# Capacity, Not Format: Rethinking Structured Reasoning Failures

arXiv: https://arxiv.org/abs/2606.09410 · HTML: https://mlsanity.com/paper/2606.09410/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 17 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 6 of 6)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Quantifying the Impact of Structured Output Format on Large Language Models through Causal Inference](https://mlsanity.com/paper/2509.21791/) (2025)

## Built on by (most cited first, 1 of 1)

- [The Unreliable Progress Bar: Can LLM Agents Reliably Report Task Progress Throughout Execution?](https://mlsanity.com/paper/2609.08589/) (2026)

## Abstract (arXiv)

Prior work treats structured output as a reasoning tax, but this framing is incomplete: the cost of formatting depends strongly on a model's spare capacity. Using information-matched prose controls and a four-level schema complexity gradient, we separate format-specific effects from prompt-length confounds across 4 models and 5 benchmarks with 0% parse failures on successfully generated responses. We find that structured formats are capacity-dependent. Models with sufficient headroom absorb JSON constraints without degradation (Sonnet: 88.7±4.0% JSON vs. 89.3±1.7% CoT on MATH-Hard). In contrast, formats severely degrade models operating near their limits through two distinct mechanisms. First, under standard token budgets, Haiku drops 36.2pp (p < 0.0001) largely due to truncation. Second, even with extended budgets eliminating truncation, GPT-4o-mini drops 28.0pp (p < 0.001), revealing pure capacity competition independent of token exhaustion. This format penalty scales with schema complexity (McNemar p < 0.0001) and cannot be explained by prompt length alone. Furthermore, these results qualify claims of frontier model immunity: on AIME competition math, Opus 4.7 drops from 96.2% to 91.0% under JSON (-5.3pp; the displayed percentages are independently rounded, exact difference is 7/133 = 5.26pp ≈ 5.3pp). A delayed-structure ablation -- reasoning freely before formatting -- recovers most of the lost accuracy (3-run mean: 80--87%), supporting the capacity competition mechanism. The practical implication is not to avoid structured output, but to match it to capacity: when a model is near its limits, think first, format later.