# Neural Concept Verifier: Scaling Prover-Verifier Games via Concept Encodings

arXiv: https://arxiv.org/abs/2507.07532 · HTML: https://mlsanity.com/paper/2507.07532/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 58 of its 80 references that are in the map.
- First posted on arXiv 10 Jul 2025.

## Builds on (most cited first, 30 of 58)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [LAION-400M: Open Dataset of CLIP-Filtered 400 Million Image-Text Pairs](https://mlsanity.com/paper/2111.02114/) (2021)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Models](https://mlsanity.com/paper/2009.11462/) (2020)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [AI safety via debate](https://mlsanity.com/paper/1805.00899/) (2018)
- [Unmasking Clever Hans Predictors and Assessing What Machines Really Learn](https://mlsanity.com/paper/1902.10178/) (2019)
- [Multimodal datasets: misogyny, pornography, and malignant stereotypes](https://mlsanity.com/paper/2110.01963/) (2021)
- [Language in a Bottle: Language Model Guided Concept Bottlenecks for Interpretable Image Classification](https://mlsanity.com/paper/2211.11158/) (2022)
- [Right for the Right Reasons: Training Differentiable Models by Constraining their Explanations](https://mlsanity.com/paper/1703.03717/) (2017)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Label-Free Concept Bottleneck Models](https://mlsanity.com/paper/2304.06129/) (2023)
- [Making deep neural networks right for the right scientific reasons by interacting with their explanations](https://mlsanity.com/paper/2001.05371/) (2020)
- [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 Feature Attribution Methods Correctly Attribute Features?](https://mlsanity.com/paper/2104.14403/) (2021)
- [Concept-based Explainable Artificial Intelligence: A Survey](https://mlsanity.com/paper/2312.12936/) (2023)
- [Right for the Right Concept: Revising Neuro-Symbolic Concepts by Interacting with their Explanations](https://mlsanity.com/paper/2011.12854/) (2020)
- [Evaluating Explanations: How much do explanations from the teacher aid students?](https://mlsanity.com/paper/2012.00893/) (2020)

## Abstract (arXiv)

While Prover-Verifier Games (PVGs) offer a promising path toward verifiability in nonlinear classification models, they have not yet been applied to complex inputs such as high-dimensional images. Conversely, expressive concept encodings effectively allow to translate such data into interpretable concepts but are often utilised in the context of low-capacity linear predictors. In this work, we push towards real-world verifiability by combining the strengths of both approaches. We introduce Neural Concept Verifier (NCV), a unified framework combining PVGs for formal verifiability with concept encodings to handle complex, high-dimensional inputs in an interpretable way. NCV achieves this by utilizing recent minimally supervised concept discovery models to extract structured concept encodings from raw inputs. A prover then selects a subset of these encodings, which a verifier, implemented as a nonlinear predictor, uses exclusively for decision-making. Our evaluations show that NCV outperforms classic concept-based models and pixel-based PVG classifier baselines on high-dimensional, logically complex datasets and helps mitigate shortcut behavior. Overall, we demonstrate NCV as a promising step toward concept-level, verifiable AI.