Gabriel Poesia
Publications
Learning to Rank the Initial Branching Order of SAT Solvers
Finding good branching orders is key to solving SAT problems efficiently, but finding such branching orders is a difficult problem. Using a learning based approach to predict a good branching order before solving, therefore, has potential. In this paper, we investigate predicting branching orders using graph neural networks as a preprocessing step to conflict-driven clause learning (CDCL) SAT solvers. We show that there are significant gains to be made in existing CDCL SAT solvers by providing a good initial branching. Further, we provide three labeling methods to find such initial branching orders in a tractable way. Finally, we train a graph neural network to predict these branching orders and show through our evaluations that a GNN-initialized ordering yields significant speedups on random 3-CNF and pseudo-industrial benchmarks, with generalization capabilities to instances much larger than the training set. However, we also find that the predictions fail at speeding up more difficult and industrial instances. We attribute this to the solver's dynamic heuristics, which rapidly overwrite the provided initialization, and to the complexity of these instances, making GNN prediction hard.
The Token Games: Evaluating Language Model Reasoning with Puzzle Duels
Evaluating the reasoning capabilities of Large Language Models is increasingly challenging as models improve. Human curation of hard questions is highly expensive, especially in recent benchmarks using PhD-level domain knowledge to challenge the most capable models. Even then, there is always a concern about whether these questions test genuine reasoning or if similar problems have been seen during training. Here, we take inspiration from 16th-century mathematical duels to design The Token Games (TTG): an evaluation framework where models challenge each other by creating their own puzzles. We leverage the format of Programming Puzzles - given a Python function that returns a boolean, find inputs that make it return True - to flexibly represent problems and enable verifying solutions. Using results from pairwise duels, we then compute Elo ratings, allowing us to compare models relative to each other. We evaluate 10 frontier models on TTG, and closely match the ranking from existing benchmarks such as Humanity's Last Exam, without involving any human effort in creating puzzles. We also find that creating good puzzles is still a highly challenging task for current models, not measured by previous benchmarks. Overall, our work suggests new paradigms for evaluating reasoning that cannot be saturated by design, and that allow testing models for other skills like creativity and task creation alongside problem solving.