[2603.23539] PLDR-LLMs Reason At Self-Organized Criticality

Computer Science > Artificial Intelligence arXiv:2603.23539 (cs) [Submitted on 12 Mar 2026] Title:PLDR-LLMs Reason At Self-Organized Criticality Authors:Burc Gokden View a PDF of the paper titled PLDR-LLMs Reason At Self-Organized Criticality, by Burc Gokden View PDF HTML (experimental) 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 ...