extended-reasoning-budgets-improve-model-s-execution-arithmetic-procedures CLM-0566Extended reasoning budgets improve a model's execution of arithmetic procedures on operands longer than those seen in training far more than they improve surface-form-to-value tasks like magnitude comparison and format conversion, because chain-of-thought supplies external working memory for carries and column alignment but cannot change how the input was tokenized.
Capability: Digit-level arithmetic
Observed on
Measured on Gemini 3 at MINIMAL vs HIGH thinking budget over Number Cookbook atomic tasks, temperature 0; in-domain procedural accuracy slightly declined under HIGH..
Sources
- Measured, but on one model family's two thinking settings across one atomic benchmark; the RG/PG split is the authors' own grouping of tasks, and no tokenizer was held fixed while reasoning varied, so the causal account is argued rather than isolated.
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Related claims
- For a same-family pair of reasoning and instruction-tuned 4B models, learning one interpolation ratio per module (attention block, FFN block, embedding, final norm) with a reward that scores correctness and ranks correct responses by length cuts average generated tokens by about 27% relative to the reasoning model while holding average accuracy, and beats fixed global-ratio merging and CMA-ES search over the same ratios.Cutting to the chase · reviewed by AI
- For a 7B code model fine-tuned on competitive-programming tasks, training it to emit a fixed-schema requirement specification (goals, input/output constraints, examples, edge cases, dependencies) before the code raises Pass@1 more than training it to emit free-form reasoning or a stepwise implementation plan of similar length, with the largest margin on an out-of-distribution benchmark.Generating and editing working code · reviewed by AI
- For small (4-8B) student agents on multi-turn tool-use tasks, transferring a stronger teacher's successful trajectories as flat task-level memory barely helps and can hurt, while splitting the same trajectories into a high-level workflow insight in prose plus concrete executable subtask examples raises accuracy sharply, with the subtask examples carrying most of the gain.Using the tools it is given · reviewed by AI
- For a domain-specific language essentially absent from pretraining corpora (FORM symbolic algebra), QLoRA fine-tuning an 8B model on a few thousand examples validated by executing them through the language's own interpreter beats frontier open-weight models of up to 756B parameters given syntax documentation in context, on execution rate and strict output match for the larger benchmarks, while general reasoning scores drop under 3 points.Generating and editing working code · reviewed by AI
- On research-level theorem-proving tasks drawn from recent FOCS/STOC/SODA papers, wrapping a frontier model in a staged harness that explores strategies, gates when to decompose, solves section-level subproblems along a dependency graph, and routes verifier findings back to the affected section raises graded proof accuracy far above prompting the same model directly (30.3% to 54.0% for Gemini 3.1 Pro on TCS-Bench), and two such runs with different backbones make complementary errors, so selecting between them by sampled critiques reaches 71.0% against an oracle ceiling of 77.3%.Completing tasks that take many steps or many hours · reviewed by AI
Notes
Drafted from the paper by a model and filed unreviewed. Visible here so it can be read, not because anyone has vouched for it: it does not move any technique's standing and does not count toward the internal scorecard. Drafted confidence: medium. Falsifier as drafted: A model whose extended-reasoning gains on magnitude comparison and format conversion match or exceed its gains on out-of-training-length arithmetic, measured on matched tasks. Drafted stance toward chain-of-thought-does-not-fix-digit-level-arithmetic: supports -- The paper finds added reasoning compensates for procedural execution but does not repair tokenization-induced representation errors, and can hurt in-domain accuracy.