LLM-Based Embeddings for Program Analysis and Optimization

Recent work has demonstrated the potential of large language models (LLMs) for program optimization, a key challenge in programming languages. We propose a blackbox adaptation method called Retrieval Augmented Search (RAS) that performs beam search over candidate optimizations; at each step, it retrieves in-context examples from a given training dataset of slow-fast program pairs to guide the LLM. Critically, we find that performing contextual retrieval based on an LLM-generated natural language description significantly outperforms retrieval based on the source code. We also propose AEGIS, a method for improving interpretability by decomposing training examples into ''atomic edits'' that are significantly more incremental in nature. We show that RAS performs up to 2.06$\times$ better than prior state-of-the-art blackbox adaptation strategies on optimizing C++ programs, and that AEGIS performs up to 1.37$\times$ better while making significantly smaller edits. We also show that using RAS improves the mean runtime percentile of Python programs by 10.27 compared to baselines.

LLM discovery and optimization systems are increasingly applied across domains, implementing a common propose-evaluate-revise loop. Such optimization or discovery progresses via context conditioning on received feedback from an environment. However, as modern LLM agents are increasingly complex in their structure, it is difficult to evaluate which components contribute the most, and when and how this exploration may fail. We answer these questions through three controlled experiments. Our findings: (1) In pure black-box optimization, LLMs act as greedy optimizers. (2) In zero-shot kernel generation, providing explicit input-size information has no measurable effect, models converge to the same kernel parameters regardless of size or temperature, as though the size instruction were invisible. Moreover, when tasked to perform kernel optimization for uncommon kernel sizes, performance sharply degrades regardless of the language used. (3) In feedback-loop kernel optimization, CUDA improves monotonically under iterative feedback, while TVM IR actively degrades, which demonstrates that kernel optimization degrades when models operate with low-density language. Our results conclude that LLMs in code optimization tasks highly depend on pretrained priors rather than provided feedback or agentic structure.

Large language models (LLMs) are increasingly used to solve complex problems by searching over program space, offering a general paradigm for scientific problems that can be naturally represented and solved as programs. Despite recent progress, identifying effective optimization directions for a candidate program remains challenging. By analogy with automatic differentiation, existing methods typically guide the search using a textual ``gradient'': a first-order update direction expressed as textual edits. Such gradients are inferred either from previously evaluated programs or from LLM-generated feedback on the implicit program-score mapping. However, these estimates become increasingly unreliable as the program--score mapping grows more complex, limiting their practical utility. We argue that explicit gradients are not essential for effective program optimization. Leveraging their prior knowledge, LLMs can propose plausible atomic edits directly from the current program, thereby enabling a zeroth-order optimization strategy. However, zeroth-order search suffers from a \textit{weakest-link effect}: when a bundle of edits is accepted or rejected as a whole, a single harmful edit can negate the benefits of all remaining edits. To address this issue, we introduce HERO, a program optimizer that prompts an LLM to generate diverse, non-overlapping atomic edits and then systematically selects and composes them into coherent program improvements using evaluator scores. We evaluate HERO across algorithmic problems, strategy games, the design of LLM-based agentic systems, and robotic path planning. Across these domains, HERO consistently discovers higher-scoring programs and converges substantially faster than prior LLM-based optimizers, while consuming fewer tokens.