# NeuroGame Transformer: Gibbs-Inspired Attention Driven by Game Theory and Statistical Physics

arXiv: https://arxiv.org/abs/2603.18761 · HTML: https://mlsanity.com/paper/2603.18761/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 32 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Scaling Vision Transformers to 22 Billion Parameters](https://mlsanity.com/paper/2302.05442/) (2023)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [A Decomposable Attention Model for Natural Language Inference](https://mlsanity.com/paper/1606.01933/) (2016)
- [Enhanced LSTM for Natural Language Inference](https://mlsanity.com/paper/1609.06038/) (2016)
- [Stable, Fast and Accurate: Kernelized Attention with Relative Positional Encoding](https://mlsanity.com/paper/2106.12566/) (2021)
- [Energy-based models for atomic-resolution protein conformations](https://mlsanity.com/paper/2004.13167/) (2020)
- [Breaking Down Video LLM Benchmarks: Knowledge, Spatial Perception, or True Temporal Understanding?](https://mlsanity.com/paper/2505.14321/) (2025)
- [Intrinsically Interpretable Attention via Sparse Post-Training](https://mlsanity.com/paper/2512.05865/) (2025)
- [ViTaPEs: Visuotactile Position Encodings for Cross-Modal Alignment in Multimodal Transformers](https://mlsanity.com/paper/2505.20032/) (2025)

## Built on by (most cited first, 2 of 2)

- [A Collective Variational Principle Unifying Bayesian Inference, Game Theory, and Thermodynamics](https://mlsanity.com/paper/2604.27942/) (2026)
- [A Game Theoretic Free Energy Analysis of Higher Order Synergy in Attention Heads of Large Language Models](https://mlsanity.com/paper/2605.09515/) (2026)

## Abstract (arXiv)

Standard attention mechanisms in transformers are limited by their pairwise formulation, which hinders the modeling of higher-order dependencies among tokens. We introduce the NeuroGame Transformer (NGT) to overcome this by reconceptualizing attention through a dual perspective: tokens are treated simultaneously as players in a cooperative game and as interacting spins in a statistical physics system. Token importance is quantified using two complementary game-theoretic concepts -- Shapley values for global, permutation-based attribution and Banzhaf indices for local, coalition-level influence. These are combined via a learnable gating parameter to form an external magnetic field, while pairwise interaction potentials capture synergistic relationships. The system's energy follows an Ising Hamiltonian, with attention weights emerging as marginal probabilities under the Gibbs distribution, efficiently computed via mean-field equations. To ensure scalability despite the exponential coalition space, we develop importance-weighted Monte Carlo estimators with Gibbs-distributed weights. This approach avoids explicit exponential factors, ensuring numerical stability for long sequences. We provide theoretical convergence guarantees and characterize the fairness-sensitivity trade-off governed by the interpolation parameter. Experimental results demonstrate that the NeuroGame Transformer achieves strong performance across SNLI, and MNLI-matched, outperforming some major efficient transformer baselines. On SNLI, it attains a test accuracy of 86.4% (with a peak validation accuracy of 86.6%), surpassing ALBERT-Base and remaining highly competitive with RoBERTa-Base. Code is available at https://github.com/dbouchaffra/NeuroGame-Transformer.