arXiv:2601. 05280v3 Announce Type: replace-cross Abstract: On the one hand, the question of whether large language models (LLMs) are Solomonoff induction estimators has become an explicit question at the intersection of Algorithmic Information Theory (AIT) and Machine Learning (ML) of great interest.
By Hector Zenil
The paper argues that Large Language Models (LLMs) do not function as Solomonoff induction estimators because their training objectives—cross‑entropy, negative log‑likelihood, and next‑token prediction—optimize fit to a supplied conditional distribution rather than a program‑weighted universal mixture. It further contends that additional computation alone does not transform these models into optimal predictors without external hyper‑parameter or architectural changes. The authors suggest that neurosymbolic machine learning, exemplified by models such as Fable and Astra, represents a shift toward symbolic model synthesis, moving beyond purely statistical LLMs.
By Hector Zenil, Abicumaran Uthamacumaran, Luan Ozelim
arXiv:2601.05280v4 Announce Type: replace-cross
Abstract: On the one hand, the question of whether Large Language Models (LLMs) are Solomonoff induction estimators has become an explicit question at...
By Hector Zenil, Abicumaran Uthamacumaran, Luan Ozelim
arXiv:2608. 01320v1 Announce Type: cross Abstract: Language generation in the limit is a theoretical framework for studying how a generator can learn to produce new valid strings from a stream of positive examples.
By Ziyi Cai, Shuangping Li, Yiheng Shen, Kangning Wang, Peng Zhang
arXiv:2608. 29503v1 Announce Type: new Abstract: Worst-case online classification is governed by sequential complexity, such as Littlestone dimension, and can be impossible even for statistically simple classes, such as thresholds of VC dimension one.
By Roi Livni, Sahil Singla
arXiv:2608. 15798v1 Announce Type: new Abstract: Language models are compared by their held-out per-token cross-entropy risk---the quantity scaling laws are fitted to.
By Hanti Lin