The Instruction Tax on Factual Recall: Base Models Can Beat Their Instruction-Tuned Counterparts

The facts a language model stores are tied to its parameter count, so small models that fit on edge devices fail on expert problems, which need specialized knowledge and follow multi-step procedures. Fine-tuning for a specific domain or task writes the knowledge into the parameters but must be repeated for every model and domain, and a retrieved passage leaves the model to find the relevant fact and apply it on its own. We introduce instruction retrieval, which distills a teacher model's expertise into a corpus of instructions tailored so that a small model can follow. For each cluster of a domain's problems, the teacher writes one instruction with the background knowledge the cluster depends on, a procedure for that kind of problem, and the common mistakes made on it. This reusable corpus needs only to be built once per domain and requires no run-time teacher access. At inference, a frozen small model retrieves the instructions nearest its question and follows them, with no fine-tuning. Across medicine, law, and mathematics benchmarks, we demonstrate the corpus improves over zero-shot on every task and over few-shot prompting, self-consistency, and other retrieved text on medicine and law. On MedQA the corpus raises mean accuracy by 10.6 points, where retrieved textbook passages raise it by 3.9 and few-shot examples from the same teacher lower it. An error analysis shows that only the background knowledge fixes the questions a small model always gets wrong, and that the procedure and common mistakes fix only the questions where it wavers between options. Our results show that automatically retrieved inference-time procedural guidance and domain knowledge can yield substantial gains for small models.

Aggregate factuality scores hide where a language model succeeds, which relations it confuses, and whether an answer survives innocuous changes to the question or decoder. We introduce PROOF, a profile-oriented benchmark for factual coverage in instruction-tuned language models. PROOF converts a frozen Wikidata snapshot into 18,486 English multiple-choice questions grounded in 11,779 semantic facts, 101 classes, 392 properties, and 14 domains. Each question has an explicit "I don't know" option, a "No correct option" control, and nine controlled formulations; 1,849 questions are no-correct-option traps. We evaluate 18 open-weight model deployments on 166,374 prompts each and separately perturb decoding on a fixed 10% subset. Base factual accuracy ranges from 6.58% to 57.59% (chance: 8.64%), yet every model has a 19.3-36.4 percentage-point spread across domains. Paired facts reveal direction-dependent retrieval, usually favoring subject-to-object queries, with the pattern reversing for one model. We find no consistent temporal penalty after exact-stratum adjustment. Neutral wording changes accuracy by as much as 26.5 percentage points, while adversarial formulations break up to 79.4% of answers that were initially correct. Direct switching to an injected false label varies from 0.04% to 27.5%, showing that accuracy loss and hint following are distinct. Selected-token confidence often indicates severe overconfidence, and decoder perturbations move accuracy by up to 15.7 percentage points and domain profiles by 16.8 points. PROOF therefore measures factual coverage as a structured, intervention-aware profile rather than a single claim about what a model "believes."

Practitioners make three prompt-design decisions with almost no controlled evidence behind them: how to format instructions and context (markdown, plain text, prose, or tabular), how many simultaneous instructions a system prompt can carry before compliance degrades, and how much context a model can hold before recall and honesty degrade. We report two controlled experiments crossing all three factors on one held, contamination-free synthetic corpus (the "Book of Veyra," 8,780 uniquely-named entities, deterministically regenerable from a fixed seed), evaluated across five models. Experiment 1 (960 calls/model) measures instruction-following decay as rule count N grows from 10 to 160, crossed with four formats and system-prompt vs. user-turn placement. Perfect-response rate collapses to zero by N=80 for every model, format, and placement. Placement produces effects at least as large as format at N=160 in most models, but the direction is model-specific. No model shows a reliable markdown advantage; one 35B model favors plain text instead. Experiment 2 (5,520 calls/model) measures recall accuracy, false-premise sycophancy, and absent-fact fabrication across a 2k-to-512k-token context ladder in the same four formats. Recall stays near ceiling through 64-128k tokens, then degrades sharply and format-dependently: one model's accuracy spread reaches 48 points at 128k tokens. Fabrication never occurs (0/5,760 probes), and sycophancy stays negligible (<=8.3%). What rises sharply near each model's context ceiling is outright refusal to answer (0% to 79-90%), distinct from sycophancy or fabrication. Neither pre-registered format ordering holds, and token overhead (+22% to +37% over plain text) further changes which format is preferable where accuracy spread is genuine. We release the full harness, corpus generator, and raw results (VeyraBench): https://github.com/iNetanel/veyrabench