# Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Models

arXiv: https://arxiv.org/abs/2605.18202 · HTML: https://mlsanity.com/paper/2605.18202/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 65 of its 101 references that are in the map.
- First posted on arXiv 18 May 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 65)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for Better Empirical Performance](https://mlsanity.com/paper/2304.11127/) (2023)
- [TorchXRayVision: A library of chest X-ray datasets and models](https://mlsanity.com/paper/2111.00595/) (2021)
- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- [Safe Testing](https://mlsanity.com/paper/1906.07801/) (2019)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [Explainable Object-induced Action Decision for Autonomous Vehicles](https://mlsanity.com/paper/2003.09405/) (2020)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [Coherent Hierarchical Multi-Label Classification Networks](https://mlsanity.com/paper/2010.10151/) (2020)
- [From Statistical Relational to Neuro-Symbolic Artificial Intelligence](https://mlsanity.com/paper/2003.08316/) (2020)
- [Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcuts](https://mlsanity.com/paper/2305.19951/) (2023)
- [Deciding Fast and Slow: The Role of Cognitive Biases in AI-assisted Decision-making](https://mlsanity.com/paper/2010.07938/) (2020)
- [Incorporating Domain Knowledge into Deep Neural Networks](https://mlsanity.com/paper/2103.00180/) (2021)
- [A Comprehensive Study of Image Classification Model Sensitivity to Foregrounds, Backgrounds, and Visual Attributes](https://mlsanity.com/paper/2201.10766/) (2022)
- [CEBaB: Estimating the Causal Effects of Real-World Concepts on NLP Model Behavior](https://mlsanity.com/paper/2205.14140/) (2022)
- [A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inference](https://mlsanity.com/paper/2212.12393/) (2022)
- [Deep Learning with Logical Constraints](https://mlsanity.com/paper/2205.00523/) (2022)
- [Abductive Knowledge Induction From Raw Data](https://mlsanity.com/paper/2010.03514/) (2020)
- [BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcuts](https://mlsanity.com/paper/2402.12240/) (2024)
- [ROAD-R: The Autonomous Driving Dataset with Logical Requirements](https://mlsanity.com/paper/2210.01597/) (2022)

## Built on by (most cited first, 1 of 1)

- [Auto-Formalizing Neuro-Symbolic Predictors](https://mlsanity.com/paper/2610.01519/) (2026)

## Abstract (arXiv)

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.