ANDREJ KARPATHY: LLM capability is jagged, peaking in digital, verifiable, valuable domains because of how and where reinforcement learning is applied

The Gist

AI got much better at things a computer can check automatically, like code passing tests or math proofs, and companies focus on what makes money. So AI is very strong in coding and math and weaker elsewhere. Other fields are improving too, though, so the gap may partly be about who has started using it. This is a steelman: a charitable reconstruction of Andrej Karpathy's posts in their strongest form, not an endorsement of their claims.

Conclusion

Because recent capability gains come largely from reinforcement learning on verifiable rewards in environments chosen partly for revenue, capability is jagged, and this explains much of the gap between professionals in programming and mathematics and those in other fields.

Premises

1. A major source of recent LLM capability gains is reinforcement learning against rewards that can be checked automatically, such as passing tests or verifying proofs.
2. Developers choose which training environments to build partly by revenue potential, and coding and technical work are especially valuable in business settings.
3. Capability therefore peaks in domains that are digital, verifiable, and economically valuable, and lags in domains where quality is harder to check.
4. Programming and mathematics fit all three conditions, and coding remains among the largest uses of frontier models.
5. This unevenness explains why professionals in mathematics and code see much more capability than professionals in other fields.

Assumptions

• The training account matches the author's published review of 2025, which describes reinforcement learning on verifiable rewards as a major new training stage.
• Rubric-based reinforcement learning is extending training to less verifiable tasks, though it remains vulnerable to reward hacking, so the peaks may broaden over time.
• Expert-comparison benchmarks of general professional tasks rose from below parity in 2025 to about 68% wins or ties for the top model by October 2026, so capability outside code is larger than jaggedness alone suggests; part of the remaining gap may be adoption rather than capability.
• The revenue-priority mechanism is inferred from public behavior, not from developers' internal planning documents.

Analysis

Argument type: Inductive.

Potential Fallacies

• Unsupported inferential leap (non sequitur) (P1 + P2 → P3) — P3 is introduced with 'therefore', but P1 and P2 only say that RL on checkable rewards is a major source of gains and that environment choice is partly revenue-driven. Getting to 'capability peaks where tasks are digital, verifiable, and valuable' needs a bridging premise: that RL allocation is the dominant determinant of domain-level capability, with pretraining data, task structure, and transfer playing smaller roles. That premise is not stated.
• Inference to the best explanation without excluding rivals (affirming the consequent pattern) (P3, P4 → P5) — Code and math are strong and fit the three conditions, so the conditions are taken to be the cause. The same pattern is predicted by abundant pretraining data, formal text-native structure, cheap verifier construction, and developers building tools for themselves. Because code and math satisfy all three conditions at once, they cannot show which condition, if any, does the work.
• Inferring motive from behavior (underdetermination) (P2, P4) — Heavy investment in coding environments is read as evidence of revenue-driven selection. Tractability, dogfooding, and research-acceleration motives predict the same behavior. A4 concedes the inference, but P2 and P3 still lean on it for explanatory weight.
• Single-cause attribution / explanatory overreach (P5 and Conclusion) — P5 says jaggedness 'explains' the perception gap, and the title states 'because of how and where RL is applied'. Perceived capability also depends on how easily users can verify output, tooling and agent harness quality, adoption friction, liability, and user skill. A3 concedes part of this, but the conclusion keeps 'explains much of the gap' without apportioning causes.
• Quantifier strengthening (P1/P2 vs. Conclusion) — The premises assert that RL on verifiable rewards is 'a major source' of gains and that revenue is 'partly' a factor. The conclusion says 'largely' and 'much of the gap'. Nothing in the premises quantifies the contributions, so the degree is strengthened without support.
• Usage share as proxy for priority; unrepresentative sample (P4) — Coding being about a third of Claude conversations is one vendor's developer-skewed usage. It shows demand, and may result from existing capability (reverse causation) as much as drive training priorities. Consumer chat usage at other vendors is far less code-heavy, so 'among the largest uses of frontier models' holds more clearly for API and enterprise use.
• Perception conflated with capability (P5) — The thing to be explained is a gap in what professionals see and report, which is not the same as a gap in underlying capability. The gap is asserted, not measured, and is shaped by evaluator skill, verification cost, and tooling, which makes it partly circular as support for P5.

Counterarguments

These challenges are not ranked.

• Premise 3 and Conclusion (High impact) — Pretraining data abundance and the formal, text-native structure of code and math explain most of the peaks. Models were already strong at code before RL on verifiable rewards became prominent, so jaggedness is a general property of statistical learners trained on uneven data, with RL as a second-order amplifier.
• Premise 5 (High impact) — The perception gap mostly reflects evaluation and adoption conditions. Programmers can verify output immediately by running tests, use mature agentic tooling, and are early adopters with more practice. Professionals in law, medicine, or finance face liability, confidentiality, error costs, and workflow barriers. A model equally flawed everywhere would still look better in code.
• Conclusion (via A3) (High impact) — If top models reach about 68% wins or ties against experts on general professional tasks, the 'jagged' framing is overstated for much of the economy, and the RL-plus-revenue story explains only a residual of the gap. The benchmark is itself skewed toward well-specified digital deliverables, which cuts both ways.
• Premise 2 (Medium impact) — Verifiable environments are simply cheaper and faster to build, and labs are staffed by programmers who build tools for themselves. Revenue and tractability are confounded, and verifiable but low-value domains (puzzles, games, formal systems) show verifiability alone can produce peaks.
• Premise 3 (Medium impact) — RL on code and math may transfer to general reasoning, so non-verifiable domains improve as a spillover. This would make jaggedness shallower and more transient than a domain-specific allocation story implies.
• Premise 4 (Low impact) — Claude's usage mix is developer-skewed. Consumer chat studies at other vendors show writing, information-seeking, and advice dominating, so coding as one of the largest uses of frontier models in general is less clearly established.

Suggested Improvements

• Bridging premise for P3 — State explicitly that RL allocation, not pretraining or intrinsic task difficulty, is the dominant driver of cross-domain differences in capability, and give evidence such as pre/post-RL comparisons across domains or matched tasks. This closes the visible gap between 'RL is a major source of gains' and 'capability peaks where RL is applied'.
• Disentangling the three conditions — Use contrast cases: verifiable but low-value domains, valuable but hard-to-verify domains, and non-digital verifiable tasks, and show which conditions predict capability. Code and math satisfy all three conditions, so they cannot discriminate among them. Contrast cases would make the account falsifiable.
• Quantifying the explained share — Replace 'explains much of the gap' with an estimate or at least a ranking of contributors (training allocation, data abundance, verification ease, tooling, adoption), or reword the claim as 'is one significant contributor'. This reconciles the conclusion with A3 and avoids implying a dominant cause that the evidence does not establish.
• Measuring the perception gap — Use blind expert evaluations of model outputs across professions, or survey data, to separate actual capability differences from differences in adoption, tooling, and verification ability. The explanandum is currently asserted and conflated with capability.
• Evidence for revenue-driven selection — Correlate public indicators of environment investment (job postings, vendor spending, product emphasis, benchmark focus) with domain market size, and compare against tractability measures. This would raise P2 above inference from behavior (A4) and separate revenue from ease of verification.
• Specify disconfirming evidence and time scope — State what observations would count against the thesis, such as rapid gains in unverifiable fields that lack new graders, and indicate how long the pattern is expected to hold given A2. This prevents the account from absorbing any outcome, since both persistence and erosion of jaggedness would otherwise count as confirmation.

Scenario Tests

• Rubric-based RL and LLM graders are applied to law, medicine, or writing, and capability there rises quickly relative to comparable domains without new graders. (Supports) — This would confirm that reward availability, not intrinsic domain difficulty, drives the peaks. It would also make the jaggedness profile transitional, as A2 anticipates.
• Models strong in code before RL on verifiable rewards became widespread show a similar jagged profile with little change after RL. (Challenges) — This would indicate that pretraining data and task structure account for most of the unevenness, leaving RL allocation a modest contributor.
• Blind expert grading shows non-coding professionals rate model outputs in their own field as comparable in quality to code outputs, yet they report lower perceived usefulness. (Challenges) — The perception gap would be mainly an adoption, verification, and tooling gap, as A3 suggests, and jaggedness would explain only a small part of it.
• Digital, verifiable, high-revenue domains with strong automatic checks (such as SQL, formal compliance checks, or accounting reconciliation) show clearly weaker capability than comparably valued non-verifiable domains. (Challenges) — The three-condition rule would be unreliable as a predictor, and the account would need extra variables such as data availability or task length.
• General professional benchmarks continue to climb beyond 68% wins or ties while adoption in non-coding fields stays low. (Neutral) — Consistent with both a broadening-peaks story and an adoption-driven gap. It underlines that part of the remaining gap is not about capability, but it does not decide how much jaggedness contributes.

Coherence & Relevance

The argument is coherent as a probabilistic causal narrative: a training mechanism, a commercial incentive, a resulting capability profile, and an observed perception gap. The author's assumptions candidly flag its main limits (inferred revenue mechanism, possible broadening, adoption confounds). Its main tension is that A3 reduces the share of the gap that jaggedness can explain, while the title and conclusion keep a strong causal framing. Read as 'RL on verifiable rewards plus commercial steering is a significant contributor to uneven capability and to differing professional experiences', it is well supported. Read as a primary or sole explanation, it is not.

• A major source of recent LLM capability gains is reinforcement learning against rewards that can be checked automatically, such as passing tests or verifying proofs. (Strong) — Establishes the mechanism but not its size relative to scale, pretraining data, or inference-time compute, so it cannot alone support 'largely' in the conclusion.
• Developers choose which training environments to build partly by revenue potential, and coding and technical work are especially valuable in business settings. (Moderate) — Adds the economic steering needed for 'where RL is applied', but is inferred from behavior and is confounded with tractability and developer familiarity.
• Capability therefore peaks in domains that are digital, verifiable, and economically valuable, and lags in domains where quality is harder to check. (Strong) — Central to the argument, but it needs an unstated bridging premise that RL allocation dominates other determinants of domain capability, and the three conditions are not separated.
• Programming and mathematics fit all three conditions, and coding remains among the largest uses of frontier models. (Moderate) — Illustrates the pattern but cannot discriminate among the conditions. The usage statistic is vendor-specific and may reflect reverse causation.
• This unevenness explains why professionals in mathematics and code see much more capability than professionals in other fields. (Moderate) — Largely restates the conclusion. It treats perception as capability and does not rule out evaluator skill, tooling, and adoption, which A3 itself concedes.

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