A free energy principle for generic quantum systems

Fields, Chris; Friston, Karl; Glazebrook, James F.; Levin, Michael

doi:10.48550/arxiv.2112.15242

Cited by 5 publications

(10 citation statements)

References 159 publications

(269 reference statements)

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“…by exploration (novelty seeking that enlarges the "training set") and further learning. This definition of VFE for generic quantum systems allows a formulation of the FEP [20,21,22,23,24] for such systems that is developed in detail elsewhere [91].…”

Section: Qrfs As Memory Resourcesmentioning

confidence: 99%

Neurons as hierarchies of quantum reference frames

Fields,

Glazebrook,

Levin

2022

Preprint

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Conceptual and mathematical models of neurons have lagged behind empirical understanding for decades. Here we extend previous work in modeling biological systems with fully scale-independent quantum information-theoretic tools to develop a uniform, scalable representation of synapses, dendritic and axonal processes, neurons, and local networks of neurons. In this representation, hierarchies of quantum reference frames act as hierarchical active-inference systems. The resulting model enables specific predictions of correlations between synaptic activity, dendritic remodeling, and trophic reward. We summarize how the model may be generalized to nonneural cells and tissues in developmental and regenerative contexts.

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Section: Qrfs As Memory Resourcesmentioning

confidence: 99%

Neurons as hierarchies of quantum reference frames

Fields,

Glazebrook,

Levin

2022

Preprint

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“…When Boolean functions are extended to support probabilities as in Appendix 1, such systems become VAEs. They can implement arbitrary Bayesian networks as discussed in [14,26].…”

Section: Cccds As Specifications Of Computationsmentioning

confidence: 99%

“…We have demonstrated, moreover, a functional relationship between two heretofore disparate formalisms: that of networks (CCCDs) of Barwise-Seligman classifiers, and that of finite cobordisms. While cobordisms are familiar in physics, such classifier networks have primarily been applied in natural-language semantics (the original application of [12]), computational semantics and ontologies [98,99,100,101,102], and the context-dependent theory of inference [14,26] -for a range of other examples cast in the isomorphic category of Chu spaces, see e.g. Ref.…”

Section: Conclusion and Outlooksmentioning

confidence: 99%

“…The above outline of ideas is the basis of the context-dependent Bayesian hierarchical structure as it is seen Chan (see [14,26] for details).…”

Section: Conclusion and Outlooksmentioning

confidence: 99%

“…In basic terms, the local logic entails a (regular) theory and the semantic consistency of information flow is regulated by logic infomorphisms between classifiers [12, §9.1, §12.1], to which we refer the reader for complete details. These concepts have also been extensively reviewed in [13,14] (see also [3,4,26]).…”

Section: Appendices Appendixmentioning

confidence: 99%

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Sequential measurements, TQFTs, and TQNNs

Fields¹,

Glazebrook²,

Marcianò³

2022

Preprint

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We introduce novel methods for implementing generic quantum information within a scalefree architecture. For a given observable system, we show how observational outcomes are taken to be finite bit strings induced by measurement operators derived from a holographic screen bounding the system. In this framework, measurements of identified systems with respect to defined reference frames are represented by semantically-regulated information flows through distributed systems of finite sets of binary-valued Barwise-Seligman classifiers. Specifically, we construct a functor from the category of cone-cocone diagrams (CCCDs) over finite sets of classifiers, to the category of finite cobordisms of Hilbert spaces. We show that finite CCCDs provide a generic representation of finite quantum reference frames (QRFs). Hence the constructed functor shows how sequential finite measurements can induce TQFTs. The only requirement is that each measurement in a sequence, by itself, satisfies Bayesian coherence, hence that the probabilities it assigns satisfy the Kolmogorov axioms. We extend the analysis so develop topological quantum neural networks (TQNNs), which enable machine learning with functorial evolution of quantum neural 2-complexes (TQN2Cs) governed by TQFTs amplitudes, and resort to the Atiyah-Singer theorems in order to classify topological data processed by TQN2Cs. We then comment about the quiver representation of CCCDs and generalized spin-networks, a basis of the Hilbert spaces of both TQNNs and TQFTs. We finally review potential implementations of this framework in solid state physics and suggest applications to quantum simulation and biological information processing.7.2.4 Quiver representations, gauge-networks and noncommutative geometry 39

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Emergence of associative learning in a neuromorphic inference network

et al. 2022

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Objective. In the theoretical framework of predictive coding and active inference, the brain can be viewed as instantiating a rich generative model of the world that predicts incoming sensory data while continuously updating its parameters via minimization of prediction errors. While this theory has been successfully applied to cognitive processes – by modelling the activity of functional neural networks at a mesoscopic scale – the validity of the approach when modelling neurons as an ensemble of inferring agents, in a biologically plausible architecture, remained to be explored. Approach. We modelled a simplified cerebellar circuit with individual neurons acting as Bayesian agents to simulate the classical delayed eyeblink conditioning protocol. Neurons and synapses adjusted their activity to minimize their prediction error, which was used as the network cost function. This cerebellar network was then implemented in hardware by replicating digital neuronal elements via a low-power microcontroller. Main results. Persistent changes of synaptic strength – that mirrored neurophysiological observations – emerged via local (neurocentric) prediction error minimization, leading to the expression of associative learning. The same paradigm was effectively emulated in low-power hardware showing remarkably efficient performance compared to conventional neuromorphic architectures. Significance. These findings show that: i) an ensemble of free energy minimizing neurons – organized in a biological plausible architecture – can recapitulate functional self-organization observed in nature, such as associative plasticity, and ii) a neuromorphic network of inference units can learn unsupervised tasks without embedding predefined learning rules in the circuit, thus providing a potential avenue to a novel form of brain-inspired artificial intelligence.

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A free energy principle for generic quantum systems

Cited by 5 publications

References 159 publications

Neurons as hierarchies of quantum reference frames

Neurons as hierarchies of quantum reference frames

Sequential measurements, TQFTs, and TQNNs

Emergence of associative learning in a neuromorphic inference network

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