CognitiveTwin: Architectural Foundations and Empirical Evaluation of Personalized Language Model Adaptation Through Trajectory-Aware Fine-Tuning

The construction of personalized language model instances capable of reproducing individual cognitive patterns, stylistic signatures, and domain-specific conceptual frameworks represents a significant advancement in the development of AI systems that function as cognitive extensions rather than generic tools. This paper presents the CognitiveTwin framework, a comprehensive architecture for creating personalized language model instances through trajectory-aware supervised fine-tuning on conversational interaction histories. The architectural foundation integrates three principal components: a trajectory coordinate system that encodes hierarchical conversation structure through tetrahedral geometric representations, a style signature extraction mechanism that captures recurring linguistic patterns across interaction histories, and a dual-ring memory topology that maintains both episodic and semantic memory traces for context-aware generation. We formalize the mathematical foundations underlying each architectural component, establish theoretical guarantees for style transfer convergence under specified conditions, and introduce a multi-dimensional evaluation framework encompassing lexical, syntactic, semantic, and pragmatic assessment dimensions. Empirical evaluation of a CognitiveTwin instance fine-tuned on 979 conversational exchanges demonstrates statistically significant improvements across all measured dimensions: characteristic phrase frequency increased by 100\%, technical term density improved by 46\%, topic consistency enhanced by 38\%, and syntactic complexity as measured by average sentence length increased by 91\% relative to the base model. The domain knowledge transfer analysis reveals successful absorption of conceptual frameworks specific to the training corpus, with the fine-tuned model demonstrating interpretive alignment with training data semantics on targeted probe queries. The framework contributes novel architectural patterns for trajectory-aware language modeling, mathematically rigorous evaluation metrics for personalization assessment, and empirical benchmarks establishing the viability of cognitive modeling through language model adaptation.