Contextual Residual Inversion in Transformer-Based Large Language Models: A Reversibility Paradigm for Studying Representational Fidelity

Contextual Residual Inversion introduces a theoretical and computational approach for estimating partial reversibility of internal residual streams in transformer-based LLMs through non-invasive linear inversion operators applied to frozen inference passes. The method defines invertibility over structured prompt families by quantifying layer-wise reconstruction fidelity using projection-constrained residual approximations. Inversion accuracy is examined under varying lexical entropy, token classes, and layer depth, revealing substantial directional drift and energy compression patterns in deeper layers. Semantic stability of inverted representations is further analyzed through KL divergence and centroid shift in token distributions, demonstrating mild correlation between residual fidelity and generative coherence. Residual operators trained on specific prompt clusters show degradation when generalized across structurally divergent prompts, suggesting sensitivity to latent representation regimes not apparent from surface form alone. Metrics including cosine similarity, semantic drift score, and re-alignment ratio provide modest insight into the underlying activation structure governing token-wise representation. Experimental data is drawn from controlled synthetic prompts using a sparse Mixture-of-Experts LLM architecture, enabling reproducible assessments of inversion fragility and directional bias. The findings offer an interpretable, layer-sensitive perspective on the reversibility and geometric constraints of contextual encoding in high-capacity generative systems.