Yikai Wu

Ori Press, Brandon Amos, Haoyu Zhao et al. · princeton, uw

Despite progress in language model (LM) capabilities, evaluations have thus far focused on models' performance on tasks that humans have previously solved, including in programming (Jimenez et al., 2024) and mathematics (Glazer et al., 2024). We therefore propose testing models' ability to design and implement algorithms in an open-ended benchmark: We task LMs with writing code that efficiently solves computationally challenging problems in computer science, physics, and mathematics. Our AlgoTune benchmark consists of 154 coding tasks collected from domain experts and a framework for validating and timing LM-synthesized solution code, which is compared to reference implementations from popular open-source packages. In addition, we develop a baseline LM agent, AlgoTuner, and evaluate its performance across a suite of frontier models. AlgoTuner uses a simple, budgeted loop that edits code, compiles and runs it, profiles performance, verifies correctness on tests, and selects the fastest valid version. AlgoTuner achieves an average 1.72x speedup against our reference solvers, which use libraries such as SciPy, sk-learn and CVXPY. However, we find that current models fail to discover algorithmic innovations, instead preferring surface-level optimizations. We hope that AlgoTune catalyzes the development of LM agents exhibiting creative problem solving beyond state-of-the-art human performance.

Yikai Wu, Haoyu Zhao, Sanjeev Arora

This position paper argues that the machine learning community should fundamentally rethink how AI-inspired methods are developed and evaluated for combinatorial optimization (CO). We present comprehensive empirical benchmarks comparing various recent AI-inspired GPU-based methods with several classical CPU-based solvers on the Maximum Independent Set (MIS) problem. Strikingly, even on in-distribution random graphs, leading AI-inspired methods are consistently outperformed by the state-of-the-art classical solver KaMIS, and some AI-inspired methods frequently fail to surpass even the simplest degree-based greedy heuristic. To better understand the source of these failures, we introduce a novel analysis, serialization, which reveals that non-backtracking AI methods, such as LTFT (based on GFlowNets), end up reasoning similarly to the simplest degree-based greedy heuristic, and thus worse than KaMIS. Our findings reveal three core issues: (1) Limited benchmarks and evaluation - AI-inspired methods are often tested only on small instances with very limited inference time, which covers up issues with scalability and resource usage; (2) Intrinsic hardness and learning limits - even under ideal, in-distribution conditions, learning-based approaches lag behind classical heuristics, highlighting inherent barriers that receive little attention; and (3) Insufficient use and understanding of classical heuristics - current learning frameworks often neglect to incorporate effective classical techniques. Although we use MIS as a testbed, similar gaps and challenges have been reported in other combinatorial optimization problems, suggesting broader relevance for our recommendations. We propose that future research must address these issues by rigorous benchmarking, deepening understanding of learning limitations, and integrating classical heuristics into AI-inspired methods.