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.

Reasoning Can Hurt the Inductive Abilities of Large Language Models

Large Language Models (LLMs) have shown remarkable progress across domains, yet their ability to perform inductive reasoning - inferring latent rules from sparse examples - remains limited. It is often assumed that chain-of-thought (CoT) prompting, as used in Large Reasoning Models (LRMs), enhances such reasoning. We investigate this assumption with creating four controlled, diagnostic game-based tasks - chess, Texas Hold'em, dice games, and blackjack - with hidden human-defined rules. We find that CoT reasoning can degrade inductive performance, with LRMs often underperforming their non-reasoning counterparts. To explain this, we present a theoretical framework that reveals how reasoning steps can amplify error through three failure modes: incorrect sub-task decomposition, incorrect sub-task solving, and incorrect final answer summarization. Based on our theoretical and empirical analysis, we introduce structured interventions that adapt CoT generation according to our identified failure types. These interventions improve inductive accuracy without retraining. Our findings suggest that effective (CoT) reasoning depends not only on taking more steps but also on ensuring those steps are well-structured.

Vision Language Models are Biased

Large language models (LLMs) memorize a vast amount of prior knowledge from the Internet that help them on downstream tasks but also may notoriously sway their outputs towards wrong or biased answers. In this work, we test how the knowledge about popular subjects hurt the accuracy of vision language models (VLMs) on standard, objective visual tasks of counting and identification. We find that state-of-the-art VLMs are strongly biased (e.g, unable to recognize a fourth stripe has been added to a 3-stripe Adidas logo) scoring an average of 17.05% accuracy in counting (e.g., counting stripes in an Adidas-like logo) across 7 diverse domains from animals, logos, chess, board games, optical illusions, to patterned grids. Insert text (e.g., "Adidas") describing the subject name into the counterfactual image further decreases VLM accuracy. The biases in VLMs are so strong that instructing them to double-check their results or rely exclusively on image details to answer improves counting accuracy by only +2 points, on average. Our work presents an interesting failure mode in VLMs and an automated framework for testing VLM biases. Code and data are available at: vlmsarebiased.github.io.

ZeroSumEval: Scaling LLM Evaluation with Inter-Model Competition

Evaluating the capabilities of Large Language Models (LLMs) has traditionally relied on static benchmark datasets, human assessments, or model-based evaluations - methods that often suffer from overfitting, high costs, and biases. ZeroSumEval is a novel competition-based evaluation protocol that leverages zero-sum games to assess LLMs with dynamic benchmarks that resist saturation. ZeroSumEval encompasses a diverse suite of games, including security challenges (PyJail), classic games (Chess, Liar's Dice, Poker), knowledge tests (MathQuiz), and persuasion challenges (Gandalf, Debate). These games are designed to evaluate a range of AI capabilities such as strategic reasoning, planning, knowledge application, and creativity. Building upon recent studies that highlight the effectiveness of game-based evaluations for LLMs, ZeroSumEval enhances these approaches by providing a standardized and extensible framework. To demonstrate this, we conduct extensive experiments with >7000 simulations across 7 games and 13 models. Our results show that while frontier models from the GPT and Claude families can play common games and answer questions, they struggle to play games that require creating novel and challenging questions. We also observe that models cannot reliably jailbreak each other and fail generally at tasks requiring creativity. We release our code at https://github.com/facebookresearch/ZeroSumEval.

pix2pockets: Shot Suggestions in 8-Ball Pool from a Single Image in the Wild

Computer vision models have seen increased usage in sports, and reinforcement learning (RL) is famous for beating humans in strategic games such as Chess and Go. In this paper, we are interested in building upon these advances and examining the game of classic 8-ball pool. We introduce pix2pockets, a foundation for an RL-assisted pool coach. Given a single image of a pool table, we first aim to detect the table and the balls and then propose the optimal shot suggestion. For the first task, we build a dataset with 195 diverse images where we manually annotate all balls and table dots, leading to 5748 object segmentation masks. For the second task, we build a standardized RL environment that allows easy development and benchmarking of any RL algorithm. Our object detection model yields an AP50 of 91.2 while our ball location pipeline obtains an error of only 0.4 cm. Furthermore, we compare standard RL algorithms to set a baseline for the shot suggestion task and we show that all of them fail to pocket all balls without making a foul move. We also present a simple baseline that achieves a per-shot success rate of 94.7% and clears a full game in a single turn 30% of the time.

Policies of Multiple Skill Levels for Better Strength Estimation in Games

Accurately estimating human skill levels is crucial for designing effective human-AI interactions so that AI can provide appropriate challenges or guidance. In games where AI players have beaten top human professionals, strength estimation plays a key role in adapting AI behavior to match human skill levels. In a previous state-of-the-art study, researchers have proposed a strength estimator trained using human players' match data. Given some matches, the strength estimator computes strength scores and uses them to estimate player ranks (skill levels). In this paper, we focus on the observation that human players' behavior tendency varies according to their strength and aim to improve the accuracy of strength estimation by taking this into account. Specifically, in addition to strength scores, we obtain policies for different skill levels from neural networks trained using human players' match data. We then combine features based on these policies with the strength scores to estimate strength. We conducted experiments on Go and chess. For Go, our method achieved an accuracy of 80% in strength estimation when given 10 matches, which increased to 92% when given 20 matches. In comparison, the previous state-of-the-art method had an accuracy of 71% with 10 matches and 84% with 20 matches, demonstrating improvements of 8-9%. We observed similar improvements in chess. These results contribute to developing a more accurate strength estimation method and to improving human-AI interaction.

Search-contempt: a hybrid MCTS algorithm for training AlphaZero-like engines with better computational efficiency

AlphaZero in 2017 was able to master chess and other games without human knowledge by playing millions of games against itself (self-play), with a computation budget running in the tens of millions of dollars. It used a variant of the Monte Carlo Tree Search (MCTS) algorithm, known as PUCT. This paper introduces search-contempt, a novel hybrid variant of the MCTS algorithm that fundamentally alters the distribution of positions generated in self-play, preferring more challenging positions. In addition, search-contempt has been shown to give a big boost in strength for engines in Odds Chess (where one side receives an unfavorable position from the start). More significantly, it opens up the possibility of training a self-play based engine, in a much more computationally efficient manner with the number of training games running into hundreds of thousands, costing tens of thousands of dollars (instead of tens of millions of training games costing millions of dollars required by AlphaZero). This means that it may finally be possible to train such a program from zero on a standard consumer GPU even with a very limited compute, cost, or time budget.

A Behavior-Based Knowledge Representation Improves Prediction of Players' Moves in Chess by 25%

Predicting player behavior in strategic games, especially complex ones like chess, presents a significant challenge. The difficulty arises from several factors. First, the sheer number of potential outcomes stemming from even a single position, starting from the initial setup, makes forecasting a player's next move incredibly complex. Second, and perhaps even more challenging, is the inherent unpredictability of human behavior. Unlike the optimized play of engines, humans introduce a layer of variability due to differing playing styles and decision-making processes. Each player approaches the game with a unique blend of strategic thinking, tactical awareness, and psychological tendencies, leading to diverse and often unexpected actions. This stylistic variation, combined with the capacity for creativity and even irrational moves, makes predicting human play difficult. Chess, a longstanding benchmark of artificial intelligence research, has seen significant advancements in tools and automation. Engines like Deep Blue, AlphaZero, and Stockfish can defeat even the most skilled human players. However, despite their exceptional ability to outplay top-level grandmasters, predicting the moves of non-grandmaster players, who comprise most of the global chess community -- remains complicated for these engines. This paper proposes a novel approach combining expert knowledge with machine learning techniques to predict human players' next moves. By applying feature engineering grounded in domain expertise, we seek to uncover the patterns in the moves of intermediate-level chess players, particularly during the opening phase of the game. Our methodology offers a promising framework for anticipating human behavior, advancing both the fields of AI and human-computer interaction.

LLM-Gomoku: A Large Language Model-Based System for Strategic Gomoku with Self-Play and Reinforcement Learning

In recent years, large language models (LLMs) have shown significant advancements in natural language processing (NLP), with strong capa-bilities in generation, comprehension, and rea-soning. These models have found applications in education, intelligent decision-making, and gaming. However, effectively utilizing LLMs for strategic planning and decision-making in the game of Gomoku remains a challenge. This study aims to develop a Gomoku AI system based on LLMs, simulating the human learning process of playing chess. The system is de-signed to understand and apply Gomoku strat-egies and logic to make rational decisions. The research methods include enabling the model to "read the board," "understand the rules," "select strategies," and "evaluate positions," while en-hancing its abilities through self-play and rein-forcement learning. The results demonstrate that this approach significantly improves the se-lection of move positions, resolves the issue of generating illegal positions, and reduces pro-cess time through parallel position evaluation. After extensive self-play training, the model's Gomoku-playing capabilities have been notably enhanced.

Rotated Bitboards in FUSc# and Reinforcement Learning in Computer Chess and Beyond

There exist several techniques for representing the chess board inside the computer. In the first part of this paper, the concepts of the bitboard-representation and the advantages of (rotated) bitboards in move generation are explained. In order to illustrate those ideas practice, the concrete implementation of the move-generator in FUSc# is discussed and we explain a technique how to verify the move-generator with the "perft"-command. We show that the move-generator of FUSc# works 100% correct. The second part of this paper deals with reinforcement learning in computer chess (and beyond). We exemplify the progress that has been made in this field in the last 15-20 years by comparing the "state of the art" from 2002-2008, when FUSc# was developed, with recent innovations connected to "AlphaZero". We discuss how a "FUSc#-Zero" could be implemented and what would be necessary to reduce the number of training games necessary to achieve a good performance. This can be seen as a test case to the general prblem of improving "sample effciency" in reinforcement learning. In the final part, we move beyond computer chess, as the importance of sample effciency extends far beyond board games into a wide range of applications where data is costly, diffcult to obtain, or time consuming to generate. We review some application of the ideas developed in AlphaZero in other domains, i.e. the "other Alphas" like AlphaFold, AlphaTensor, AlphaGeometry and AlphaProof. We also discuss future research and the potential for such methods for ecological economic planning.