Søren Riis

Bei Zhou, Søren Riis

AlphaZero-style reinforcement learning (RL) algorithms have achieved superhuman performance in many complex board games such as Chess, Shogi, and Go. However, we showcase that these algorithms encounter significant and fundamental challenges when applied to impartial games, a class where players share game pieces and optimal strategy often relies on abstract mathematical principles. Specifically, we utilise the game of Nim as a concrete and illustrative case study to reveal critical limitations of AlphaZero-style and similar self-play RL algorithms. We introduce a novel conceptual framework distinguishing between champion and expert mastery to evaluate RL agent performance. Our findings reveal that while AlphaZero-style agents can achieve champion-level play on very small Nim boards, their learning progression severely degrades as the board size increases. This difficulty stems not merely from complex data distributions or noisy labels, but from a deeper representational bottleneck: the inherent struggle of generic neural networks to implicitly learn abstract, non-associative functions like parity, which are crucial for optimal play in impartial games. This limitation causes a critical breakdown in the positive feedback loop essential for self-play RL, preventing effective learning beyond rote memorisation of frequently observed states. These results align with broader concerns regarding AlphaZero-style algorithms' vulnerability to adversarial attacks, highlighting their inability to truly master all legal game states. Our work underscores that simple hyperparameter adjustments are insufficient to overcome these challenges, establishing a crucial foundation for the development of fundamentally novel algorithmic approaches, potentially involving neuro-symbolic or meta-learning paradigms, to bridge the gap towards true expert-level AI in combinatorial games.

Long Phan, Alice Gatti, Ziwen Han et al. · amazon-science, apple-ml

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 2,500 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai.

Søren Riis

This paper provides a theoretical framework that validates and explains the results in the work with Bei Zhou experimentally finding that AlphaZero-style reinforcement learning algorithms struggle to learn optimal play in NIM, a canonical impartial game proposed as an AI challenge by Harvey Friedman in 2017. Our analysis resolves a controversy around these experimental results, which revealed unexpected difficulties in learning NIM despite its mathematical simplicity compared to games like chess and Go. Our key contributions are as follows: We prove that by incorporating recent game history, these limited AlphaZero models can, in principle, achieve optimal play in NIM. We introduce a novel search strategy where roll-outs preserve game-theoretic values during move selection, guided by a specialised policy network. We provide constructive proofs showing that our approach enables optimal play within the \(\text{AC}^0\) complexity class despite the theoretical limitations of these networks. This research demonstrates how constrained neural networks when properly designed, can achieve sophisticated decision-making even in domains where their basic computational capabilities appear insufficient.