Model-guided directed evolution seeks to identify high-fitness protein variants under limited oracle budgets. Protein language models (PLMs) provide rich representations for this task, but existing methods either rely on task-agnostic zero-shot scores or perform search in high-dimensional embedding spaces where surrogate modeling and uncertainty estimation can be sample-inefficient. We propose the Linear Fitness Subspace (LFS) hypothesis: mutation-induced fitness variation encoded by PLMs is concentrated in a low-dimensional linear subspace of residue-level representation changes. This view explains why zero-shot PLM scores are often useful but incomplete: they behave as fixed, task-agnostic projections, whereas few-shot supervision can recover assay-specific fitness directions. Building on this observation, we introduce Subspace-Guided Evolutionary Search (SGES), which learns the LFS from a small initial sample and performs surrogate modeling, uncertainty estimation, and acquisition directly in the learned subspace. Across 10 core ProteinGym assays and an extended set of 87 assays, SGES improves fitness prediction, budgeted search efficiency, computational cost, and biological interpretability over zero-shot PLMs and recent ML-guided protein optimization baselines. These results suggest that PLMs encode protein fitness in a geometry that is more linear, lower-dimensional, and more directly exploitable than previously assumed.

Quantization is widely used to deploy large language models, but its effect on uncertainty behavior, such as confidence, margins, and abstention, is rarely treated as a primary objective. We frame calibration-data selection for quantization as a *target-dependent uncertainty-preservation problem*. Different deployments emphasize different regions of the input distribution, yet prior work mainly optimizes accuracy-oriented compression metrics or adjusts scores after quantization. We formalize this goal with distributional and boundary preservation risks, and provide a simple mixture-mismatch argument explaining why no single calibration recipe should be expected to fit all targets. We introduce Doubt-Preserving Quantization (DPQ), a lightweight pre-quantization recipe family that uses full-precision predictions to construct target-aligned calibration mixtures of high-doubt examples and generic anchors. Across 8 language models, 9 NLP benchmarks, and 22 comparison methods, the leading recipe changes with the preservation target: DPQ-r75 leads on SQuAD2 answerability-boundary preservation, while broad multiple-choice QA favors a different set of milder or single-signal recipes, with confidence-only leading and variants such as entropy-only and DPQ-r50 outperforming the boundary-heavy DPQ-r75. These results show that calibration data should be selected for the specific full-precision score behavior a deployment needs to preserve, rather than treated as a fixed quantization detail. Code is available at https://github.com/xi-xiaoran/DPQ.

LLM agents are moving from single-prompt use to long task streams in which reusable memory becomes a core capability for terminal, software-engineering, and web tasks. Such memory is useful only when stored experience remains reliable across hundreds of interactions, but two failure modes break that assumption in practice. The first is unreliable admission: failed trajectories, accidental successes, and misleading observations enter memory because they appear relevant, then mislead later decisions. The second is memory drift: long-running banks accumulate duplicate, stale, and conflicting records that retrieval alone cannot repair. MemGuard’s key distinction is to treat verifier output not as a one-shot filter, but as persistent lifecycle metadata. It converts multi-criteria score-token verification into reward, confidence, label, and uncertainty descriptors that are attached to every candidate before activation and reused during retrieval, conflict resolution, summarization, and archival. We evaluate MemGuard on Terminal-Bench 2.0, SWE-Bench Verified, WebArena, and Mind2Web across four backbones, comparing against four memory baselines plus a verifier-only control under matched runtime budgets. Averaged over five seeds, MemGuard achieves the best success metric and lowest average steps in all 16 backbone–benchmark settings, improving over ReasoningBank, the strongest prior baseline among the memory methods we evaluate, with a largest gain of 7.9 success-rate points on WebArena, 5.6 step-success-rate points on Mind2Web, and 2.4–3.5 points on terminal and software-engineering benchmarks. Code is available at [https://github.com/whyyyyy123/MemGuard](https://github.com/whyyyyy123/MemGuard).