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

arXiv: https://arxiv.org/abs/2604.01210 · HTML: https://mlsanity.com/paper/2604.01210/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Web, search, and research agents, one of 16 directions in LLM agents and tool use.
- Builds on 29 of its 66 references that are in the map.
- First posted on arXiv 1 Apr 2026.

## Placed in

- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training](https://mlsanity.com/paper/2305.14342/) (2023)
- [SOAP: Improving and Stabilizing Shampoo using Adam](https://mlsanity.com/paper/2409.11321/) (2024)
- [Large Language Models to Enhance Bayesian Optimization](https://mlsanity.com/paper/2402.03921/) (2024)
- [Fantastic Pretraining Optimizers and Where to Find Them](https://mlsanity.com/paper/2509.02046/) (2025)
- [LLaMEA: A Large Language Model Evolutionary Algorithm for Automatically Generating Metaheuristics](https://mlsanity.com/paper/2405.20132/) (2024)
- [mHC: Manifold-Constrained Hyper-Connections](https://mlsanity.com/paper/2512.24880/) (2025)
- [Hyper-Connections](https://mlsanity.com/paper/2409.19606/) (2024)
- [Practical Efficiency of Muon for Pretraining](https://mlsanity.com/paper/2505.02222/) (2025)
- [Algorithm Evolution Using Large Language Model](https://mlsanity.com/paper/2311.15249/) (2023)
- [MAtt: A Manifold Attention Network for EEG Decoding](https://mlsanity.com/paper/2210.01986/) (2022)
- [LLM4AD: A Platform for Algorithm Design with Large Language Model](https://mlsanity.com/paper/2412.17287/) (2024)
- [Scientific Algorithm Discovery by Augmenting AlphaEvolve with Deep Research](https://mlsanity.com/paper/2510.06056/) (2025)
- [Evolve Cost-aware Acquisition Functions Using Large Language Models](https://mlsanity.com/paper/2404.16906/) (2024)
- [mHC-lite: You Don't Need 20 Sinkhorn-Knopp Iterations](https://mlsanity.com/paper/2601.05732/) (2026)
- [Curve Your Attention: Mixed-Curvature Transformers for Graph Representation Learning](https://mlsanity.com/paper/2309.04082/) (2023)
- [Automated Design of Metaheuristic Algorithms: A Survey](https://mlsanity.com/paper/2303.06532/) (2023)
- [KromHC: Manifold-Constrained Hyper-Connections with Kronecker-Product Residual Matrices](https://mlsanity.com/paper/2601.21579/) (2026)
- [LLaMEA-BO: A Large Language Model Evolutionary Algorithm for Automatically Generating Bayesian Optimization Algorithms](https://mlsanity.com/paper/2505.21034/) (2025)
- [JPmHC Dynamical Isometry via Orthogonal Hyper-Connections](https://mlsanity.com/paper/2602.18308/) (2026)
- [Riemannian Self-Attention Mechanism for SPD Networks](https://mlsanity.com/paper/2311.16738/) (2023)
- [mHC-GNN: Manifold-Constrained Hyper-Connections for Graph Neural Networks](https://mlsanity.com/paper/2601.02451/) (2026)
- [Spectral-Sphere-Constrained Hyper-Connections](https://mlsanity.com/paper/2603.20896/) (2026)
- [LLMs, Reasoning and Plagiarism](https://mlsanity.com/paper/2601.02380/) (2025)
- [Geometric Mixture-of-Experts with Curvature-Guided Adaptive Routing for Graph Representation Learning](https://mlsanity.com/paper/2603.22317/) (2026)
- [Early Discoveries of Algorithmist I: Promise of Provable Algorithm Synthesis at Scale](https://mlsanity.com/paper/2603.22363/) (2026)

## Abstract (arXiv)

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 .