Act 3 · Frontier & Caveats
13. Frontier Reasoners I: o1, o3, and the Two-Axis Scaling Curve
By page 12, compute had split in two: the compute spent at answer time (pages 5 to 11: votes, judges, search) and the compute already sunk into the weights (page 12: the reasoning trained in). o1 is the first commercial model to turn both dials, and it kept the recipe. Its signature is a curve with two compute axes: how much of the score did the training buy, and how much did the thinking?
1. The human leaves the loopconfirmed frame only
Page 12 closed on a promise: same shape, disguise dropped. OpenAI confirmed the frame, that o1 is trained with large-scale reinforcement learning to think in a long private chainreference 1, and its own researchers later named the category: “large reasoning models (LRMs): language models trained via reinforcement learning to ‘reason’ and ‘think through’ extended chains of thought”.reference 2 The algorithm itself was never published.
generate ×k
page 12 took one greedy try; k sampled chains explore instead
reward
page 12's filter, made explicit: still the answer key, still free
reinforce
page 12 fine-tuned the base; this updates the current model, so gains compound
Even at this resolution one thing is legible by its absence: a human. RLHF pays people to judge outputs; here nobody writes an example and nobody grades one, because the model authors the reasoning and the answer key scores it. And the training set never touches page 3's finite stock of human text: the model writes its own curriculum.
2. One law, two knobsauthored redrawing · anchors verbatim
Page 11's law: model size picks your curve; test-time compute slides you along it. o1's announcement charts are the same picture with the curve-picker swapped: RL training picks your curve now.reference 1 Both are log-linear, accuracy against the logarithm of compute, whichever axis it arrives on.
Both dials count compute, not attempts. ×100 RL training is one run given a hundred times the training compute, not a hundred runs; ×100 thinking is one answer whose private chain is allowed to run a hundred times as long, not a hundred sampled answers; sampling many chains and voting is a separate purchase, and section 3 stacks it on top. The score being climbed is pass@1 on AIME 2024, the same competition maths as section 3: fifteen problems, one chain each, graded against the answer key.
All three runs are drawn below: the same line, slid one decade right for every decade of RL forgone. The training dial picks your curve; the thinking dial slides your marker along it, and the bracket at your marker prices what the missing RL would have bought.
all three RL runs are drawn in full and the dials never move them; only the highlight and your marker respond. The staircase says it without dragging: up one curve and along one decade buy the same +29.5.
Thinking slides you along the curve; only training lifts it. The two dials pay the same +29.5 per decade, and on this surface they trade one for one: a decade of thinking buys back exactly the decade of RL you skipped, which is why ×1 training with ×100 thinking scores the same 21.0 as ×100 training with ×1 thinking. What differs is how often you pay. The RL is bought once, before any question arrives, and in a currency page 3's wall does not price: chains the model writes itself, not the finite stock of human text. The thinking is bought again on every answer.
OpenAI published two separate charts, one per axis, both with the compute axis unlabeled: a log scale in undisclosed, relative units. Joining them into one surface, so that a decade of either dial buys the same points and training is a clean sideways shift, is this deck's construction and not a published result; so are the ×1 to ×100 span and the +29.5-per-decade slope. The dashed GPT-4o line and the o1 dot are verbatim. The slope is the claim; the absolute compute is a secret.
3. Stack the toolbox, or turn the knobs?
First answer: stack. Act 2 did not become obsolete; it became the second storey: put one of its mechanisms over the learned chain and the score moves. Below, one o1 on competition maths (AIME 2024) read three ways, against a strong LLM with no learned chain at all:
o1, one model read three ways
One recipe, no domain tricksEl-Kishky et al. 2025 · IOI 2024
Second answer: turn the knobs, and OpenAI ran the ablation itself. Take o1 and bolt on hand-engineered, contest-specific strategies (o1-ioi), which is Act 2's move done by hand at the frontier, or just turn the two knobs further. The knob-turning branch, an early o3, beat the hand-built specialist on its own contest, no tricks attached.reference 2 Their conclusion, verbatim: scaling “general-purpose reinforcement learning, rather than relying on domain-specific techniques, offers a robust path toward state-of-the-art AI”.reference 2 Stacking pays once; the knobs compound.
4. The questions o1 cannot answer
The two knobs are priced precisely: a decade of either buys the same +29.5. What no amount of measuring from outside can tell you is what you get for the money. Four questions the curve does not answer:
What are you actually buying when you turn the thinking dial?
One chain allowed to run longer, or many chains sampled and voted on behind the API? The bill counts tokens either way, and nothing visible from outside tells the two apart.
Are the thinking tokens doing the work, or describing it?
They are priced by the thousand and never shown, so there is no way to check whether the private chain is the reasoning itself or a narration running alongside it.
What does the model do with ten times the thinking that it would not do with one?
From outside you watch the score climb and the bill climb with nothing in between. The mechanism the whole test-time axis rests on is the one part never shown.
Does the law need a frontier-scale model at all?
o1 sells in one size, at one price. If trained-in reasoning survives in something small enough to run yourself, thinking gets cheap and the economics of the entire curve change.
Every one of them asks what is behind the thinking dial, and that is exactly what a closed lab keeps. It will sell you the curve; it will not show you the machine that makes it.