Transformers Can Learn Rules They've Never Seen: Proof of Computation Beyond Interpolation
A central question in the debate over large language models is whether transformers can learn rules they have never seen, or whether they can only interpolate: predict new cases from their similarity to training examples. We test this in a controlled setting where interpolation provably fails, so success can only come from computation beyond interpolation. We train small transformers to predict the rollout of a cellular automaton whose update rule is pure XOR, and remove one entry of the rule's truth table from all direct supervision. The missing entry's output is never shown to the model; its only trace is indirect, as wrong values corrupt visible predictions at later timesteps. Because ...
| Authors | Andy Gray |
|---|---|
| Primary category | cs.LG |
| Published | 17 March 2026 |
| Last updated at source | 29 July 2026 |
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