Danqing Wang

Kexun Zhang, Shang Zhou, Danqing Wang et al.

Sampling is a basic operation in many inference-time algorithms of large language models (LLMs). To scale up inference efficiently with a limited compute, it is crucial to find an optimal allocation for sample compute budgets: Which sampling configurations (model, temperature, language, etc.) do we use? How many samples do we generate in each configuration? We formulate these choices as a learning problem and propose OSCA, an algorithm that Optimizes Sample Compute Allocation by finding an optimal mix of different inference configurations. Our experiments show that with our learned mixed allocation, we can achieve accuracy better than the best single configuration with 128x less compute on code generation and 25x less compute on 4 reasoning tasks. OSCA is also shown to be effective in agentic workflows beyond single-turn tasks, achieving a better accuracy on SWE-Bench with 3x less compute than the default configuration. Our code and generations are released at https://github.com/LeiLiLab/OSCA.

Kexun Zhang, Danqing Wang, Jingtao Xia et al.

Large language models (LLMs) excel at implementing code from functionality descriptions but struggle with algorithmic problems that require not only implementation but also identification of the suitable algorithm. Moreover, LLM-generated programs lack guaranteed correctness and require human verification. To address these challenges, we propose ALGO, a framework that synthesizes Algorithmic programs with LLM-Generated Oracles to guide the generation and verify their correctness. ALGO first generates a reference oracle by prompting an LLM to exhaustively enumerate all the combinations of relevant variables. This oracle is then utilized to guide an arbitrary search strategy in exploring the algorithm space and to verify the synthesized algorithms. Our study shows that the LLM-generated oracles are correct for 88% of the cases. With the oracles as verifiers, ALGO can be integrated with any existing code generation model in a model-agnostic manner to enhance its performance. Experiments show that when equipped with ALGO, we achieve an 8x better one-submission pass rate over the Codex model and a 2.6x better one-submission pass rate over CodeT, the current state-of-the-art model on CodeContests. We can also get 1.3x better pass rate over the ChatGPT Code Interpreter on unseen problems. The problem set we used for testing, the prompts we used, the verifier and solution programs, and the test cases generated by ALGO are available at https://github.com/zkx06111/ALGO.