Procedural-skill SFT across capacity tiers: A W-Shaped pre-SFT Trajectory and Regime-Asymmetric Mechanism on 0.8B-4B Qwen3.5 Models

Large language models increasingly write, review, and judge code, and a fast-growing practice equips them with prompt 'skills' that ask the model to reason like a scientist. A prominent example tells the model to act as a Popperian falsificationist, and such skills are reported to improve generated code. But these gains are almost always read off an LLM-as-a-judge, an instrument with documented positional, self-preference, and stylistic biases. We ask: if it appears to help, is the gain from the skill's Popperian content, or from the structure any scaffold imposes? We pre-register a two-tier ablation with three controls: a length-matched placebo, a labels-only scaffold that keeps the Popperian headers but strips the procedure, and an execution oracle (HumanEval+ unit tests), plus a vocabulary-halo sentinel and a same-model self-judge audit. On a frontier model (Claude Sonnet 4.6, N=163) all conditions sit near the benchmark ceiling and do not separate, so the pre-registered +5-point improvement is not supported (a ceiling-limited non-detection). On a small model (Qwen2.5-Coder-0.5B, N=164) structured arms lift best-of-eight correctness by 20-22 points, but the full skill shows no separable benefit over a labels-only scaffold (aggregate F@8=L@8 vs V@8=34.8%), and the placebo trails by only 2.4 points. A 0.5B self-judge applying the Popperian rubric does not beat random selection and concentrates 60% of its picks on one index. In the two settings tested, the skill's Popperian procedural content adds no separable execution-correctness benefit beyond a labels-only scaffold, so the gains track scaffold structure. We contribute a calibrated negative result and a reusable disambiguation protocol; the finding bounds an engineering claim about one prompt-skill family and is not an evaluation of Popperian methodology in general.

Large language models (LLMs) often achieve strong performance on reasoning benchmarks, but final-answer accuracy alone does not show whether they faithfully execute the procedure specified in a prompt. We introduce a controlled diagnostic benchmark for procedural execution, where models are given a step-wise arithmetic procedure and two numeric inputs, and must return the final computed value. Complexity is varied through procedure length and look-back dependencies over intermediate variables. Average first-answer accuracy drops from 63% on 5-step procedures to 20% on 95-step procedures. Generation-level analysis shows that failures often involve missing answers, premature answers, self-correction after an initial error and under-executed traces. These findings suggest that apparent reasoning ability can mask substantial weaknesses in faithful long-horizon procedural execution.

Procedural memory is increasingly used to improve LLM agents on recurring workplace tasks, yet its ability to produce reusable skills remains poorly understood. We introduce AFTER, a benchmark of 382 realistic enterprise tasks spanning six professional roles and 22 procedural skills, designed to evaluate how skills transfer across tasks, roles, and model backbones. The benchmark includes controlled evaluation settings for local improvement, cross-task transfer, cross-role transfer, and cross-model generalization. Experiments show that procedural memory delivers consistent gains in industrial workflows: a single refinement round improves aggregate performance by 3.7-6.7 points, while skills evolved from diverse multi-model execution traces achieve 73.1% cross-model test accuracy, outperforming all single-model trace sources. We further find that some skills generalize broadly across tasks and models, whereas others become specialized to role-specific workflows and lose effectiveness under transfer. These results provide practical guidance for building, evaluating, and deploying procedural memory systems in production agent platforms.