Invariants for neural automata

Computational modeling of neurodynamical systems often deploys neural networks and symbolic dynamics. One particular way for combining these approaches within a framework called vector symbolic architectures leads to neural automata. Specifically, neural automata result from the assignment of symbol...

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Bibliographic Details
Published in:Cognitive neurodynamics 2023-05, Vol.18 (6), p.3291-3307
Main Authors: Uria-Albizuri, Jone, Carmantini, Giovanni Sirio, beim Graben, Peter, Rodrigues, Serafim
Format: Article
Language:English
Subjects:
Activation analysis
Artificial Intelligence
Automata theory
Biochemistry
Biomedical and Life Sciences
Biomedicine
Coding
Cognition & reasoning
Cognitive Psychology
Computer Science
Computer simulation
Correlation analysis
Dynamical systems
Dynamics
Electroencephalography
Fractals
Invariants
Language
Mathematics
Neural networks
Neurosciences
Research Article
Semantics
State vectors
Statistical analysis
Statistical correlation
Step functions
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Summary:Computational modeling of neurodynamical systems often deploys neural networks and symbolic dynamics. One particular way for combining these approaches within a framework called vector symbolic architectures leads to neural automata. Specifically, neural automata result from the assignment of symbols and symbol strings to numbers, known as Gödel encoding. Under this assignment, symbolic computation becomes represented by trajectories of state vectors in a real phase space, that allows for statistical correlation analyses with real-world measurements and experimental data. However, these assignments are usually completely arbitrary. Hence, it makes sense to address the problem which aspects of the dynamics observed under a Gödel representation is intrinsic to the dynamics and which are not. In this study, we develop a formally rigorous mathematical framework for the investigation of symmetries and invariants of neural automata under different encodings. As a central concept we define patterns of equality for such systems. We consider different macroscopic observables, such as the mean activation level of the neural network, and ask for their invariance properties. Our main result shows that only step functions that are defined over those patterns of equality are invariant under symbolic recodings, while the mean activation, e.g., is not. Our work could be of substantial importance for related regression studies of real-world measurements with neurosymbolic processors for avoiding confounding results that are dependant on a particular encoding and not intrinsic to the dynamics.
ISSN:1871-4080
1871-4099
DOI:10.1007/s11571-023-09977-5