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.
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...
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.
arXiv:2610.32104v1 Announce Type: cross Abstract: Several formal theories have been developed to characterize the capabilities and limitations of the transformer architecture, each employing differen...
arXiv:2610.14007v1 Announce Type: cross Abstract: A familiar line of reasoning runs as follows: language models are flexible approximators trained under a strictly proper loss, so scale brings them c...
arXiv:2606. 17289v1 Announce Type: new Abstract: AI systems based on artificial neural networks are being developed with aspirations of pushing the boundary of human mathematical knowledge.
arXiv:2606. 27721v1 Announce Type: new Abstract: Compositional generalization, the ability to solve complex problems by combining solutions to simpler sub-problems, is a fundamental capability of both natural and artificial intelligence, and a key mechanism underlying chain-of-thought reasoning.
The paper investigates how well practical machine‑learning algorithms approximate Solomonoff’s universal predictor when trained by minimizing log‑loss over diverse datasets. It establishes tight bounds on the worst‑case increase in prediction error caused by approximating the Bayesian mixture predictor, showing that while the excess error can be large in low‑prior environments, it remains bounded on average and under distribution shifts. The authors also extend their analysis to finite‑sample settings relevant to neural networks and Transformers.
arXiv:2606. 30442v1 Announce Type: new Abstract: The Bitter Lesson, which posits that general-purpose methods that scale with computation and data ultimately outperform those with built-in human knowledge, has become a dominant paradigm in the era of Large Language Models.
arXiv:2610.27157v1 Announce Type: cross Abstract: Inference-time harnesses, i.e., external procedures that call a model many times and keep state across calls, can substantially improve model capabil...
arXiv:2603. 25414v4 Announce Type: replace-cross Abstract: A prevailing assumption in machine learning is that model correctness must be enforced after the fact.
arXiv:2606. 02008v1 Announce Type: cross Abstract: Pre-training has become a fundamental paradigm in modern machine learning, with one of its key empirical benefits being reduced downstream sample complexity as the scale of pre-training data increases.