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

arXiv: https://arxiv.org/abs/2506.04892 · HTML: https://mlsanity.com/paper/2506.04892/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [Aligning Superhuman AI with Human Behavior: Chess as a Model System](https://mlsanity.com/paper/2006.01855/) (2020)
- [Amortized Planning with Large-Scale Transformers: A Case Study on Chess](https://mlsanity.com/paper/2402.04494/) (2024)
- [Maia-2: A Unified Model for Human-AI Alignment in Chess](https://mlsanity.com/paper/2409.20553/) (2024)
- [Giraffe: Using Deep Reinforcement Learning to Play Chess](https://mlsanity.com/paper/1509.01549/) (2015)

## Built on by (most cited first, 4 of 4)

- [Causal Masking on Spatial Data: An Information-Theoretic Case for Learning Spatial Datasets with Unimodal Language Models](https://mlsanity.com/paper/2510.27009/) (2025)
- [Supervised Contrastive Frame Aggregation for Video Representation Learning](https://mlsanity.com/paper/2512.12549/) (2025)
- [RePAIR: Predictive Self-Supervised Representation Learning in Chess](https://mlsanity.com/paper/2606.11860/) (2026)
- [Beyond Search-Imitation: Prior-Directed Exploration for Searchless Chess](https://mlsanity.com/paper/2608.27757/) (2026)

## Abstract (arXiv)

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.