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[2411.06403] Mastering NIM and Impartial Games with Weak Neural Networks: An AlphaZero-inspired Multi-Frame Approach
Summary
This paper explores the application of weak neural networks in mastering impartial games like NIM, utilizing an AlphaZero-inspired multi-frame approach to improve performance in fixed-latency environments.
Why It Matters
Understanding how weak neural networks can effectively master complex games like NIM is crucial for advancing AI strategies in game theory and artificial intelligence. This research highlights the importance of structural priors in neural network design, which could influence future developments in AI applications beyond gaming.
Key Takeaways
- Single-frame agents struggle to master NIM due to representational limitations.
- Multi-policy-head and multi-frame architectures significantly enhance performance.
- Explicit structural priors are essential for effective learning in fixed-scale environments.
- Empirical results demonstrate that advanced architectures can achieve near-perfect accuracy.
- The study provides insights into the design of neural networks for complex decision-making tasks.
Computer Science > Artificial Intelligence arXiv:2411.06403 (cs) [Submitted on 10 Nov 2024 (v1), last revised 15 Feb 2026 (this version, v3)] Title:Mastering NIM and Impartial Games with Weak Neural Networks: An AlphaZero-inspired Multi-Frame Approach Authors:Søren Riis View a PDF of the paper titled Mastering NIM and Impartial Games with Weak Neural Networks: An AlphaZero-inspired Multi-Frame Approach, by S{\o}ren Riis View PDF HTML (experimental) Abstract:We study impartial games under fixed-latency, fixed-scale quantised inference (FSQI). In this fixed-scale, bounded-range regime, we prove that inference is simulable by constant-depth polynomial-size Boolean circuits (AC0). This yields a worst-case representational barrier: single-frame agents in the FSQI/AC0 regime cannot strongly master NIM, because optimal play depends on the global nim-sum (parity). Under our stylised deterministic rollout interface, a single rollout policy head from the structured family analysed here reveals only one fixed linear functional of the invariant, so increasing rollout budget alone does not recover the missing bits. We derive two structural bypasses: (1) a multi-policy-head rollout architecture that recovers the full invariant via distinct rollout channels, and (2) a multi-frame architecture that tracks local nimber differences and supports restoration. Experiments across multiple settings are consistent with these predictions: single-head baselines stay near chance, while two-frame mod...
