When Does GEPA Merge Help? A Mechanism-Level Diagnostic

Model merging has emerged as a lightweight paradigm for enhancing Large Language Models (LLMs), yet its underlying mechanisms remain poorly understood. In this work, we analyze late-stage pre-training trajectories and uncover a Rank-1 Subspace phenomenon: while raw optimization steps oscillate violently, consecutive merged checkpoints collapse onto a stable, approximately one-dimensional linear manifold. We theoretically ground this observation in a river-valley landscape analysis: averaging acts as a geometric low-pass filter that dampens high-curvature noise to reveal the optimal descent direction. Capitalizing on this insight, we propose Extra-Merge, a training-free strategy that extrapolates along this subspace to minimize loss without additional gradient updates. Extensive experiments across GPT-2 and LLaMA families (124M to 2B) demonstrate that Extra-Merge consistently outperforms standard merging baselines. Notably, it yields consistent zero-shot accuracy gains on Pythia-12B downstream tasks and generalizes effectively to the Muon optimizer \citep{jordan2024muon}.

Large language models fine-tuned from a shared base can be merged by averaging their task vectors, but some merges collapse far below the base model, and common merge operators give no warning before evaluation. We show that one statistic of the specialists' task vectors both predicts this collapse and calibrates its repair. The power that averaging removes equals the variance of the task vectors across specialists, our measure of interference. Under a working noise model, the disturbance that a merge injects grows with the merge coefficient and with interference, yielding a pre-merge score. In our experiments on twenty-two merge configurations from four model families, only destructive merges exceed a threshold on this score. We find that statistics of sign conflict between specialists, a common target of existing merge operators, are anti-predictive. We then predicted the outcomes of fourteen merges before evaluating them, and twelve predictions were correct, including the destructive outcome of a specialist pair pushed past the threshold by continued pretraining. To address this collapse, we introduce PRISM, an operator that averages the task vectors first and then soft-thresholds each layer at a level set by the layer's interference. Without data or tuning, PRISM keeps all five destructive merges above the threshold within evaluation noise of the base model, where plain averaging falls at least 14.4 points below it or collapses entirely. We apply PRISM only above the threshold and keep the plain average for merges below it, which include all fifteen harmless ones. Code is available at https://github.com/js-lee-AI/PRISM.

Prompt optimization methods either analyze individual failures in isolation or compare prompt variants across examples, operating on single execution traces with no access to the reasoning process distinguishing success from failure on the same input. We introduce ContraPrompt, built on the observation that when a model fails but succeeds on a retry with feedback, the difference between its two chain-of-thought traces constitutes an optimization signal not captured by prior methods. Unlike prior contrastive methods, we compare complete intermediate reasoning processes: the two traces share model, input, and base prompt, so remaining differences reflect reasoning strategy and appended error feedback -- we call this dyadic reasoning trace analysis. The multi-attempt solving phase is an instrumented agentic retry loop that generates contrastive data automatically without human annotation. Extracted rules are organized into an input-aware decision tree routing instructions by observable input characteristics. On four reasoning and compliance benchmarks, ContraPrompt outperforms GEPA (Agrawal et al., 2026) on all four, with absolute gains of +8.29 pp on HotPotQA (+20.8% rel.), +2.21 pp on GDPR-Bench (+18.2% rel.), +7.14 pp on GPQA Diamond (+10.6% rel.), and +0.74 pp on BBH (+0.85% rel.). Ablations confirm dyadic trace contrastivity is the critical component, with a -16% relative average drop upon its removal. On 53 EvalSet black-box optimization problems, ContraPrompt beats GEPA on 11, ties on 41, and loses on 1 at equal budget. On FiNER-139 financial named entity recognition (Loukas et al., 2022), ContraPrompt achieves +7.77 pp over the unoptimized baseline (+11.6% rel.) and +1.94 pp over GEPA (+2.66% rel.), with branch conditions aligning with standard US GAAP financial-instrument categories.