Fill in the s1 budget forcing trick that stretches or stops thinking

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In the s1 paper's budget forcing technique, the model is pushed to reason longer by suppressing the end of thinking delimiter and appending the token "", nudging it to re-examine its work, and pushed to spend less by the thinking trace once the token budget is reached.

The s1 paper from Stanford in 2025 showed something surprising: you can push a strong reasoning model into very different amounts of thinking by intervening at decode time, without any fine-tuning. **Stretching the trace.** When the model is about to emit its end of thinking delimiter, suppress that token and force-append the word **Wait** into the trace instead. The model treats Wait as a continuation cue and starts re-examining its own working. Often it catches an arithmetic slip or revisits an assumption. Repeating the trick can extend the trace several times. **Shrinking the trace.** When the cumulative thinking-token count reaches the budget, just **truncate** the trace, append the end of thinking delimiter, and let the model emit its answer based on whatever thinking it had completed. **Why this matters.** Budget forcing is a cheap test-time lever: no training, no special model, just decoder logic. It works because reasoning traces are sequences of self-conditioned text, and a small intervention at the right token boundary changes the distribution over what the model produces next. The s1 paper used these two interventions together to produce a controllable accuracy versus compute curve on math benchmarks like AIME and MATH.

**Budget forcing** is the s1 paper's test-time technique for controlling how long a reasoning model thinks, with two opposite interventions applied at decode. **To spend more (stretch):** detect when the model is about to emit its end of thinking delimiter, suppress that token, and append the word **Wait** to the trace. The model conditions on the new prefix and continues thinking, typically by second-guessing its prior step. The intervention can be repeated to push the trace further; each application costs only the additional generated tokens. **To spend less (truncate):** when the running thinking-token count reaches the configured budget, force-terminate the trace by appending the end of thinking delimiter and let the model emit the visible answer using whatever it had reasoned through so far. Both interventions are decoder-side, not model-side. No fine-tuning, no special model checkpoint, no chain-of-thought prompt template. The s1 paper used budget forcing on top of a small distilled checkpoint (s1-32B, distilled from a teacher's traces) to produce a clean accuracy versus compute curve on AIME and MATH. The headline result was that controllable test-time scaling can be achieved cheaply: pick a token budget, hit it, observe accuracy. The technique is general enough to apply to any reasoning model that exposes an end of thinking delimiter and a logits hook, which is most open-weight checkpoints in 2026.

TL;DR

To spend more, suppress the end of thinking token and append Wait so the model second-guesses; to spend less, truncate the thinking trace once the budget is hit.

Memory aid

Easy to grasp

Imagine a student writing a maths exam who is about to write 'Therefore, the answer is...' You hand them a sticky note that says 'Wait', and they pause and re-check the working before committing. That is one half of the trick. The other half is simpler: when the bell rings, the invigilator takes the paper away whether the student is done or not. Stretch by interrupting with a doubt-prompt. Shrink by cutting at the buzzer. The s1 paper shows both work as cheap test-time levers without retraining the model.

Key concepts

Reasoning Models

Concept explanation~2 min read

Everything you need to truly understand this topic: intuition, mechanics, step by step explanation, code, formulas, and worked example. Click to expand.

Budget forcing is one of the cleanest test-time scaling results of the 2025 wave. Stanford's s1 paper showed that a small distilled reasoning model, with no extra training, can be pushed across a controllable accuracy versus compute curve by intervening in two places at decode time. The technique is simple enough to implement in an afternoon on top of a self-hosted serving stack, which is partly why it spread quickly.

This deep dive walks through the two interventions, the reason the Wait cue specifically works, the truncation subtlety that separates a clean implementation from a brittle one, and the operational scope of where budget forcing applies in 2026 deployments versus where coarser knobs win.

The two interventions

A reasoning model trained to think before answering emits its trace inside a delimited region. The exact delimiter varies by model; conceptually, the model issues an end of thinking token when it has finished reasoning, then begins the visible reply. Budget forcing intervenes at this delimiter.

Stretching the trace

When the decoder is about to emit the end of thinking token, suppress it (via a logits processor that masks the token in the next-token distribution), and instead force-emit the literal text Wait followed by a newline. The model now sees ...prior reasoning... Wait as its prefix and continues generating. The continuation almost always takes the form of self-correction: re-checking a calculation, revisiting an assumption, considering an alternative case.

The stretch can be applied multiple times. Each application extends the trace by the length of the new continuation, costing only the additional generated tokens.

Truncating the trace

A separate logits processor watches the cumulative thinking-token count. When the count exceeds the configured budget, the processor forces the model to emit the end of thinking token immediately, terminating the trace. The model then produces its visible reply using only the thinking it had completed.

The two interventions are independent and can coexist: stretch is fired on a quota that limits how many times Wait can be injected, truncate is fired on the total budget. The s1 paper plots accuracy as a function of the budget and produces a smooth curve.

Why Wait works

The truncation subtlety: grace windows

Where budget forcing applies in 2026

Budget forcing in the 2026 toolkit

Situations where this technique stops working.

2–4 min · Everything important, quickly.

Real products, models, and research that use this idea.

Stanford's s1 paper introduced budget forcing on a 32B distilled model trained on roughly 1,000 reasoning traces and showed competitive AIME and MATH results at controlled compute budgets
Self-hosted serving stacks like vLLM and SGLang expose logits processors that make budget forcing implementable in a few dozen lines of code

What an interviewer would ask next. Try answering before peeking at the approach.

QWhy does the word Wait specifically lift accuracy more than other continuation cues?

The model has seen many training examples where Wait or similar pause-words precede self-correction in human reasoning text. Conditioning on Wait shifts the next-token distribution toward 'let me reconsider' continuations. Other cues like however or actually have similar but weaker effects in the s1 ablation.

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Red flags & common mistakes

The phrases that signal junior thinking. Click to expand.

Most common mistake

Treating budget forcing as a learned policy when it is a decoding-time intervention; the model is unchanged, only the decoder's stop and continuation logic are.

60 second bullets to scan on the way to the call.

What budget forcing intervenes on at decode time
Why the Wait token specifically works to extend thinking

Primary sources. Browse if you want the original framing.

Muennighoff et al., s1: Simple test-time scaling