The paper introduces a new complexity measure, based on a restricted class of "layered zipline programs," which is weaker than the previously defined Arithmetic Repetition Complexity (ARC). This measure allows for a prediction algorithm that operates in quasilinear time and polylogarithmic space on highly-structured sequences, offering a more efficient solution at the cost of reduced expressivity compared to ARC. The work highlights a tradeoff between algorithmic efficiency and the breadth of sequences that can be effectively predicted.
arXiv:2607. 17369v1 Announce Type: cross Abstract: In a previous paper, we began the study of sequence prediction algorithms adapted to stringological word complexity measures.
arXiv:2608. 19908v1 Announce Type: cross Abstract: Probability estimation over large alphabets under log loss is a well-studied problem, with celebrated methods such as the Good-Turing estimator.
The paper investigates integer‑sequence benchmarks from the OEIS by applying a two‑part minimum description length (MDL) learner that searches for P‑recursive recurrences. It finds that MDL difficulty correlates with a combinatorial parameter count, that most sequences fit a recurrence on a prefix but not at full length (the “wilderness” regime), and that language models do not hallucinate in the wilderness but instead hedge, showing that memorisation dominates perceived competence. The study provides a cheap, contamination‑free difficulty signal for OEIS‑derived benchmarks.
arXiv:2607. 23361v1 Announce Type: cross Abstract: Language generation in the limit is an elegant model introduced by Kleinberg and Mullainathan [KM24] to formally study language generation by an algorithm that learns solely based on example strings.
arXiv:2503.15242v3 Announce Type: replace Abstract: We introduce BigO(Bench), a novel coding benchmark designed to evaluate the capabilities of generative language models in understanding and generat...
arXiv:2605. 05066v2 Announce Type: replace-cross Abstract: We identify and prove a fundamental trade-off governing long-sequence models: no model can simultaneously achieve (i) per-step computation independent of sequence length (Efficiency), (ii) state size independent of sequence length (Compactness), and (iii) the ability to recall a number of historical facts proportional to sequence length (Recall).
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:2607. 01903v1 Announce Type: new Abstract: LLM-integrated applications blend natural language prompts with program code, and much of their runtime behavior originates in the prompt layer rather than in the code itself.
LLM-integrated applications blend natural language prompts with program code, and much of their runtime behavior originates in the prompt layer rather than in the code itself. Existing complexity metrics, however, operate solely at the code level and therefore overlook this behavioral logic entirely.
arXiv:2609. 29881v1 Announce Type: cross Abstract: Choosing Shellsort gaps is a well-known open problem.
ElementCheck is a new framework for evaluating the factuality of long-form text that addresses limitations of the traditional decompose‑retrieve‑verify pipeline. Rather than breaking sentences into atomic sub‑claims, it extracts entity pairs linked by verifiable connections to form an element graph, using the graph’s topology to gauge sentence complexity. This allows simple sentences to be verified directly while complex ones undergo targeted element‑level refinement, and the authors introduce the FastFact‑Sent benchmark to support fine‑grained evaluation, demonstrating consistent improvements across multiple backbone models.
arXiv:2609.35869v1 Announce Type: new Abstract: Pre-tokenisation restricts which text fragments can become prediction units, but its compression cost is obscured when tokenisers are compared only und...