EVIL: Evolving Interpretable Algorithms for Zero-Shot Inference on Event Sequences and Time Series with LLMs

Large language models (LLMs) perform inference by following a fixed depth and order, non-recurrent execution of all layers. We reveal the wide existence of training-free, flexible, dynamic program-of-layers (PoLar), where pretrained layers can be packed as modules and then skipped or looped to form a customized program for each input. For most inputs, substantially shorter program executions can achieve the same or better accuracy, while incorrect predictions of the original LLM can be corrected by alternative programs with fewer layers. These observations indicate that inference admits multiple valid latent computations beyond the standard forward pass. To efficiently achieve PoLar in practice, we propose a lightweight PoLar prediction network, which learns to generate execution programs that dynamically skip or repeat pretrained layers for each input. Experiments on mathematical reasoning benchmarks demonstrate that PoLar consistently improves accuracy over standard inference and prior dynamic-depth methods, often while executing fewer layers, and that these gains persist under out-of-distribution evaluation. Our results suggest that fixed-depth execution captures only a narrow subset of an LLM's latent reasoning capacity.

LLM-based program evolution systems such as FunSearch and AlphaEvolve have shown strong ability to discover novel algorithms, but typically optimize each task in isolation, discarding search experience after completion. We introduce $\varepsilon$-MemEvo, a framework for cross-task knowledge transfer in LLM program evolution. $\varepsilon$-MemEvo stores prior experience as task-agnostic tactic memories: compact natural-language summaries of successful algorithmic strategies rather than raw code, enabling transfer across tasks with different APIs and evaluators. To avoid negative transfer from semantically mismatched memories, $\varepsilon$-MemEvo uses an adaptive injection gate that decides whether retrieved memories should be injected, and at what intensity. We evaluate $\varepsilon$-MemEvo on 8 diverse optimization benchmarks spanning mathematical optimization and systems engineering, using a content-level Leave-One-Out protocol that excludes target-task memory entries. On the primary GPT-5 backbone, $\varepsilon$-MemEvo improves AUCC over AdaEvolve on all 8 tasks, with a mean relative gain of +8.7%, and improves early-stage convergence by +9.4% on average. Ablations show that naive memory injection can fail catastrophically, while adaptive gating remains safe across all five ablation tasks. The data-updated posterior is interpretable in observed states: it favors skip during improving search and shifts from skip to hint across early and late plateaus. These gains incur less than 1% computational overhead.

Large Language Model (LLM)-guided evolutionary search is increasingly used for automated algorithm discovery, yet most current methods track search progress primarily through executable programs and scalar fitness. Even when natural-language reasoning is used through heuristic descriptions or reflection, it typically remains transient mutation context or unstructured memory, rather than organized as persistent population-level state over strategic directions. As a result, evolutionary search can struggle to distinguish syntactically different implementations of the same idea, preserve lower-fitness but strategically promising directions, or detect when an entire family of strategies has saturated. We introduce \model, a modular strategy-space layer that turns language-level strategic reasoning into first-class population-level evolutionary state in LLM-driven program search. \model represents each candidate program with an explicit natural-language strategy, clusters the archive by strategy semantics, retrieves behaviorally complementary inspirations, and periodically navigates the strategy landscape to avoid saturated directions. Without modifying the underlying evolutionary algorithms, \model improves existing evolutionary backbones across algorithm discovery, systems optimization, and agent-scaffold design tasks in most settings. Across four systems benchmarks, \model achieves a 20.6% average relative improvement, with the best single run on Prism scoring 3$\times$ higher. These results suggest that persistent strategy representations provide a practical mechanism for improving the effectiveness and cost-efficiency of LLM-guided evolutionary search, pointing toward compound AI systems whose search capabilities benefit from the structured accumulation and reuse of algorithmic strategies.