Mastering NIM and Impartial Games with Weak Neural Networks: An AlphaZero-inspired Multi-Frame Approach

We introduce a practical circuit-complexity model for fixed-precision neural networks to explain and overcome a persistent learnability barrier in impartial games like NIM. We show that bounded-depth, polynomial-size, fixed-precision neural inference, including recurrent and attention-style architectures, is simulable by AC0 circuits. This places them below TC0 and explains their inability to compute exact parity or the nim-sum.