# Beyond Search-Imitation: Prior-Directed Exploration for Searchless Chess

arXiv: https://arxiv.org/abs/2608.27757 · HTML: https://mlsanity.com/paper/2608.27757/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 47 references that are in the map.
- First posted on arXiv 27 Aug 2026.

## Builds on (most cited first, 30 of 35)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Unifying Count-Based Exploration and Intrinsic Motivation](https://mlsanity.com/paper/1606.01868/) (2016)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Regularizing Neural Networks by Penalizing Confident Output Distributions](https://mlsanity.com/paper/1701.06548/) (2017)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Maximum a Posteriori Policy Optimisation](https://mlsanity.com/paper/1806.06920/) (2018)
- [Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints](https://mlsanity.com/paper/2309.16240/) (2023)
- [Aligning Superhuman AI with Human Behavior: Chess as a Model System](https://mlsanity.com/paper/2006.01855/) (2020)
- [Information asymmetry in KL-regularized RL](https://mlsanity.com/paper/1905.01240/) (2019)
- [Amortized Planning with Large-Scale Transformers: A Case Study on Chess](https://mlsanity.com/paper/2402.04494/) (2024)
- [Behavior Priors for Efficient Reinforcement Learning](https://mlsanity.com/paper/2010.14274/) (2020)
- [The Choice of Divergence: A Neglected Key to Mitigating Diversity Collapse in Reinforcement Learning with Verifiable Reward](https://mlsanity.com/paper/2509.07430/) (2025)
- [Evidence of Learned Look-Ahead in a Chess-Playing Neural Network](https://mlsanity.com/paper/2406.00877/) (2024)
- [KL-Regularized Reinforcement Learning is Designed to Mode Collapse](https://mlsanity.com/paper/2510.20817/) (2025)
- [Unlocking Reasoning Capabilities in LLMs via Reinforcement Learning Exploration](https://mlsanity.com/paper/2510.03865/) (2025)
- [Chessformer: A Unified Architecture for Chess Modeling](https://mlsanity.com/paper/2605.19091/) (2026)

## Abstract (arXiv)

Searchless chess networks reach human master strength from a single forward pass by imitating a stronger teacher: the strongest, Leela Chess Zero's (Lc0) released Chessformer, distills the visit counts of an AlphaZero-style Monte Carlo Tree Search (MCTS). Imitating a search is a poor proxy for playing without one, so we fine-tune for single-pass strength with self-play reinforcement learning (RL). Its exploration is usually supplied by an entropy bonus, the reverse Kullback-Leibler (KL) divergence to uniform. We replace it with a forward, mass-covering KL toward the network's own MCTS prior (prior-directed exploration), so exploration covers the moves the prior judges promising, and pair it with an entropy-adaptive sampling temperature, set by the value head's outcome uncertainty, that sharpens once a position is decided. In about two thousand steps it raises puzzle accuracy from 93.9% to 94.9% on a 100,000-puzzle suite and mate-in-four accuracy from 77% to 81% while holding searchless strength at or slightly above the base. Measuring tactical accuracy and playing strength together across a matched-compute sweep, we find the two dissociate: accuracy gains fall in a one-point band while ratings straddle the base, and a control fine-tuned on puzzles alone posts the study's largest tactical gains while shedding roughly 260 Elo; a better puzzle-solver is not thereby a stronger player. Distribution-level measurements show what anchoring buys: without a regularizer self-play collapses onto a single line of play, and the puzzles newly solved are the near misses whose winning move the prior kept alive. The forward-KL prior tops the rating ladder, statistically tied with a reverse-KL anchor that concentrates twice as hard and drops the hardest solutions the mass-covering prior keeps in support.