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. 01005v1 Announce Type: new Abstract: Solomonoff Induction, or SolInd, provides an ideal unbounded model of a priori sequence prediction but cannot naturally describe extrapolation from a given training dataset, as performed by Large Language Models.
By Nathan Young
arXiv:2607. 28667v1 Announce Type: cross Abstract: Recent work has shown that classifying large language models (LLMs)' responses can be distinguished by modeling token embeddings as trajectories of a black-box dynamical system (DS) and comparing prediction residuals of two DSs.
By Mohamed Akrout, Dan Wilson
The paper introduces F-ICL, a benchmark that measures in‑context algorithmic reasoning in language models by exhaustively enumerating 86 million valid programs of length ≤13 on a Turing‑complete machine and computing the exact posterior under a bounded Levin–Solomonoff prior. Unlike typical benchmarks, F‑ICL provides a distributional reference rather than just answers, allowing the evaluation of models’ inductive priors. Across 105 configurations of models ranging from 0.8 B to 675 B parameters, models achieve up to 92 % accuracy, yet many still deviate from the Bayes‑optimal reference, and the study derives theoretical bounds on cumulative loss for predictors with positive prior weight on the reference.
By Luan Ozelim, Hector Zenil
Emergent Abilities in Large Language Models: A Survey reviews how scaling LLMs leads to previously unseen capabilities such as advanced reasoning, in-context learning, coding, and problem-solving. The paper critically examines definitions, inconsistencies, and the conditions that foster these abilities, including scaling laws, task complexity, pre‑training loss, quantization, and prompting strategies. It also discusses the extension to Large Reasoning Models and highlights safety concerns like deception, manipulation, and reward hacking, calling for improved evaluation and governance.
By Leonardo Berti, Flavio Giorgi, Gjergji Kasneci
The paper introduces mentored decoding, a formal framework for lossy speculative decoding that can accelerate inference of autoregressive language models while potentially improving output quality. It connects this inference technique to boosting theory and extends it to all f‑divergences, revealing geometric insights for total variation, simple approximations tied to boosting compliance, and a divergence‑independent data structure enabling efficient optimal parameter queries and mentored distribution construction.
By Vivien Tran-Thien, Richard Nock
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.
By Phoebe Zeng, Thomas L. Griffiths, Brenden M. Lake
Whether large language models perform genuine algorithmic reasoning or mere pattern completion is hard to test, because most benchmarks lack a ground truth for correct inductive inference. We introduce F-ICL, an in-context-learning benchmark that supplies one exactly.
arXiv:2606. 30923v1 Announce Type: cross Abstract: Imitation Learning is a natural framework for learning in sequential decision-making systems and has emerged as the dominant paradigm through which we understand language model training.
By Ved Sriraman, Peihan Liu, Daniel Hsu, Adam Block
arXiv:2608. 01575v1 Announce Type: new Abstract: Whether large language models perform genuine algorithmic reasoning or mere pattern completion is hard to test, because most benchmarks lack a ground truth for correct inductive inference.
By Hector Zenil, Luan Ozelim
arXiv:2512. 22088v3 Announce Type: replace-cross Abstract: The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources.
By Chiwun Yang