PLDR-LLMs Reason At Self-Organized Criticality

TL;DR

This paper demonstrates that PLDR-LLMs pretrained at self-organized criticality exhibit reasoning capabilities at inference, with their outputs showing phase transition-like behavior and the potential to quantify reasoning through global model parameters.

Contribution

It introduces the concept that reasoning in large language models can be understood as a phase transition phenomenon at criticality, linking model behavior to physical concepts like universality and renormalization.

Findings

Reasoning correlates with criticality in PLDR-LLMs.

Model performance improves near criticality, as indicated by benchmark scores.

Reasoning ability can be quantified by an order parameter derived from model outputs.

Abstract

We show that PLDR-LLMs pretrained at self-organized criticality exhibit reasoning at inference time. The characteristics of PLDR-LLM deductive outputs at criticality is similar to second-order phase transitions. At criticality, the correlation length diverges, and the deductive outputs attain a metastable steady state. The steady state behaviour suggests that deductive outputs learn representations equivalent to scaling functions, universality classes and renormalization groups from the training dataset, leading to generalization and reasoning capabilities in the process. We can then define an order parameter from the global statistics of the model's deductive output parameters at inference. The reasoning capabilities of a PLDR-LLM is better when its order parameter is close to zero at criticality. This observation is supported by the benchmark scores of the models trained at near-criticality and sub-criticality. Our results provide a self-contained explanation on how reasoning manifests in large language models, and the ability to reason can be quantified solely from global model parameter values of the deductive outputs at steady state, without any need for evaluation of curated benchmark datasets through inductive output for reasoning and comprehension.