# When Chain-of-Thought Helps and When It Hurts: An Empirical Investigation of the Serial-Depth Bottleneck in LLM Reasoning

arXiv: https://arxiv.org/abs/2608.09942 · HTML: https://mlsanity.com/paper/2608.09942/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 11 of its 20 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

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

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [Theoretical limitations of multi-layer Transformer](https://mlsanity.com/paper/2412.02975/) (2024)

## Abstract (arXiv)

It is widely assumed that chain-of-thought (CoT) prompting universally improves LLM reasoning. We investigate this through the conceptual framework of the H_dp bandwidth bound (Chen et al., 2024): although the formal bound binds only asymptotically (at astronomically large prompt lengths), it identifies a real architectural bottleneck -- serial computation exceeding a transformer's single-pass capacity must be externalised, which is what CoT does. Our central finding is a within-benchmark serial-depth gradient: single-pass (no-CoT) accuracy degrades monotonically with per-item serial depth, while CoT is approximately depth-invariant. We measure CoT effects across three instruction-tuned models (Qwen-2.5-7B/32B, Llama-3.1-8B) and five standard NLP benchmarks at practical context lengths. On high-depth P-complete tasks (GSM8K, MATH), CoT gives a +54 to +68 pp recovery gap across all models. On shallow TC^0 tasks (MMLU, ARC), CoT is structurally redundant (Delta in [0.0, +4.6] pp, no significant negative effect) -- though high no-CoT baselines (up to 95% on ARC) may reflect contamination, so this null is not a clean architectural test. The intermediate class L (HumanEval) shows a model-size-dependent transition: +23.2 pp (32B), +9.1 pp (8B), -28.7 pp (7B). The cross-benchmark depth-recovery correlation is Spearman rho = 0.661 (p = 0.007, n = 15); 9 of 15 benchmark-level McNemar tests are significant after Bonferroni correction. Pre-registered on OSF, our results indicate that CoT is not a universal reasoning enhancer but acts as a bandwidth bypass: it helps serial computation that strains single-pass capacity and is redundant for tasks that already fit.