
- [Concept frustration: Aligning human concepts and machine representations](https://mlsanity.com/paper/2603.29654/) (2026)

## Abstract (arXiv)

Concept Bottleneck Models (CBNMs) are deep learning models that provide interpretability by enforcing a bottleneck layer where predictions are based exclusively on human-understandable concepts. However, this constraint also restricts information flow and often results in reduced predictive accuracy. Concept Sidechannel Models (CSMs) address this limitation by introducing a sidechannel that bypasses the bottleneck and carry additional task-relevant information. While this improves accuracy, it simultaneously compromises interpretability, as predictions may rely on uninterpretable representations transmitted through sidechannels. Currently, there exists no principled technique to control this fundamental trade-off. In this paper, we close this gap. First, we present a unified probabilistic concept sidechannel meta-model that subsumes existing CSMs as special cases. Building on this framework, we introduce the Sidechannel Independence Score (SIS), a metric that quantifies a CSM's reliance on its sidechannel by contrasting predictions made with and without sidechannel information. We propose SIS regularization, which explicitly penalizes sidechannel reliance to improve interpretability. Finally, we analyze how the expressivity of the predictor and the reliance of the sidechannel jointly shape interpretability, revealing inherent trade-offs across different CSM architectures. Empirical results show that state-of-the-art CSMs, when trained solely for accuracy, exhibit low representation interpretability, and that SIS regularization substantially improves their interpretability, intervenability, and the quality of learned interpretable task predictors. Our work provides both theoretical and practical tools for developing CSMs that balance accuracy and interpretability in a principled manner.