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.
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.
Far from equilibrium, neural systems self-organize across multiple scales. Exploiting multiscale self-organization in neuroscience and artificial intelligence requires a computational framework for modeling the effective non-equilibrium dynamics of stochastic neural trajectories. Non-equilibrium thermodynamics and representational geometry offer theoretical foundations, but we need scalable data-driven techniques for modeling collective properties of high-dimensional neural networks from partial subsampled observations. Renormalization is a coarse-graining technique central to studying emergent scaling properties of many-body and nonlinear dynamical systems. While widely applied in physics and machine learning, coarse-graining complex dynamical networks remains unsolved, affecting many computational sciences. Recent diffusion-based renormalization, inspired by quantum statistical mechanics, coarse-grains networks near entropy transitions marked by maximal changes in specific heat or information transmission. Here I explore diffusion-based renormalization of neural systems by generating symmetry-breaking representations across scales and offering scalable algorithms using tensor networks. Diffusion-guided renormalization bridges microscale and mesoscale dynamics of dissipative neural systems. For microscales, I developed a scalable graph inference algorithm for discovering community structure from subsampled neural activity. Using community-based node orderings, diffusion-guided renormalization generates renormalization group flow through metagraphs and joint probability functions. Towards mesoscales, diffusion-guided renormalization targets learning the effective non-equilibrium dynamics of dissipative neural trajectories occupying lower-dimensional subspaces, enabling coarse-to-fine control in systems neuroscience and artificial intelligence.
The resemblance between the methods used in studying quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent that TNs can be used for machine learning. Previous results used one-dimensional TNs in image recognition, showing limited scalability and a high bond dimension. In this work, we train two-dimensional hierarchical TNs to solve image recognition problems, using a training algorithm derived from the multipartite entanglement renormalization ansatz (MERA). This approach overcomes scalability issues and implies novel mathematical connections among quantum many-body physics, quantum information theory, and machine learning. While keeping the TN unitary in the training phase, TN states can be defined, which optimally encodes each class of the images into a quantum many-body state. We study the quantum features of the TN states, including quantum entanglement and fidelity. We suggest these quantities could be novel properties that characterize the image classes, as well as the machine learning tasks. Our work could be further applied to identifying possible quantum properties of certain artificial intelligence methods.
This preprint presents a rigorous, self-contained mathematical framework for numerically approximating the Riemann Zeta function using Multiscale Entanglement Renormalization Ansatz (MERA) tensor networks. By formally establishing a unitary equivalence between the MERA coarse-graining operator and a discretized Mellin integral (Lemma 3.1), we analytically derive the theoretical infrared fixed point (Theorem 3.1) to be γtarget=log(2π)2π2≈0.0931γtarget=2π2log(2π)≈0.0931. This derivation leverages the polygamma function evaluated at the center of the critical strip. A numerical implementation with bond dimension χ=2χ=2 achieves this target with an absolute error of 1.3×10−51.3×10−5 and a relative error of +0.0139%+0.0139%. We also provide strict, exponentially converging error bounds based on the singular value decomposition of Hankel/Mellin-type operators (Theorem 3.2). Notably, this mathematically derived fixed point provides the fundamental scale parameter for the Renormalization Group Scale (RG-S) within the R5+ modified gravity model. Keywords: Riemann Zeta Function, MERA, Tensor Networks, Mellin Transform, Renormalization Group, Functional Equation, Fixed Point, Numerical Analysis, R5+ Gravity.
Quantum consciousness, the hypothesized subjective experience arising from quantum processes, has remained largely a philosophical debate with limited empirical validation. Traditional approaches to studying consciousness rely heavily on correlational studies, which often struggle to capture the nuances of subjective experience. This paper proposes a novel metric, the "Cognitive Resonance" measure, designed to quantify the level of conscious experience within a system by integrating neural network activity and quantum system dynamics. We argue that this metric offers a potential pathway to move beyond correlation-based measures, establishing a quantifiable link between subjective experience and fundamental quantum phenomena. The core mechanism centers around creating a metric that directly assesses the coherence and synchronized emergence of neural networks and quantum states, offering a potential testable framework for understanding the nature of consciousness. This work builds upon existing research in neural networks, quantum information theory, and subjective experience, aiming to provide a mathematically rigorous and potentially transformative approach to investigating this enduring mystery.
This preprint presents a rigorous, self-contained mathematical framework for numerically approximating the Riemann Zeta function using Multiscale Entanglement Renormalization Ansatz (MERA) tensor networks. By formally establishing a unitary equivalence between the MERA coarse-graining operator and a discretized Mellin integral (Lemma 3.1), we analytically derive the theoretical infrared fixed point (Theorem 3.1) to be γtarget=log(2π)2π2≈0.0931γtarget=2π2log(2π)≈0.0931. This derivation leverages the polygamma function evaluated at the center of the critical strip. A numerical implementation with bond dimension χ=2χ=2 achieves this target with an absolute error of 1.3×10−51.3×10−5 and a relative error of +0.0139%+0.0139%. We also provide strict, exponentially converging error bounds based on the singular value decomposition of Hankel/Mellin-type operators (Theorem 3.2). Notably, this mathematically derived fixed point provides the fundamental scale parameter for the Renormalization Group Scale (RG-S) within the R5+ modified gravity model. Keywords: Riemann Zeta Function, MERA, Tensor Networks, Mellin Transform, Renormalization Group, Functional Equation, Fixed Point, Numerical Analysis, R5+ Gravity.
Contemporary consciousness science confronts profound theoretical fragmentation. Quantum theories of consciousness (particularly Orchestrated Objective Reduction, (Orch-OR), quantum biology frameworks (coherence modulation in biological systems), and classical neuroscience approaches (Global Neuronal Workspace, Integrated Information Theory) have developed largely in isolation, often viewed as mutually exclusive competitors rather than potentially complementary descriptions of a multi-scale phenomenon. This fragmentation has impeded scientific progress and fostered unproductive debates. We argue that this apparent conflict stems from a failure to recognize that these theories operate at fundamentally different spatiotemporal scales and address qualitatively distinct aspects of the consciousness problem. Objectives: This paper presents the first comprehensive, empirically testable synthesis of these approaches within a unified five-layer hierarchical architecture. Our primary objectives are: (1) to demonstrate that quantum foundations (Orch-OR), quantum coherence modulation, and classical neural computation are complementary rather than competing; (2) to derive explicit mathematical transduction mechanisms linking adjacent scales; (3) to resolve the decoherence objection through rigorous quantum simulations calibrated against photosynthetic systems; and (4) to generate specific, falsifiable predictions that distinguish this unified framework from its component theories. Methods: We formalize transduction mechanisms between adjacent hierarchical scales using first-principles physics, statistical mechanics, and network theory. We derive quantitative coupling constants—most notably the “Perry Constant” (κ)—that govern quantum-to-classical information transfer. We conduct quantum Monte Carlo simulations of coherence dynamics calibrated against empirical measurements from photosynthetic light-harvesting complexes, demonstrating realistic protection mechanisms against thermal decoherence. We develop detailed experimental pro-tocols integrating nitrogen-vacancy (NV) center quantum sensing, multi-electrode array electrophysiology, and consciousness assessment methodologies.