The second axis

A second axis

On September 12, 2024, the day OpenAI released o1-preview, Noam Brown posted to X what he had been telling smaller rooms for two years. The model had been trained, by reinforcement learning, to think before it answered, in a private chain of thought no user would see; the longer it thought, the better it scored.

This opens up a new dimension for scaling. We’re no longer bottlenecked by pretraining. We can now scale inference compute too.

The phrase Brown and his collaborators use for what o1 was doing is “inference-time compute” — the cycles a model spends searching, drafting, and revising at the moment it answers, as opposed to the cycles spent in the months of training that produced its weights. The claim, distilled, is that this compute is its own scaling axis. The same model, given more time and tokens to think, gets monotonically better on hard problems; the curve is log-linear and, on Brown’s reading, has a long way to run.

Brown is OpenAI’s vice president of research and was formerly a PhD student under Tuomas Sandholm at Carnegie Mellon. The work he did before OpenAI is the foundation his argument rests on: a long empirical lineage in which search at decision time stood in for a much larger model. Across poker, Hanabi and Diplomacy, Brown has put the gain at the equivalent of a model a thousand to a hundred thousand times bigger.

Tesauro’s TD-Gammon in the early nineties; DeepMind’s AlphaGo Zero in 2017; Brown’s own Libratus, the first system to beat top-tier humans at heads-up no-limit poker that same year; Andy Jones’s 2021 Hex paper, in which a smaller network with more search time consistently beat a larger one with less. None of these were transformer-based. None were even neural in the same way. The architectures were independently chosen and the games were structurally different. In each, more thinking at decision time bought performance that would otherwise have taken far more training.

Brown’s argument is that o1 placed that exchange rate on a transformer language model for the first time. He reads the sequence from o1 to o3 to the IMO-gold experimental model (the OpenAI reasoning model that scored at gold-medal threshold on the 2025 International Mathematical Olympiad) as the curve continuing to bend. Whether the curve generalizes is the open question. François Chollet, the Keras creator and, since leaving Google, co-founder of Ndea, designed a benchmark family to test what he calls “skill-acquisition efficiency.” The term means the capacity to make sense of an unfamiliar problem from a small number of examples. On that family the curve bent far more slowly, until September 2026.

The trajectory the case rests on

The within-distribution evidence is the strongest part of Brown’s record, and the most easily mistaken for the whole record. Between September 2024 and April 2026, the o-series and its peers — o1, o3, the IMO-gold experimental model, Gemini 3 Deep Think, Claude with extended and adaptive thinking — moved hard on every benchmark in wide public use eighteen months earlier. Brown points to the shape rather than the scoreboard.

The scoreboard, as the labs and evaluators reported it:

The shape is a single family of models, trained essentially the same way, getting better on harder problems as more compute is spent at inference. The IMO-gold model thought “for hours” per problem — Brown’s word — rather than the seconds o1 spent or the minutes Deep Research had needed. A month later, the same model, no scaffold redesign, no fine-tune for the new domain, placed first among AI participants in the International Olympiad in Informatics, the high-school competitive-programming championship. Brown’s framing in his September 2025 retrospective tweet: “When we at OpenAI released o1-preview a year ago, it would think for seconds. Today, our best reasoning models can think for hours, browse the web, and write code.” Seconds, minutes, hours, the same approach, the same curve.

The mechanism, made concrete, comes from poker. At TED AI in October 2024, Brown said that letting his bot think for twenty seconds a hand matched scaling up the model, and its training, 100,000-fold. That exchange rate is what he asks the o-series results to bear out, and on closed-domain reasoning, the pattern is what he says it is.

It is also the source of the boundary problem.

Where the curve met ARC-AGI

The benchmark family that fit the curve least is ARC-AGI, the “skill-acquisition efficiency” test Chollet built to resist memorized expertise. The tasks are grids of colored squares; each task gives the solver two or three input-output pairs and asks for the output of a fourth input. Humans solve them at very high rates. In December 2024, OpenAI’s o3-preview scored 87.5% on ARC-AGI-1’s Semi-Private set. That version of the benchmark had resisted scaling for five years. The run used a high-compute configuration that drew 1,024 samples per task. ARC Prize later estimated its cost, at o3-pro pricing, at about $4,560 per task.

Then ARC-AGI-2 shipped, in March 2025. Greg Kamradt’s analysis at the ARC Prize Foundation a month later: the released o3, in its medium-compute configuration, dropped from 53% on ARC-AGI-1 to 2.9% on ARC-AGI-2, both on Semi-Private sets — about an eighteen-fold collapse. No matched high-compute comparison exists: the December 87.5% came from o3-preview, a different model, and ARC Prize judged its high-effort runs of the released o3 on ARC-AGI-2 too incomplete to report. The ARC Prize launch post stated the case more starkly than any critic did: “Pure LLMs score 0% on ARC-AGI-2, and public AI reasoning systems achieve only single-digit percentage scores.”

The collapse repeated, larger, on ARC-AGI-3, released March 25, 2026 at a Y Combinator launch event. The third version turned the benchmark from static grids into interactive environments. Its score measures action efficiency, not the share of environments solved: an agent scores 100 percent on a level when it needs no more actions than the human testers did. The semi-private leaderboard at release (ARC-AGI-3 Technical Report): Gemini 3.1 Pro Preview at 0.37%, GPT-5.4 High at 0.26%, Claude Opus 4.6 Max at 0.25%, Grok-4.20 Beta at 0.00%. The ARC Prize framing at launch: “Humans score 100%. Frontier AI scores 0.51%.”

A purpose-built agent had done better the summer before. In ARC Prize’s 30-day preview competition in July and August 2025, played on a few preview environments, Tufa Labs’ StochasticGoose scored 12.58 percent. The two results come from different competitions and environment sets, so they are not a matched comparison. StochasticGoose is not a frontier reasoning model; it is a convolutional network with reinforcement learning, trained to predict which actions will change the frame.

Brown’s own reading of the o3 result is on the public record, in a December 27, 2024 X post. “I think people are overindexing on the OpenAI o3 ARC-AGI results,” he wrote. He credited Chollet and Mike Knoop, Chollet’s Ndea co-founder, for “always being very clear that beating ARC-AGI wouldn’t imply AGI or superintelligence.” Brown was cooling the hype around his own lab’s model.

ARC-AGI-3 opened with frontier systems below one percent. In September 2026, ARC Prize reported OpenAI’s GPT-6 Astra at 62.7 percent on ARC-AGI-3’s Semi-Private set under its Standard harness at max reasoning effort. Under its separately scored Provider Adapter harness, at high reasoning effort, Astra reached 99.95 percent.

The within-distribution trajectory looks the way Brown said it would. The out-of-distribution boundary, as Chollet defines it, moved far more slowly.

Marcus, head-on

Gary Marcus has been arguing for two and a half decades that the failure modes of neural networks on out-of-distribution problems are categorical, not quantitative. In June 2025, after Apple researchers led by Parshin Shojaee published “The Illusion of Thinking” (arXiv:2506.06941), which showed reasoning models failing Tower-of-Hanoi puzzles once the number of disks pushed complexity past a certain level, Marcus titled the Substack post that engaged the result “A knockout blow for LLMs?” and wrote: “even the latest of these new-fangled ‘reasoning models’ still — even having scaled beyond o1 — fail to reason beyond the distribution reliably.”

The paper usually cited beside Marcus’s argument is “Inverse Scaling in Test-Time Compute,” which Anthropic’s own researchers Aryo Pradipta Gema, Alexander Hägele, and collaborators posted to arXiv in July 2025 and published in the Transactions on Machine Learning Research that December. The paper documents five named failure modes that emerge, or worsen, with longer thinking. Claude models become increasingly distractible. OpenAI’s o-series resists distractors but overfits to problem framings. Models shift from reasonable priors to spurious correlations. All struggle with constraint-tracking on harder deductive tasks. And, in the result that drew the most attention, extended reasoning increased self-preservation expressions in Claude Sonnet 4. The authors’ own conclusion: test-time compute scaling “may inadvertently reinforce problematic reasoning patterns.”

Through the spring of 2026, Brown had not directly engaged this critique. There was no public exchange between Brown and Marcus, no Brown post citing the Anthropic paper. There was, instead, a pattern: the IMO-gold result; the IOI gold; the GPT-5.2 derivation of a theoretical-physics result Brown highlighted on LinkedIn in early 2026; the FrontierMath progression.

The read is that benchmark escalation is itself the test. Marcus’s argument is that the post-o1 family fails categorically out of distribution. Brown’s response, which he does not articulate as a response, is to expand the distribution. The IMO and IOI results are not benchmarks o1 was trained for; the same reasoning model wins both without scaffold redesign. If the failure were truly categorical — if the systems trained to think before answering could not generalize at all past training distribution — the IMO-gold model would not have written natural-language proofs of the kind Brown reported on his X feed at the time, in which mathematicians stopped combing for the silently-flipped inequalities earlier systems would produce.

The argument is not airtight. ARC-AGI-3 is precisely the test Marcus would want — humans solve every environment, and at launch the same lineage that won IMO and IOI scored below one percent. Brown’s December 2024 cooling tweet acknowledges the frame. Astra’s September score is a large move on Chollet’s benchmark, though not by itself proof that the failure modes Marcus describes are gone.

The April 23 reframing

In April 2026 Nvidia reported a cost per million tokens nearly thirty-five times lower on its Blackwell hardware than on Hopper: about $0.12 against $4.20 for DeepSeek-R1, comparing a GB300 NVL72 system with an HGX H200 under Nvidia’s own benchmark assumptions. On April 23, the day OpenAI shipped GPT-5.5, internally codenamed “Spud”, Brown posted to X what he called a hill he would die on:

A hill that I will die on: with today’s AI models, intelligence is a function of inference compute. Comparing models by a single number hasn’t made sense since 2024. What matters is intelligence per token or per $.

The reframing reads, on first pass, like a retreat from the original axis claim. The original September 2024 framing was that “inference-time compute” opens a new dimension. The April 2026 framing is that the dimension is doing enough work that the right unit of measurement is cost per unit of thinking, not raw scale. “Intelligence per token or per $” is the live form of the axis claim.

The bear reading of the same numbers is also live. Gundlach and colleagues warn, in The Price of Progress, that the demand for larger models and greater reasoning has offset, and sometimes overcompensated, per-token efficiency gains. Per-token cost is collapsing; per-task cost at the absolute frontier may not be falling at the same rate, because users spend the savings on more thinking tokens per task. This is the form of the constraint Brown himself flagged at TED AI in October 2024. The economic axis, on his own framing, runs out before the technical one if the curves do not converge.

The cost data supports the reframing. Epoch AI’s survey of inference prices by Ben Cottier and collaborators (March 2025) found the price of reaching a fixed performance threshold falling between 9- and 900-fold a year, depending on the threshold. Reaching GPT-4’s score on GPQA Diamond, a set of PhD-level science questions, got about 40 times cheaper a year. Gundlach and colleagues, tracking frontier models from April 2024 to November 2025, put the decline at five- to tenfold a year across knowledge, reasoning, math and software-engineering benchmarks.

Epoch’s September 2026 analysis, The plunging price of thought, puts the cost of a given benchmark score falling 47 percent a quarter overall. For scores that are newly state of the art, the fall is 66 percent a quarter.

On ARC-AGI-1’s Semi-Private set, o3-preview scored 87.5 percent in December 2024; ARC Prize later estimated its cost, at o3-pro pricing, at about $4,560 per task. In December 2025, ARC Prize verified GPT-5.2 Pro at 90.5 percent on the same benchmark’s Semi-Private set, at XHigh reasoning effort, for $11.64 per task. That is about 390 times cheaper for a slightly higher score, though the preview configuration differed from the o3 OpenAI later released. At frontier capability, raw price is falling fast, and faster still at the cost-performance frontier. Brown’s reframing absorbs this into the original thesis.

Silver, from inside

David Silver dissents from inside the lineage. He was the DeepMind reinforcement-learning lead behind AlphaGo, AlphaZero and AlphaProof, work Brown cites as the second pillar of the lineage that produced the o-series. In an April 27, 2026 interview with WIRED’s Will Knight, at the launch of his new lab, Ineffable Intelligence, Silver said he thinks the industry’s route to superintelligence through large language models will fail. LLMs, in his account, learn from human intelligence rather than building their own. He called human data “a kind of fossil fuel that has provided an amazing shortcut,” and set against it systems that learn for themselves from experience.

The distinction concerns where the learning starts. AlphaZero learned from self-play, and AlphaProof learned to prove theorems against Lean, a formal checker that accepts or rejects each proof. Reasoning models also learn by reinforcement. OpenAI trained o1 with large-scale reinforcement learning on its chain of thought, and DeepSeek-R1 used rule-based rewards that check math answers and run code against tests. The difference is the starting point: reasoning models begin from a model pretrained on human text. Silver’s example of the limit is a language model released into a world that believed the earth was flat. Unable to interact with the world, he says, it would stay a flat-earther. The dissent is interior. It does not reject the lineage. It argues about what counts as continuing it.

Brown’s response, on the public record, began with the IMO-gold result and the DeepMind IMO parallel. His July 21, 2025 X post on DeepMind’s own IMO gold congratulated the team and used the phrase “their parallel success highlights how fast AI progress is. Their approach was a bit different than ours.” In the Brown frame, Anthropic’s extended thinking, DeepMind’s Deep Think and DeepSeek-R1’s January 2025 replication of the o1 curve are the same approach working in different recipes. R1 combined supervised fine-tuning with reinforcement learning; its sibling, R1-Zero, was the pure-RL variant.

In September 2026 the record extended to OpenAI’s reported Navier–Stokes result. OpenAI said the work took about 10,000 concurrent agents, 130 billion output tokens and 88 hours, followed by a further 17 hours of formalization and verification. In a September 17 interview with Dwarkesh Patel, Brown gave multi-agent coordination less than 10 percent of the credit and put the weight on the general-purpose model underneath.

Read through Silver’s argument, what looks parallel is a fork: systems that learn from their own experience on one branch, models that start from human text and add reinforcement learning on the other. Whether the two branches converge or diverge is the open question his argument leaves.

The bet

Brown’s case is that compute spent at inference is a real second axis of scaling on the within-distribution problems where his lineage applies. The trajectory from o1 to o3 to the IMO-gold model — months apart, the same approach, harder problems — is the part of the case that has held. The April 2026 reframing into “intelligence per token or per $” is the live form of the original claim. The parallel evidence at DeepMind and Anthropic is, on Brown’s reading, the approach working across labs.

The boundary, equally clearly, has been Chollet’s benchmark family. The released o3, at medium compute, fell roughly eighteen-fold from ARC-AGI-1 to ARC-AGI-2. ARC-AGI-3 opened with the post-o1 family below one percent against humans at one hundred. In September 2026 GPT-6 Astra reached 62.7 percent on ARC-AGI-3. Marcus’s specific critique — that the failure modes are categorical, that “Inverse Scaling in Test-Time Compute” documents the categorical patterns — is on the public record. Through the spring of 2026, Brown had not engaged it directly. His benchmark escalation can be read as an experiment, and by September 2026 it had produced a result on the hardest version of Chollet’s benchmark.

Silver’s interior dissent, voiced in April, bears on whether what has held within distribution continues the lineage Brown invokes. In his account, models built on human data will fall short, and systems that learn from their own experience are the way forward.

Where the post-o1 family helps is the closed-domain, verifiable-reasoning quadrant: AIME, GPQA, Codeforces, IMO, IOI, FrontierMath. Where it helped least, on the public record through the spring of 2026, was the fluid-intelligence quadrant where ARC-AGI-2 and ARC-AGI-3 sit. The axis Brown named in September 2024 is real on the within-distribution problems where his lineage applies; whether it reaches past them is the question ARC-AGI-3 was built to test.

Brown’s answer, on Latent Space in June 2025, is that there are “a lot of things that people are building right now that will eventually be washed away by scale.” He named harnesses, and said scaffolds and routers would give way to more capable models. He allowed that they are worth building when they lift a product today. Chollet’s answer, on the AI Startup School stage that same month:

even after a 50,000x scale-up of pre-trained base [models], the performance in ARC stayed near zero. So we can decisively conclude that fluid intelligence does not emerge from scaling up pre-training.