Reasoning as a footprint: distilling chains of thought into small models

By TheSequence · July 21, 2026.

This issue of TheSequence Knowledge revisits an episode that the newsletter itself describes as one of the most important reasoning-distillation results of the past decade: the case of DeepSeek R1, in January 2025.

According to the email, DeepSeek took its large reasoning model, R1, and used it to generate around 800,000 step-by-step worked solutions: long and sometimes messy chains of thought, with false starts, self-corrections and moments of "wait, let me reconsider." The team filtered those traces for correctness and readability and then applied the simplest possible technique to them: plain supervised fine-tuning (SFT) on existing open models, specifically Qwen at 1.5B, 7B, 14B and 32B sizes, and Llama at 8B and 70B. The email explicitly stresses what was NOT used in this process: no reinforcement learning, no reverse KL, no on-policy sampling and no "teacher-as-critic" scheme. Simply next-token prediction over the transcripts generated by the teacher model.

The result, according to the text, was surprisingly good. The distilled 32B model began solving competition-level math problems that, in the article's words, it "had no business being able to solve." The 7B model, for its part, started verifying its own work and branching its reasoning mid-generation—emergent behaviors that no one trained directly. Taken together, a varied group of small dense models came to reason as if they were, in the email's phrasing, "ten times bigger."

The interesting part of the argument—and this is how the newsletter itself presents it—is the apparent contradiction with earlier installments of the TheSequence series. The email recalls that a previous installment had argued at length why naive sequence-level imitation is the wrong tool for distilling reasoning, precisely because the student model will never, at inference time, be on the same trajectories as the teacher model; hence the argumentative shift toward reverse KL over forward KL. And yet the DeepSeek R1 result described here is, plainly, naive sequence-level imitation, and it worked spectacularly well.

The text frames this tension as the true subject of the article: neither "imitation works" without nuance, nor "imitation doesn't work" without nuance, but something more interesting that it promises to develop next under the title "The Trace, Not the Answer," suggesting that the key is not to imitate the teacher's final answer, but to imitate the entire reasoning process—including doubts, corrections and branches—as a transfer mechanism.

The body of the email received corresponds to the introduction of the full article published on Substack; the content provided cuts off just before TheSequence develops in detail the technical argument for why trace imitation (unlike answer imitation) avoids the distribution problem that motivated the turn toward reverse KL in earlier installments of the series.

Overall, as industry context, distilling reasoning capabilities from large models into small models through fine-tuning on chains of thought generated by the teacher model itself has become a widely discussed technique since DeepSeek's release of R1, given its relatively low computational cost compared with approaches based on pure reinforcement learning.