CliffSearch: Structured Agentic Co-Evolution over Theory and Code for Scientific Algorithm Discovery

Abstract

Scientific algorithm discovery is iterative: hypotheses are proposed, implemented, stress-tested, and revised. Current LLM-guided search systems accelerate proposal generation, but often under-represent scientific structure by optimizing code-only artifacts with weak correctness/originality gating. We present CliffSearch, an agentic evolutionary framework in which the core evolution operators (pair selection, crossover, mutation, and review) are implemented as LLM agents, and the loop is designed around three principles: (1) each node is a structured scientific artifact, instantiated in either theory+code or code_only mode, (2) reviewer judgments of correctness and originality are first-class selection gates alongside optimization of the benchmark metric of interest, and (3) mutation is split into exploration and correction pathways with distinct objectives. Exploration mutation imports ideas from adjacent scientific domains to increase novelty, while correction mutation performs targeted evidence-guided repair using reviewer signals over theory, code, benchmark results, and runtime errors. We illustrate the framework on three benchmark-grounded studies: transformer hyper-connection evolution, optimizer discovery on a fixed nanoGPT stack, and a smaller native-optimizer ablation. Across these settings, the same loop supports explicit metric direction, reproducible persistence, and reviewer-gated comparison of discoveries under controlled search conditions. The result is a discovery workflow that prioritizes scientific interpretability and correctness while optimizing task metrics under controlled novelty constraints, rather than maximizing candidate throughput alone. Full run artifacts, interactive visualizations, and exported best nodes for the reported studies are available at https://cliffsearch.ai .

Figures (5)

• Figure 1: Structured node artifact evolved across generations. In code_only, theory_content is present but empty, while summary_md still carries the node's explanatory prose.
• Figure 2: Two mutation operators with distinct routing and objectives.
• Figure 3: One generation cycle: bucket routing, agent operators, composition, benchmark, and review.
• Figure 4: Distributed multi-island execution with asynchronous migration packets.
• Figure 5: Full generation graph for the reported transformer theory+code single-island run, rendered directly from ga_data.json. Each node is annotated with its flat id, recovered alias, and benchmark primary metric. Nodes with $m=\infty$ denote benchmark execution failures due to implementation/runtime incompatibilities, not valid high-loss models. Edges follow recorded parent links; generation columns correspond to iterations 0 through 3.

Theorems & Definitions (1)

• Remark