Tensor Network Neuroscience: A Rigorous Mathematical Framework

Abstract

We propose that neural activity can be rigorously modeled as tensor network states, with cortical hierarchies mapping onto a Multi-scale Entanglement Renormalization Ansatz (MERA) architecture. Within this framework, we identify the effective bond dimension as a measurable neural correlate of consciousness, providing a computationally tractable alternative to integrated information theory. We prove that a tensor-network-based integration measure preserves key properties of established consciousness theories while remaining efficiently computable. The hierarchical organization of the visual cortex—from primary through associative areas—is shown to follow quantitative coarse-graining laws consistent with renormalization group structure. We derive explicit bounds on information capacity and learning complexity, and specify experimental protocols using standard neuroimaging technology. The framework yields falsifiable predictions: bond dimension values across cortical regions, exponential decay of bond dimension under anesthesia, and a universal consciousness threshold at loss of consciousness. Each claim is assigned an explicit epistemic level, separating proven mathematical theorems from empirically testable hypotheses and speculative interpretations. This approach opens pathways toward objective consciousness diagnostics in disorders of awareness and personalized anesthesia monitoring.