Opaque serial depth is a measure of how much sequential computation a model can perform internally, without writing out interpretable intermediate steps such as a chain of thought. It was formalized in "Quantifying the Necessity of Chain of Thought through Opaque Serial Depth," a paper submitted to arXiv on March 10, 2026 by Jonah Brown-Cohen, David Lindner and Rohin Shah, which defines it as "the length of the longest computation that can be done without the use of interpretable intermediate steps like chain of thought" (Source: arxiv.org). The quantity underpins the argument that current reasoning models must externalize long reasoning in legible text, and has been proposed as a quantity that could be capped by regulation to preserve Chain-of-Thought Monitorability.
Origin
The paper starts from the observation that large language models tend to externalize their reasoning in their chain of thought, which makes the chain of thought a good target for monitoring, and from the claim in the 2025 multi-lab position paper on chain-of-thought monitorability that this is partly an inherent feature of the transformer architecture: "sufficiently long serial cognition must pass through the chain of thought" (Source: arxiv.org; arxiv.org). Opaque serial depth is the formalization of that claim.
Findings
According to its abstract, the paper computes numeric upper bounds on the opaque serial depth of Gemma 3 models, gives asymptotic results for architectures beyond standard language models, open-sources an automated method for calculating upper bounds on the opaque serial depth of arbitrary neural networks, and uses that method to show that Mixture-of-Experts models likely have lower depth than dense models. The authors conclude that the measure "is a useful tool for understanding the potential for models to do significant reasoning that is not externalized" (Source: arxiv.org).
Proposed use as a limit
In a September 2026 DeepMind Institute essay, Shah and Anca Dragan describe opaque serial depth as "essentially the longest step-by-step computation a model can do without needing to use a human-readable mechanism like Chain of Thought," and propose limiting it as "a natural way to preserve transparency." They state that "regulations or AI developers themselves could set a reasonable limit on the opaque serial depth" (The Case for Reasoning Transparency (Shah and Dragan, DeepMind Institute, September 2026)).
Their argument that such a limit would be cheap rests on scaling: the opaque serial depth of a transformer "scales very slowly with the overall size of the training run," so that limiting future models to 10x the opaque serial depth of current models "would allow an overall compute scale-up of more than 1,000x on top of today's models, with the current paradigm and model architectures." The limit would bind if developers adopted architectures that reason in latent space, which the authors describe as potentially more efficient and powerful "but at the expense of transparency" (The Case for Reasoning Transparency (Shah and Dragan, DeepMind Institute, September 2026)).
Related findings
UK AISI's external evaluation in the GPT-6 Astra system card reports "a greatly increased ability to reason within a single forward-pass," which Shah and Dragan cite as evidence that chain-of-thought transparency is under threat (The Case for Reasoning Transparency (Shah and Dragan, DeepMind Institute, September 2026)). OpenAI chief scientist Jakub Pachocki gives, as one cause of declining reliance on chain-of-thought monitoring, that improved pretraining makes models "much smarter even without using verbalized reasoning at all" (An Alien Mind (Jakub Pachocki, OpenAI, September 2026)). Neither source uses the term opaque serial depth.
Redwood Research's Alexa Pan judges it plausible that competent sandbagging "doesn't depend on lots of serial computation that requires externalized reasoning," so that it "may be hard to detect via CoT monitoring even if CoT monitorability is preserved for difficult tasks" (SOTA Alignment Assessments Don't Strongly Update Us Against Misalignment (Pan, Redwood Research, July 2026)).
Relationships
- supports: Chain-of-Thought Monitorability — formal basis for the claim that long serial reasoning must pass through the chain of thought
- related: The Case for Reasoning Transparency (Shah and Dragan, DeepMind Institute, September 2026) — proposes a regulatory or developer-set limit
- related: Reasoning Models and Chain-of-Thought, Monitorability Tax
- related: GPT-6 Astra System Card (OpenAI, September 2026), An Alien Mind (Jakub Pachocki, OpenAI, September 2026), SOTA Alignment Assessments Don't Strongly Update Us Against Misalignment (Pan, Redwood Research, July 2026)
- related: Rohin Shah — co-author of the formalizing paper and of the proposal to cap it