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: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:2606. 17945v1 Announce Type: new Abstract: Large language models provide a tractable system for asking how intelligence itself emerges, rather than only how LLMs can be engineered.
arXiv:2608. 16118v1 Announce Type: new Abstract: How should we assess whether large language models can perform mathematical invention?
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.
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:2608. 06839v1 Announce Type: new Abstract: Artificial Neural networks (ANNs) are often treated as black-box models, making explainability a central challenge in deep learning.
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...
arXiv:2609.37635v1 Announce Type: new Abstract: LLMs have been studied in recent linguistics as potential models of humans' linguistic abilities. Here we discuss an entirely different use of AI, name...
arXiv:2606. 30481v1 Announce Type: cross Abstract: Current large language models are extraordinary statistical engines.
The paper introduces a method for evaluating the intrinsic interestingness of mathematical theorems by comparing the length of their proofs to the length of their statements. It trains a 27B language model to predict proof difficulty, enabling the generation and selection of more interesting theorems while significantly reducing overlap with existing Mathlib. The approach allows iterative expansion of a self‑building, machine‑verified mathematical library guided by quantifiable metrics.
We advance the hypothesis that human mathematical reasoning, constrained by both the undecidability and the computational intractability of even modest logical fragments, relies fundamentally on pattern matching from domains external to pure deduction. The most prolific reservoir of such patterns is the natural world, whose physical laws and biological systems have undergone billions of years of ``pre-computation'' and already exhibit surprisingly innovative solutions.
The paper introduces Self‑Play Pretraining with Zero Data, a proof‑of‑concept method that lets a model generate its own training data by searching over all computable processes using a universal Turing machine. Two models— a generator that proposes byte‑sequence programs and a learner that predicts those sequences—train together, with the generator rewarded for producing data at the learner’s frontier, creating an adaptive curriculum. Experiments show that zero‑shot performance on natural datasets scales predictably with compute, and the models exhibit in‑context learning and discover mathematical sequences during training.