The Long Delay to Arithmetic Generalization
Read the original on arXiv AI →The Flow has not summarised this story yet — read it at arXiv AI.
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arXiv:2604. 13082v2 Announce Type: replace-cross Abstract: Grokking in transformers trained on algorithmic tasks is characterized by a long delay between training-set fit and abrupt generalization, but the source of that delay remains poorly understood.
The paper presents quantitative generalization bounds for fixed‑precision transformer models, addressing both in‑distribution statistical generalization and length generalization. It derives guarantees based on model parameters, quantization space, and alphabet size, and shows how training length and sample size trade off, with longer training being exponentially more efficient. Experiments confirm the theoretical predictions.
arXiv:2512. 01870v3 Announce Type: replace Abstract: We study whether a transformer network can learn the deterministic sequence of trees generated by the iterated prime factorization of the natural numbers.
arXiv:2609.08851v1 Announce Type: new Abstract: Recent advancements in transformer length generalization theory enable us to reliably predict when a transformer can learn to solve a task. In particul...
arXiv:2603. 17019v2 Announce Type: replace Abstract: 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.
arXiv:2608.31067v1 Announce Type: new Abstract: Learning generalizable algorithmic computations remains a challenge for neural networks, as reflected in persistent failures on compositional and lengt...