Can Large Language Models Reinvent Foundational Algorithms?

Large language models (LLMs) demonstrate remarkable breadth of knowledge, yet their ability to reason about computational processes remains poorly understood. Closing this gap matters for practitioners who rely on LLMs to guide algorithm selection and deployment. We address this limitation using causal discovery as a testbed and evaluate eight frontier LLMs against ground truth derived from algorithm executions. We find systematic, near-total failure across models. The predicted ranges are far wider than true confidence intervals yet still fail to contain the true algorithmic mean in most cases. Most models perform worse than random guessing. The best model's marginal improvement points to benchmark memorization rather than principled reasoning. We term this failure algorithmic blindness and argue it reflects a fundamental gap between declarative knowledge about algorithms and calibrated procedural prediction.

Large Language Models (LLMs) have been used for novel discovery of algorithms, theorems, drugs, and other tasks through the use of harnesses that prompt an LLM to iteratively optimize an objective. In this work, we study the relationship between the population of previous iterates and eventual discovery success. We generalize past work on harness design to develop a suite of 12 harnesses called 'Modular' and characterize their performance across 5 diverse discovery tasks, finding that discovery success is brittle and sensitive to harness design. We uncover mode collapse, characterized by a dramatic drop in the diversity of iterates, as a common failure mode. We find that popular state-of-the-art harnesses and diversity-inducing harness interventions, which aim to prolong this collapse, yield inconsistent gains. Our results instead uncover that the performance of early discoveries is predictive of eventual success. We therefore propose a universally applicable intervention that performs an initial stage of parallel exploration in order to initialize subsequent iterative optimization. Our method provides consistent gains across many harnesses and target applications, confirming the importance of initialization in LLM-driven discovery.

What happens when you teach an LLM-based agent the scientific method? Motivation: Scientific discovery emerges from cycles of hypothesis, implementation, empirical testing, and feedback. Can this process be automated? We approach automated algorithm design through the lens of the scientific method, where an LLM-based agent goes through each step of the process in an ordered, iterative fashion. Results: We present The Little Scientist, a framework in which a "Scientist agent" works inside an evaluation environment that benchmarks its code and returns structured per-instance diagnostics. When the Scientist plateaus at a local optimum, a "Kuhn agent" injects a paradigm-shifting conjecture paired with a cross-disciplinary inspiration, forcing exploration of a different region of the LLM's latent space. We demonstrate the framework on two problems that require fundamentally different modes of discovery. For protein fitness prediction, the Scientist discovered Delta V, an ensemble calibration strategy that ranks first on the ProteinGym DMS Substitutions Zero-Shot leaderboard across all five official evaluation metrics, exceeding the #2 model (VenusREM) by +0.033 mean Spearman correlation across 217 DMS assays. For DNA motif discovery, the Scientist wrote an algorithm from scratch--DALE (Dual-seed Algorithm for Latent Enumeration)--that outperforms STREME (the default in the MEME Suite) across 132 ENCODE transcription factors (mean AUROC 0.842 vs. 0.803, Wilcoxon p < 10^{-6}) while running 11x faster. This demonstrates that the framework can produce genuinely novel algorithms, not just optimize existing components. Together, these results show that an LLM agent stepping through the scientific method can discover both new algorithms and new ensemble strategies that outperform prior solutions. The entire research program consumed 704M tokens on a single virtual machine with no GPUs