arXiv:2603. 05556v2 Announce Type: replace Abstract: Integer sequences in the OEIS span values from single-digit constants to astronomical factorials and exponentials, making prediction challenging for standard tokenised models that cannot handle out-of-vocabulary values or exploit periodic arithmetic structure.
arXiv:2606. 17399v1 Announce Type: cross Abstract: When small transformers grok modular multiplication, prior work reports that the learned embedding has a "dense" Fourier spectrum requiring all frequencies.
arXiv:2506. 04985v2 Announce Type: replace Abstract: Large language models (LLMs) require substantial compute, and thus energy, at inference time.
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.
arXiv:2606. 23044v2 Announce Type: replace-cross Abstract: Numbers have algebraic structure that standard neural embeddings often fail to expose.
arXiv:2608. 10010v2 Announce Type: replace Abstract: Low-precision formats usually optimize scalar fidelity while inheriting conventional product arithmetic.
arXiv:2507. 11768v3 Announce Type: replace-cross Abstract: Bayesian accounts of in-context learning face a direct objection: exact posterior predictives for exchangeable data are invariant to task-preserving order, yet transformers change next-token probabilities when the same examples are serialized differently.
arXiv:2608. 10010v1 Announce Type: new Abstract: Low-precision datatypes reduce language-model cost, but most formats optimize scalar fidelity while leaving the arithmetic induced by their products unchanged.
arXiv:2607. 17166v1 Announce Type: new Abstract: Transformer-based large language models (LLMs) continue to achieve state-of-the-art performance across various natural language processing tasks.
arXiv:2607. 16212v1 Announce Type: new Abstract: Large language models hallucinate numbers and units when summarizing scientific text, a failure mode that can silently invert a scientific claim.
arXiv:2608. 13129v1 Announce Type: new Abstract: Large language models (LLMs) achieve strong results on mathematical reasoning benchmarks yet remain unreliable on elementary numerical tasks, including magnitude comparison, large-integer arithmetic, fractions, and scientific notation.
arXiv:2504. 19451v4 Announce Type: replace-cross Abstract: This paper presents two concrete applications of Artificial Intelligence to algorithmic and analytic number theory.
arXiv:2607. 07066v1 Announce Type: cross Abstract: Transformers have demonstrated a remarkable ability to learn algorithmic reasoning, yet mechanistic analyses have mostly focused on globally invertible operations such as cyclic addition and group composition.