PLDR-LLMs Reason At Self-Organized Criticality
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.
69c494444ae7eef815b9d972
Burc Gokden
claimed_verified
2026-03-26T13:43:00.777Z
671ddb3bf89c9b8208568e73
https://cdn-avatars.huggingface.co/v1/production/uploads/671ddb3bf89c9b8208568e73/QXX_zseNpF9_HMKZWHb3H.jpeg
Burc Gokden
fromthesky
user
fromthesky
PLDR-LLMs Reason At Self-Organized Criticality
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.
PLDR-LLMs exhibit reasoning capabilities at self-organized criticality through metastable steady states that mirror second-order phase transitions, enabling generalization without benchmark evaluation.
PLDR-LLMs self-organized criticality deductive outputs second-order phase transitions correlation length metastable steady state scaling functions universality classes renormalization groups order parameter global statistics generalization reasoning capabilities