No Error Signal, No Discovery

Tom Zahavy, a Google DeepMind researcher and co-author of AlphaProof, argues in an ICML 2026 position paper that large language models have mechanized induction and deduction but lack a mechanism for abduction, the mode of inference needed for scientific discovery. Using Einstein's development of general relativity as a case study, Zahavy contends that discovery requires inventing new hypotheses without an error signal, a capability current AI systems do not possess. The paper suggests that AI progress is verifier-gated, and abduction remains the bottleneck for true innovation.

AI https://sourcefeed.dev/c/ai Article No Error Signal, No Discovery An AlphaProof co-author's ICML position paper pins down the one reasoning mode LLMs haven't mechanized. Rachel Goldstein https://sourcefeed.dev/u/rachel goldstein Tom Zahavy is not an AI skeptic. He's a researcher at Google DeepMind and a co-author of AlphaProof https://deepmind.google/discover/blog/ai-solves-imo-problems-at-silver-medal-level/ , the system that hit silver-medal standard on International Mathematical Olympiad problems in 2024. Which is exactly what makes his ICML 2026 position paper, "LLMs can't jump" https://openreview.net/forum?id=klU4737opt , worth your attention now that it's bouncing around the Hacker News front page. This isn't an outsider dunking on transformers. It's someone who helped mechanize formal reasoning drawing a precise line around what got mechanized — and what didn't. The paper's claim, stripped of the philosophy-of-science scaffolding: machine learning has industrialized two of the three modes of inference and has no mechanism for the third. Induction — extracting rules from piles of examples — is what pretraining is. Deduction — deriving consequences from fixed premises — is falling fast, with AlphaProof's silver followed by gold-level IMO performance in 2025 and proof assistants like Lean https://lean-lang.org/ providing the verification substrate. The missing mode is abduction: inventing a new explanatory hypothesis when the data is thin and nothing is obviously broken. A discovery with no error signal Zahavy's case study is Einstein and general relativity, and the detail that matters is one most retellings skip: in 1907, Newtonian gravity wasn't failing. The equivalence of inertial and gravitational mass had been confirmed to one part in a billion. The lone anomaly — Mercury's drifting perihelion — was blamed on an undiscovered planet, "Vulcan," not on the theory. In loss-function terms, Newton's residuals were near zero. There was no gradient pointing away from it. That's the paper's sharpest move, because it kills the comfortable story that discovery is compression — find the simpler program that explains the data. A compression-driven optimizer sitting on 1907's data would patch Newton with a Vulcan parameter, not detonate absolute time and rebuild physics on curved spacetime, a step that makes the theory more complex before it gets simpler. Einstein's actual mechanism was a simulated sensation: an observer in free fall feels no gravity, so gravity and acceleration must be one phenomenon. Hypothesis first, evidence later — Eddington's eclipse measurements arrived years after the theory. Zahavy is careful about what he's not claiming. He concedes that an LLM initialized with Einstein's 1915 postulates could plausibly grind out the field equations and the Mercury prediction — that's deduction, and we're good at automating it. The bottleneck is upstream, where the postulates come from. The part worth stealing for your roadmap Here's the synthesis the paper gestures at but doesn't spell out: essentially every reliable LLM capability gain of the last two years has been verifier-gated. Coding agents work because tests and compilers are error signals. AlphaProof works because Lean rejects bad proofs. Reinforcement learning with verifiable rewards works precisely where a reward can be checked. Even DeepMind's AlphaEvolve, as the paper notes, optimizes against an explicit metric. Progress compounds wherever a gradient exists. Abduction is, by definition, the regime where no gradient exists — nothing is failing, so nothing tells the optimizer where to go. That gives you a brutally practical scoping question for any AI feature: what's the verifier? Migrating a codebase against a test suite, generating SQL you can execute, refactoring behind a type checker — verifier-shaped, automate aggressively and expect the ceiling to keep rising. Naming the right abstraction, deciding which product hypothesis to test, root-causing an incident that matches no known pattern — premise-shaped, and today's architectures give you no reason to expect autonomous competence. That split also explains why "AI scientist" products underwhelm: Zahavy's own read is that systems like Sakana's AI Scientist recombine existing symbolic concepts to optimize metrics — deduction and induction in a lab coat. Where the argument overreaches "Structurally incapable" is a theorem-shaped claim supported by an essay. The paper offers no impossibility proof and no benchmark, and it generalizes from a single, maximally exceptional historical episode. The HN thread landed the obvious counterpunch: the "LLMs can't X" genre has a rough track record, usually resolving to "they can, just badly at first." ARC-AGI https://arcprize.org/ already probes exactly this regime — inferring rules from a handful of examples, too sparse for statistics — and models have climbed it, expensively but measurably. Historians also note Lorentz and Poincaré had much of the mathematics before 1905; though that arguably strengthens Zahavy's point, since Einstein's leap was interpretive, not derivational. The prescription is the weakest part. Zahavy's proposed fix — action-controllable world models in the lineage of DeepMind's Genie, giving agents a synthetic lab for counterfactual "thought experiments" — is a coherent research bet, but the empirical record for world models generating hypotheses rather than pretty rollouts is thin, and text-first labs keep shipping frontier reasoning without them. Zahavy himself moved to defuse the hype cycle, clarifying publicly that this is a personal position, not DeepMind's, and not a claim that LLMs can't contribute to discovery. The taxonomy outlives the verdict My call: the impossibility claim won't age well as stated — test-time search, tool loops, and whatever eats ARC-AGI next will keep blurring the boundary. But the Peirce-flavored taxonomy is immediately useful and most teams don't have one. It converts "AI can't really think" hand-waving into an operational question — is there an error signal here? — that cleanly predicts where agents already deliver and where they stall. Draw the line through your own backlog: everything downstream of a verifier is automation surface; everything upstream is where your senior people earn their comp, setting the axioms the machines then grind on. LLMs can't jump yet. They are, however, extraordinarily good at landing — once you tell them where. Sources & further reading - Position: LLMs Can't Jump https://openreview.net/forum?id=klU4737opt — openreview.net - LLMs can't jump full paper PDF https://www.tomzahavy.com/files/llms-cant-jump.pdf — tomzahavy.com - ICML 2026 Poster: Position: LLMs can't jump https://icml.cc/virtual/2026/poster/67091 — icml.cc - Position: LLMs Can't Jump - Hacker News discussion https://news.ycombinator.com/item?id=49181083 — news.ycombinator.com - Tom Zahavy's reflections on the LLMs Can't Jump paper https://x.com/TZahavy/status/2082401499628376180 — x.com Rachel Goldstein https://sourcefeed.dev/u/rachel goldstein · Dev Tools Editor Rachel has been embedded in the developer tooling ecosystem for nearly eight years, covering everything from IDE wars and package-manager drama to the quiet rise of AI-assisted coding. She has a soft spot for open-source maintainers and an unhealthy number of terminal emulators installed on a single laptop. Discussion 0 No comments yet Be the first to weigh in.