NeuroGame Transformer: Gibbs-Inspired Attention Driven by Game Theory and Statistical Physics
arXiv:2603.18761v1 Announce Type: new Abstract: 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
arXiv:2603.18761v1 Announce Type: new Abstract: 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.
Executive Summary
This article introduces the NeuroGame Transformer (NGT), a novel attention mechanism for transformers that overcomes the limitations of standard attention mechanisms by reconceptualizing attention through a dual perspective of tokens as players in a cooperative game and interacting spins in a statistical physics system. NGT uses game-theoretic concepts, such as Shapley values and Banzhaf indices, to quantify token importance and captures synergistic relationships through pairwise interaction potentials. The system's energy follows an Ising Hamiltonian, with attention weights emerging as marginal probabilities under the Gibbs distribution. Experimental results demonstrate strong performance across several benchmark datasets, outperforming some major efficient transformer baselines. The approach also ensures scalability and numerical stability for long sequences. The code is available online.
Key Points
- ▸ NGT reconceptualizes attention through a dual perspective of tokens as players in a cooperative game and interacting spins in a statistical physics system.
- ▸ NGT uses game-theoretic concepts to quantify token importance and captures synergistic relationships through pairwise interaction potentials.
- ▸ The system's energy follows an Ising Hamiltonian, with attention weights emerging as marginal probabilities under the Gibbs distribution.
- ▸ NGT ensures scalability and numerical stability for long sequences through importance-weighted Monte Carlo estimators with Gibbs-distributed weights.
Merits
Strength in Capturing Higher-Order Dependencies
NGT's dual perspective enables the modeling of higher-order dependencies among tokens, a limitation of standard attention mechanisms.
Scalability and Numerical Stability
NGT's use of importance-weighted Monte Carlo estimators with Gibbs-distributed weights ensures scalability and numerical stability for long sequences.
Demerits
Complexity and Computational Requirements
NGT's dual perspective and game-theoretic concepts may add complexity and computational requirements, potentially limiting its adoption.
Interpretability and Explainability
NGT's use of game-theoretic concepts may make it challenging to interpret and explain the results, potentially limiting its adoption.
Expert Commentary
The introduction of the NeuroGame Transformer (NGT) represents a significant advancement in attention mechanisms for transformers. By reconceptualizing attention through a dual perspective of tokens as players in a cooperative game and interacting spins in a statistical physics system, NGT addresses the limitations of standard attention mechanisms and provides a novel approach to attention in transformers. The use of game-theoretic concepts, such as Shapley values and Banzhaf indices, to quantify token importance and capture synergistic relationships is particularly noteworthy. However, the added complexity and computational requirements of NGT may limit its adoption. Nonetheless, NGT's potential applications in natural language processing tasks, such as language translation, sentiment analysis, and text classification, make it an exciting development. Further research is needed to fully explore the implications of NGT and its potential applications.
Recommendations
- ✓ Recommendation 1: Further research is needed to explore the limitations and potential applications of NGT, particularly in the context of natural language processing tasks.
- ✓ Recommendation 2: The development of NGT highlights the need for further research in the field of natural language processing and its applications, particularly in the context of attention mechanisms and statistical physics.
