We propose a self-play approach to generating strategies for playing in multi-player games, where strategies are represented as computer code. We use large language models (LLMs) to generate pieces of code to play in the game, which we refer to as generated bots. We engage the LLM generated bots in competitions, designed to generate increasingly stronger strategies. We follow game theoretic principles in organizing these tournaments, and use a Policy Space Response Oracle (PSRO) approach. We start with an initial set of LLM generated bots, and continue in rounds for adding new bots into the population. Each round adds a bot to the population by asking the LLM to produce code for playing against a bot representing the Nash equilibrium mixture over the current population. Our analysis shows that even a few rounds are sufficient to produces strong bots for playing the game. Our demo shows the process for the game of Checkers. We allow users to select initial bots in the population, run the process, inspect how the bots evolve over time, and play against the generated bots.

AI research agents are demonstrating great potential to accelerate scientific progress by automating the design, implementation, and training of machine learning models. We focus on methods for improving agents' performance on MLE-bench, a challenging benchmark where agents compete in Kaggle competitions to solve real-world machine learning problems. We formalize AI research agents as search policies that navigate a space of candidate solutions, iteratively modifying them using operators. By designing and systematically varying different operator sets and search policies (Greedy, MCTS, Evolutionary), we show that their interplay is critical for achieving high performance. Our best pairing of search strategy and operator set achieves a state-of-the-art result on MLE-bench lite, increasing the success rate of achieving a Kaggle medal from 39.6% to 47.7%. Our investigation underscores the importance of jointly considering the search strategy, operator design, and evaluation methodology in advancing automated machine learning.

Rapidly improving large language models (LLMs) have the potential to assist in scientific progress. One critical skill in this endeavor is the ability to faithfully reproduce existing work. To evaluate the capability of AI agents to reproduce complex code in an active research area, we introduce the Automated LLM Speedrunning Benchmark, leveraging the research community's contributions to the $\textit{NanoGPT speedrun}$, a competition to train a GPT-2 model in the shortest time. Each of the 19 speedrun tasks provides the agent with the previous record's training script, optionally paired with one of three hint formats, ranging from pseudocode to paper-like descriptions of the new record's improvements. Records execute quickly by design and speedrun improvements encompass diverse code-level changes, ranging from high-level algorithmic advancements to hardware-aware optimizations. These features make the benchmark both accessible and realistic for the frontier problem of improving LLM training. We find that recent frontier reasoning LLMs combined with SoTA scaffolds struggle to reimplement already-known innovations in our benchmark, even when given detailed hints. Our benchmark thus provides a simple, non-saturated measure of an LLM's ability to automate scientific reproduction, a necessary (but not sufficient) skill for an autonomous research agent.

Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a prominent problem in knowledge representation and databases. This problem can be solved using the chase algorithm, which extends the given set of facts with fresh facts in order to satisfy the rules. If the chase terminates, then CQs can be evaluated directly in the resulting set of facts. The chase, however, does not terminate necessarily, and checking whether the chase terminates on a given set of rules and facts is undecidable. Numerous acyclicity notions were proposed as sufficient conditions for chase termination. In this paper, we present two new acyclicity notions called model-faithful acyclicity (MFA) and model-summarising acyclicity (MSA). Furthermore, we investigate the landscape of the known acyclicity notions and establish a complete taxonomy of all notions known to us. Finally, we show that MFA and MSA generalise most of these notions. Existential rules are closely related to the Horn fragments of the OWL 2 ontology language; furthermore, several prominent OWL 2 reasoners implement CQ answering by using the chase to materialise all relevant facts. In order to avoid termination problems, many of these systems handle only the OWL 2 RL profile of OWL 2; furthermore, some systems go beyond OWL 2 RL, but without any termination guarantees. In this paper we also investigate whether various acyclicity notions can provide a principled and practical solution to these problems. On the theoretical side, we show that query answering for acyclic ontologies is of lower complexity than for general ontologies. On the practical side, we show that many of the commonly used OWL 2 ontologies are MSA, and that the number of facts obtained by materialisation is not too large. Our results thus suggest that principled development of materialisation-based OWL 2 reasoners is practically feasible.