# Broken Chains: The Cost of Incomplete Reasoning in LLMs

arXiv: https://arxiv.org/abs/2602.14444 · HTML: https://mlsanity.com/paper/2602.14444/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 11 of its 16 references that are in the map.
- First posted on arXiv 16 Feb 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 11 of 11)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Token-Budget-Aware LLM Reasoning](https://mlsanity.com/paper/2412.18547/) (2024)
- [SALT: Steering Activations towards Leakage-free Thinking in Chain of Thought](https://mlsanity.com/paper/2511.07772/) (2025)
- [FRIT: Using Causal Importance to Improve Chain-of-Thought Faithfulness](https://mlsanity.com/paper/2509.13334/) (2025)
- [Punctuation and Predicates in Language Models](https://mlsanity.com/paper/2508.14067/) (2025)
- [Optimizing Chain-of-Thought Confidence via Topological and Dirichlet Risk Analysis](https://mlsanity.com/paper/2511.06437/) (2025)

## Built on by (most cited first, 4 of 4)

- [Both Ends Count! Just How Good are LLM Agents at "Text-to-Big SQL"?](https://mlsanity.com/paper/2602.21480/) (2026)
- [Why Limit the Residual Stream to Layers and Not Tokens? Persistent Memory for Continuous Latent Reasoning](https://mlsanity.com/paper/2606.07720/) (2026)
- [Mind the Cap: Output-Budget Regimes Change the Measured Multilingual Reasoning Gap](https://mlsanity.com/paper/2608.04160/) (2026)
- [Visible Reasoning Is Not a Universal Optimizer: Persona- and Thinking-Dependent Effects in Analytics Code Generation](https://mlsanity.com/paper/2610.10639/) (2026)

## Abstract (arXiv)

Reasoning-specialized models like OpenAI's 5.1 and DeepSeek-V3.2 allocate substantial inference compute to extended chain-of-thought (CoT) traces, yet reasoning tokens incur significant costs. How do different reasoning modalities of code, natural language, hybrid, or none do perform under token constraints? We introduce a framework that constrains models to reason exclusively through code, comments, both, or neither, then systematically ablates token budgets to 10%, 30%, 50%, and 70% of optimal. We evaluate four frontier models (GPT-5.1, Gemini 3 Flash, DeepSeek-V3.2, Grok 4.1) across mathematical benchmarks (AIME, GSM8K, HMMT). Our findings reveal: (1) truncated reasoning can hurt as DeepSeek-V3.2 achieves 53% with no reasoning but only 17% with truncated CoT at 50% budget; (2) code degrades gracefully as Gemini's comments collapse to 0% while code maintains 43-47%; (3) hybrid reasoning underperforms single modalities; (4) robustness is model-dependent as Grok maintains 80-90% at 30% budget where OpenAI and DeepSeek collapse to 7-27%. These results suggest incomplete reasoning chains actively mislead models, with implications for deploying reasoning-specialized systems under resource constraints.