PRefLexOR: Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning and Agentic Thinking

PRefLexOR (Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning) combines preference optimization with concepts from Reinforcement Learning to enable models to self-teach through iterative reasoning improvements. We propose a recursive learning approach that engages the model in multi-step reasoning, revisiting, and refining intermediate steps before producing a final output in training and inference phases. Through multiple training stages, the model first learns to align its reasoning with accurate decision paths by optimizing the log odds between preferred and non-preferred responses. During this process, PRefLexOR builds a dynamic knowledge graph by generating questions from random text chunks and retrieval-augmentation to contextualize relevant details from the entire training corpus. In the second stage, preference optimization enhances model performance by using rejection sampling to fine-tune reasoning quality by continually producing in-situ training data while masking the reasoning steps. Recursive optimization within a thinking token framework introduces iterative feedback loops, where the model refines reasoning, achieving deeper coherence, consistency, and adaptability. Implemented in small language models with only 3 billion parameters, we should that even tiny models can iteratively teach themselves to reason with greater depth and reflectivity. Our implementation is straightforward and can be incorporated into any existing pretrained LLM. We focus our examples on applications in biological materials science and demonstrate the method in a variety of case studies that range from in-domain to cross-domain applications. Using reasoning strategies that include thinking and reflection modalities we build a multi-agent recursive self-improving inference approach to successively improve responses via repeated sampling in inference time.