Analysis and Explainability of LLMs Via Evolutionary Methods

Open-weight large language models (LLMs) are increasingly developed through complex, multi-stage pipelines, leading to intricate lineage relationships that reflect model origin, ownership, and evolution. Understanding these relationships is important for model provenance, governance, and supply-chain integrity. In this work, we investigate the notion of LLM "biometrics" (analogous to human biometrics) to ask whether LLMs exhibit intrinsic fingerprints in weight space alone, without access to input data, that reveal their origin and lineage. We formulate this as a lineage discrimination problem, distinguishing among independent-origin, same-series, and shared-base models. To characterize these relationships, we propose a unified geometric fingerprinting framework that analyzes weight matrices from two complementary perspectives: (i) spectral energy, captured by singular value distributions to encode global magnitude patterns, and (ii) subspace alignment, quantified via subspace deviations to capture directional geometry. Our analysis uncovers a clear hierarchy of structural similarity in weight space: spectral energy reliably distinguishes independently trained models and different model families, while subspace alignment enables fine-grained discrimination among closely related models, including variations in dataset scale and post-training procedures. Extensive experiments on over 110 diverse open-weight LLM pairs demonstrate that weight-space geometry provides a robust and interpretable signal for model lineage, enabling coarse-grained regime separation and fine-grained discrimination within shared-base models.

Large language model (LLM)-driven evolution has shown promise for program search and algorithm discovery, but relying on strong models throughout long evolutionary runs is costly. A natural alternative is to combine cheap and strong models under a fixed inference budget. However, existing approaches typically allocate models at the level of individual queries or mutation steps, overlooking that evolutionary search is \textit{stateful}: each generated candidate changes the population from which subsequent mutations are produced. We empirically analyze LLM-driven evolutionary trajectories and find that search progress is strongly front-loaded, early trajectory performance is informative but noisy, and cheap models recover much of the early progress achieved by strong models at lower cost. Motivated by these findings, we propose \textbf{\model}, a training-free framework that shifts budget allocation from individual calls to evolving populations through adaptive \textit{population handoff}. A cheap model explores multiple trajectories in short blocks allocated by a bandit scheduler. Relay Gain, defined as the marginal improvement of a compact, quality-diverse candidate bank constructed for handoff, serves as the scheduler reward and determines when to hand off. The curated candidates initialize a shared strong model population for refinement. Across four benchmarks and three budgets, \model achieves the highest mean score in 11 of 12 settings, outperforming competitive baselines. Our results suggest that in stateful search, budget allocation should be organized around the population, not the individual call.

Large language models (LLMs) are increasingly integrated with evolutionary computation to support optimization tasks. This survey primarily focuses on evolutionary optimization, i.e., optimization based on evolutionary computation. For brevity, we use the term optimization throughout to denote this scope. However, existing surveys typically examine isolated roles of LLMs and do not provide a unified view that connects optimization modeling with optimization solving. To address this gap, we systematically review recent developments through a workflow-oriented framework. First, we organize the literature into two primary stages: LLMs for optimization modeling and LLMs for optimization solving (in this survey, the terms optimization modeling and optimization solving are used as concise forms of optimization problem modeling and optimization problem solving, respectively). Second, we divide the solving stage into three paradigms according to the role of the LLM: stand-alone optimizers, low-level components embedded in optimization algorithms, and high-level managers for algorithm selection and generation. Third, we analyze representative methods, identify their technical limitations, and clarify their relationships with traditional optimization approaches. We further substantiate this taxonomy through benchmark systematization, baseline comparisons, and practitioner-oriented guidance, and we review interdisciplinary applications across the natural sciences, engineering, and machine learning. Based on the resulting analysis, we identify research directions toward dynamic, self-evolving, and agentic optimization ecosystems. An up-to-date collection of related literature is maintained at https://github.com/ishmael233/LLM4OPT.