# Concept Flow Models: Anchoring Concept-Based Reasoning with Hierarchical Bottlenecks

arXiv: https://arxiv.org/abs/2606.19489 · HTML: https://mlsanity.com/paper/2606.19489/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 46 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)

## Builds on (most cited first, 29 of 29)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [YOLO9000: Better, Faster, Stronger](https://mlsanity.com/paper/1612.08242/) (2016)
- [ConceptNet 5.5: An Open Multilingual Graph of General Knowledge](https://mlsanity.com/paper/1612.03975/) (2016)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [RegionCLIP: Region-based Language-Image Pretraining](https://mlsanity.com/paper/2112.09106/) (2021)
- [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)
- [Promises and Pitfalls of Black-Box Concept Learning Models](https://mlsanity.com/paper/2106.13314/) (2021)
- [Interpreting CLIP with Sparse Linear Concept Embeddings (SpLiCE)](https://mlsanity.com/paper/2402.10376/) (2024)
- [Do Concept Bottleneck Models Learn as Intended?](https://mlsanity.com/paper/2105.04289/) (2021)
- [Interactive Concept Bottleneck Models](https://mlsanity.com/paper/2212.07430/) (2022)
- [Learning Concise and Descriptive Attributes for Visual Recognition](https://mlsanity.com/paper/2308.03685/) (2023)
- [VLG-CBM: Training Concept Bottleneck Models with Vision-Language Guidance](https://mlsanity.com/paper/2408.01432/) (2024)
- [Stochastic Concept Bottleneck Models](https://mlsanity.com/paper/2406.19272/) (2024)
- [NBDT: Neural-Backed Decision Trees](https://mlsanity.com/paper/2004.00221/) (2020)
- [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)
- [Contrastive Localized Language-Image Pre-Training](https://mlsanity.com/paper/2410.02746/) (2024)
- [Learning to Intervene on Concept Bottlenecks](https://mlsanity.com/paper/2308.13453/) (2023)
- [Causal Concept Graph Models: Beyond Causal Opacity in Deep Learning](https://mlsanity.com/paper/2405.16507/) (2024)
- [Integrating domain knowledge: using hierarchies to improve deep classifiers](https://mlsanity.com/paper/1811.07125/) (2018)
- [Editable Concept Bottleneck Models](https://mlsanity.com/paper/2405.15476/) (2024)
- [Eliminating Information Leakage in Hard Concept Bottleneck Models with Supervised, Hierarchical Concept Learning](https://mlsanity.com/paper/2402.05945/) (2024)
- [Concept Bottleneck Models Without Predefined Concepts](https://mlsanity.com/paper/2407.03921/) (2024)
- [Leakage and Interpretability in Concept-Based Models](https://mlsanity.com/paper/2504.14094/) (2025)
- [Blockout: Dynamic Model Selection for Hierarchical Deep Networks](https://mlsanity.com/paper/1512.05246/) (2015)
- [Tree-Based Leakage Inspection and Control in Concept Bottleneck Models](https://mlsanity.com/paper/2410.06352/) (2024)
- [Towards Compositionality in Concept Learning](https://mlsanity.com/paper/2406.18534/) (2024)

## Abstract (arXiv)

Concept Bottleneck Models (CBMs) enhance interpretability by projecting learned features into a human-understandable concept space. Recent approaches leverage vision-language models to generate concept embeddings, reducing the need for manual concept annotations. However, these models suffer from a critical limitation: as the number of concepts approaches the embedding dimension, information leakage increases, enabling the model to exploit spurious or semantically irrelevant correlations and undermining interpretability. In this work, we propose Concept Flow Models (CFMs), which replace the flat bottleneck with a hierarchical, concept-driven decision tree. Each internal node in the hierarchy focuses on a localized subset of discriminative concepts, progressively narrowing the prediction scope. Our framework constructs decision hierarchies from visual embeddings, distributes semantic concepts at each hierarchy level, and trains differentiable concept weights through probabilistic tree traversal. Extensive experiments on diverse benchmarks demonstrate that CFMs match the predictive performance of flat CBMs, while substantially mitigating information leakage by reducing effective concept usage. Furthermore, CFMs yield stepwise decision flows that enable transparent and auditable model reasoning with hierarchical class structures.