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

Source: [Neural Concept Verifier: Scaling Prover-Verifier Games via Concept Encodings](<https://www.sota2.com/research/paper/68fa79fa1e209131cea8064b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-06-24T05:00:13.022Z

Authors: Berkant Turan, Suhrab Asadulla, David Steinmann, Kristian Kersting, Wolfgang Stammer, Sebastian Pokutta

Published: 2025-07-10T08:28:46.000Z

## Abstract

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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Image Classification on CIFAR-100 (Completeness and Soundness)](<https://www.sota2.com/research/sota/image-classification-on-cifar-100-completeness-and-soundness.md>): Image Classification; CIFAR-100; Completeness Accuracy: 83.32.

- [Image Classification on COCOLogic](<https://www.sota2.com/research/sota/image-classification-on-cocologic.md>): Image Classification; COCOLogic; Completeness (Accuracy): 75.42.

- [Image Classification on CLEVR-Hans3](<https://www.sota2.com/research/sota/image-classification-on-clevr-hans3.md>): Image Classification; CLEVR-Hans3; Completeness (Accuracy): 98.92.

- [Image Classification on CLEVR-Hans7](<https://www.sota2.com/research/sota/image-classification-on-clevr-hans7.md>): Image Classification; CLEVR-Hans7; Completeness Accuracy: 97.89.

- [Image Classification on ImageNet-1k (Accuracy and Robustness Metrics)](<https://www.sota2.com/research/sota/image-classification-on-imagenet-1k-accuracy-and-robustness-metrics.md>): Image Classification; ImageNet-1K; Completeness (Accuracy): 67.04.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2507.07532>)

[PDF](<https://arxiv.org/pdf/2507.07532.pdf>)