← Back to all news
arXiv AI By Hector Zenil, Abicumaran Uthamacumaran, Luan Ozelim

Large Language Models As Shannon Lossy Compressors Not Solomonoff Induction Estimators: The Singularity Is Not Near Without Symbolic Model Synthesis

Read the original on arXiv AI →

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.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

Related stories

arXiv AI
Aug 12

On Solomonoff Induction in Large Language Models and the Limits of Self-Improving: The Singularity Is Not Near Without Symbolic Model Synthesis

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
llms
More like this →
arXiv Machine Learning
2d ago

Mentored Decoding: Faster Inference meets Boosting

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
llms
More like this →
arXiv AI
Aug 25

Measuring in-context algorithmic reasoning in language models against an exact Bayes-optimal reference

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
llmsbenchmarkssafety
More like this →