Computer Science > Artificial Intelligence
arXiv:2603.09786 (cs)
[Submitted on 10 Mar 2026]
Title:Quantifying the Necessity of Chain of Thought through Opaque Serial Depth
View a PDF of the paper titled Quantifying the Necessity of Chain of Thought through Opaque Serial Depth, by Jonah Brown-Cohen and 2 other authors
View PDF
HTML (experimental)
Abstract:Large language models (LLMs) tend to externalize their reasoning in their chain of thought, making the chain of thought a good target for monitoring. This is partially an inherent feature of the Transformer architecture: sufficiently long serial cognition must pass through the chain of thought (Korbak et al., 2025). We formalize this argument through the notion of opaque serial depth, given by the length of the longest computation that can be done without the use of interpretable intermediate steps like chain of thought. Given this formalization, we compute numeric upper bounds on the opaque serial depth of Gemma 3 models, as well as asymptotic results for additional architectures beyond standard LLMs. We also open-source an automated method that can calculate upper bounds on the opaque serial depth of arbitrary neural networks, and use it to demonstrate that Mixture-of-Experts models likely have lower depth than dense models. Overall, our results suggest that opaque serial depth is a useful tool for understanding the potential for models to do significant reasoning that is not externalized.
| Subjects: | Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2603.09786 [cs.AI] |
| (or arXiv:2603.09786v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2603.09786
Focus to learn more
arXiv-issued DOI via DataCite
|
Full-text links:
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
View a PDF of the paper titled Quantifying the Necessity of Chain of Thought through Opaque Serial Depth, by Jonah Brown-Cohen and 2 other authors
References & Citations
export BibTeX citation
Loading...
Bookmark
Bibliographic Tools
Code, Data, Media
Demos
Related Papers
About arXivLabs
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
Links to Code Toggle
Papers with Code (What is Papers with Code?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
