Einstein Had No Error Signal

A DeepMind researcher asks whether a modern model, handed everything known in 1915, could have invented General Relativity. His answer is no. The reason is not scale, and it is not a benchmark. It is that the loss was already zero.

Tom Zahavy published LLMs can't jump on January 27, 2026. It is an ICML 2026 position paper, ten pages, no experiments and no benchmarks. Zahavy is a core contributor to AlphaProof, the system that reached silver medal standard at the mathematics olympiad. So the argument comes from inside the building, from someone who helped ship the deduction half.

The setup is a single question treated as a computational case study. Give a model the full state of physics in 1915. Could it produce General Relativity? Zahavy argues it could do the second half of the job and not the first, and that the gap between the halves is a whole category of reasoning nobody has a mechanism for.

In a letter to his friend Maurice Solovine, Einstein sketched how discovery actually works. Sense experience at the bottom. A curved line leaping up to a system of axioms. Then straight lines coming back down: the theorems you deduce, checked against the world. Zahavy labels the leap J, for Jump, and builds the paper around it.

The formal spine is Peirce, who sorted inference by which two of three things you already hold. A Rule, a Case, and a Result. Which one is missing tells you which kind of thinking you are doing. Zahavy gives each one a programming analogy, which is the part worth keeping.

The dominant story in machine learning is that discovery is compression. Find the shortest program that explains the data, and creativity falls out of the search. Zahavy's counter is not philosophical. It is arithmetic. In 1907 there was no data to compress and no error to shrink.

Newtonian gravity was not in crisis. It was the most precisely confirmed thing anyone had. The one loose thread, a small drift in Mercury's orbit, was not read as a flaw in the theory. It was read as a missing planet, and it had a name.

This is the sentence worth carrying out of the paper: scientific invention often happens with no supervised error signal at all. Every training loop, evaluation harness and agent scaffold you have ever built assumes a measurable gap between what the system produced and what it should have produced. Einstein did not have one. The confirmations came later, the Eddington eclipse measurement years after the theory was already written down.

Einstein's own account is that he imagined a man falling freely off a roof, and realised that in those seconds the man feels no gravity in his immediate surroundings. He has every right to call himself at rest. Later the same idea gets sealed into a box accelerating through deep space: release an object inside and the floor rushes up to meet it, and everything falls the same regardless of what it is made of.

The simulated sensation of acceleration was indistinguishable from the remembered sensation of gravity. So he decided they were the same phenomenon, and wrote that down as an axiom. Zahavy calls this manipulative abduction, after Magnani: thinking by doing, running a mental experiment with your hands on the controls. Not a permutation of symbols. A manipulation of felt experience.

The paper's blunt framing of what models do instead is that they operate as high-dimensional Chinese Rooms, moving the language of physics around without access to what that language points at. ARC gets a nod as testing the logical half of the leap, inferring a hidden rule from two to five examples, but Zahavy notes it misses the manipulative half entirely.

Here is the uncomfortable symmetry. The jump took one thought. The grind afterwards took seven years, and the grind is exactly what current systems are getting good at.

Not scale. World models you can act inside. Zahavy draws a sharp line between video prediction and interactive simulation: a video model drops the apple correctly because falling is the dominant continuation in its training distribution, not because it holds gravity anywhere. The interesting direction is architectures like Genie that learn an action space, because intervention is the prerequisite. To run the elevator experiment a system cannot watch a video of a lift. It has to be able to cut the cable.

He applies the same test to today's automated discovery systems and finds them on the wrong side of it. The AI Scientist recombines existing symbolic concepts to move a metric. AlphaEvolve optimises brilliantly inside a fixed frame, but it needs a gradient to climb. Einstein had neither a metric nor a gradient.

The closing move is the honest one. He limits the claim to the physical sciences, where the grounding is external material reality, and grants that in mathematics the grounding might be something else entirely, high dimensional structure or a taste for generality. The jump stays necessary. What you simulate has to match the field.

Strip the physics and the useful shape is this. Your systems are extremely strong wherever a target already exists: a test to pass, a proof to close, a metric to move, a diff to shrink. They are weak exactly where the target has to be invented, and that weakness is invisible in evaluation, because an eval is a target by definition.

So when an agent stalls on something open ended, it is worth asking which half of the loop you actually handed it. If you gave it premises, expect good work. If you expected it to choose the premises, you asked for the jump, and nothing in the stack does that yet.

The paper, ten pages
Project page and summary
The conference listing
Norton on Einstein's pathway, the historical source the paper leans on

The nice thing about a claim this specific is that it has an expiry date. Somebody builds a model that proposes a genuinely new physical axiom out of a simulation it can steer, and the paper is wrong on the record. Until then it is the sharpest description I have read of what the current stack cannot do.

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