AAI_2025_Capstone_Chronicles_Combined

Evaluating Deep Learning Model Convergence in Chess via Nash Equilibria

10 enough information for a model to capture these relationships of relative piece placement and piece count to map to the three class evaluation of a position.

Experimental Methods Though modern methods involving chess position classification involve transformers, the limited computational budget of a single Titan RTX GPU limited this study to Convolutional Neural Network architectures (Monroe & Chalmers, 2024). CNNs and ResNets are not without their advantages; however, the spatial relationships within the 8x8x36 position tensors can be exploited by the convolutional kernels. Strong chess engines, like AlphaZero, Leela Chess Zero, and Stoofvlees utilize ResNets as heuristic functions during search (Silver et al., 2017). This paper limits its study to ResNet with 4 residual blocks consisting of 512 3x3 kernel filters. The ResNet also utilizes Squeeze Excitation Layers following Global Average Pooling to increase model capacity without extending the depth of the network (Hu et al., 2019). The final ResNet Block is passed through a convolutional layer of 32 1x1 filters and a final convolutional layer of a single 1x1 filter. This final convolutional layer is shaped as an 8x8 plane with the purpose of juxtaposing the activations onto a chess board for later analysis. The final 8x8 plane is flattened as passed through a multilayer perceptron with 128 hidden nodes and outputting three classes: Win, Draw, or Loss. The 4x512 ResNet with a batch size of 64 and dropout rate of 25% using Nadam for categorical cross entropy on three classes. Each epoch consists of 100,000 training steps (6.4 million positions). The first 22 epochs utilized a learning rate of 5e-4, and the last 26 epochs utilized a learning rate of 1e-5. In total, the model trained on 307 million unique positions or approximately 3 million games. However, since the large database of 1800+ elo chess games

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