Learning to Plan via Supervised Contrastive Learning and Strategic Interpolation: A Chess Case Study

Modern chess engines achieve superhuman performance through deep tree search and regressive evaluation, while human players rely on intuition to select candidate moves followed by a shallow search to validate them. To model this intuition-driven planning process, we train a transformer encoder using supervised contrastive learning to embed board states into a latent space structured by positional evaluation. In this space, distance reflects evaluative similarity, and visualized trajectories display interpretable transitions between game states. We demonstrate that move selection can occur entirely within this embedding space by advancing toward favorable regions, without relying on deep search. Despite using only a 6-ply beam search, our model achieves an estimated Elo rating of 2593. Performance improves with both model size and embedding dimensionality, suggesting that latent planning may offer a viable alternative to traditional search. Although we focus on chess, the proposed embedding-based planning method can be generalized to other perfect-information games where state evaluations are learnable. All source code is available at https://github.com/andrewhamara/SOLIS.

Is ReLU Adversarially Robust?

The efficacy of deep learning models has been called into question by the presence of adversarial examples. Addressing the vulnerability of deep learning models to adversarial examples is crucial for ensuring their continued development and deployment. In this work, we focus on the role of rectified linear unit (ReLU) activation functions in the generation of adversarial examples. ReLU functions are commonly used in deep learning models because they facilitate the training process. However, our empirical analysis demonstrates that ReLU functions are not robust against adversarial examples. We propose a modified version of the ReLU function, which improves robustness against adversarial examples. Our results are supported by an experiment, which confirms the effectiveness of our proposed modification. Additionally, we demonstrate that applying adversarial training to our customized model further enhances its robustness compared to a general model.