# LogicCBMs: Logic-Enhanced Concept-Based Learning

arXiv: https://arxiv.org/abs/2512.07383 · HTML: https://mlsanity.com/paper/2512.07383/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 48 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Builds on (most cited first, 30 of 40)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Zero-Shot Learning -- A Comprehensive Evaluation of the Good, the Bad and the Ugly](https://mlsanity.com/paper/1707.00600/) (2017)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Language in a Bottle: Language Model Guided Concept Bottlenecks for Interpretable Image Classification](https://mlsanity.com/paper/2211.11158/) (2022)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Label-Free Concept Bottleneck Models](https://mlsanity.com/paper/2304.06129/) (2023)
- [How to use and interpret activation patching](https://mlsanity.com/paper/2404.15255/) (2024)
- [Compositional Explanations of Neurons](https://mlsanity.com/paper/2006.14032/) (2020)
- [CLIP-Dissect: Automatic Description of Neuron Representations in Deep Vision Networks](https://mlsanity.com/paper/2204.10965/) (2022)
- [Promises and Pitfalls of Black-Box Concept Learning Models](https://mlsanity.com/paper/2106.13314/) (2021)
- [Probabilistic Concept Bottleneck Models](https://mlsanity.com/paper/2306.01574/) (2023)
- [Concept Bottleneck Model with Additional Unsupervised Concepts](https://mlsanity.com/paper/2202.01459/) (2022)
- [Interactive Concept Bottleneck Models](https://mlsanity.com/paper/2212.07430/) (2022)
- [GlanceNets: Interpretabile, Leak-proof Concept-based Models](https://mlsanity.com/paper/2205.15612/) (2022)
- [Deep Differentiable Logic Gate Networks](https://mlsanity.com/paper/2210.08277/) (2022)
- [VLG-CBM: Training Concept Bottleneck Models with Vision-Language Guidance](https://mlsanity.com/paper/2408.01432/) (2024)
- [Scallop: A Language for Neurosymbolic Programming](https://mlsanity.com/paper/2304.04812/) (2023)
- [Interpretable Neural-Symbolic Concept Reasoning](https://mlsanity.com/paper/2304.14068/) (2023)
- [Stochastic Concept Bottleneck Models](https://mlsanity.com/paper/2406.19272/) (2024)
- [Logic Explained Networks](https://mlsanity.com/paper/2108.05149/) (2021)
- [A Framework for Learning Ante-hoc Explainable Models via Concepts](https://mlsanity.com/paper/2108.11761/) (2021)
- [Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks](https://mlsanity.com/paper/2112.03324/) (2021)
- [Energy-Based Concept Bottleneck Models: Unifying Prediction, Concept Intervention, and Probabilistic Interpretations](https://mlsanity.com/paper/2401.14142/) (2024)

## Built on by (most cited first, 5 of 5)

- [Neurosymbolic Framework for Concept-Driven Logical Reasoning in Skeleton-Based Human Action Recognition](https://mlsanity.com/paper/2605.07140/) (2026)
- [In Defense of Information Leakage in Concept-based Models](https://mlsanity.com/paper/2606.10669/) (2026)
- [NeRD: Neuro-Symbolic Rule Distillation for Efficient Ontology-Grounded Chain-of-Thought in Medical Image Diagnosis](https://mlsanity.com/paper/2606.15617/) (2026)
- [A Neurosymbolic Framework for Interpretable Skeleton-Based Seizure Detection via Concept-Driven Logical Reasoning](https://mlsanity.com/paper/2606.21252/) (2026)
- [Overcoming Kernel Redundancy for Scaling Logic Gate Networks](https://mlsanity.com/paper/2610.01069/) (2026)

## Abstract (arXiv)

Concept Bottleneck Models (CBMs) provide a basis for semantic abstractions within a neural network architecture. Such models have primarily been seen through the lens of interpretability so far, wherein they offer transparency by inferring predictions as a linear combination of semantic concepts. However, a linear combination is inherently limiting. So we propose the enhancement of concept-based learning models through propositional logic. We introduce a logic module that is carefully designed to connect the learned concepts from CBMs through differentiable logic operations, such that our proposed LogicCBM can go beyond simple weighted combinations of concepts to leverage various logical operations to yield the final predictions, while maintaining end-to-end learnability. Composing concepts using a set of logic operators enables the model to capture inter-concept relations, while simultaneously improving the expressivity of the model in terms of logic operations. Our empirical studies on well-known benchmarks and synthetic datasets demonstrate that these models have better accuracy, perform effective interventions and are highly interpretable.