Abstract
In this chapter we hypotesize that Information Semifields are the underlying calculi that brains operate on and we postulate that strong artificial intelligences should try to imitate them. Information semifields have recently been proposed to describe the calculations that pertain to the manipulation of Renyi entropies. These are semifields that emerge from the pseudo-calculus by the rational choice of generator functions that respect the classical postulates of information theory, and align with the Renyi entropy and divergence. To support our hypothesis we gather evidence in this respect from Neuroscience, Machine Learning, Cognitive Computation, Information Theory and Complex Systems theory. This evidence would also constrain other attempts at describing the workings of an intelligence embodied in a brain.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
Neuromorphic in a wide sense not necessarily hardware systems.
References
Hutson, M.: Core progress in AI has stalled in some fields. Science 368(6494), 927 (2020)
Sejnowsky, T.J.: The unreasonable effectiveness of deep learning in artificial intelligence. Proceedings of the National Academy of Sciences (2020)
Smolensky, P.: Information processing in dynamical systems: foundations of harmony theory. In: Parallel Distributed Processing, pp. 194–281. MIT Press, Cambridge (1986)
Hinton, G.E., Osindero, S., Teh, Y.-W.: A fast learning algorithm for deep belief nets. Neural Comput. 18(7), 1527–1554 (2006)
Rajendran, B., Sebastian, A., Schmuker, M., Srinivasa, N., Eleftheriou, E.: Low-power neuromorphic hardware for signal processing applications: a review of architectural and system-level design approaches. IEEE Signal Process. Mag. 36(6), 97–110 (2019)
Sevuktekin, N.C., Varshney, L.R., Hanumolu, P.K., Singer, A.C.: Signal processing foundations for time-based signal representations: neurobiological parallels to engineered systems designed for energy efficiency or hardware simplicity. IEEE Signal Process. Mag. 36(6), 38–50 (2019)
Li, G., Deng, L., Chua, Y., Li, P., Neftci, E.O., Li, H.: Editorial: spiking neural network learning, benchmarking, programming and executing. Front. Neurosci. 14, 276 (2020)
Russell, S.J., Norvig, P.: Artificial Intelligence - A Modern Approach (3. internat. ed.) (2010)
Varela, F.J., Thompson, E., Rosch, E.: The Embodied Mind. Cognitive Science and Human Experience, revised edn. MIT Press, Cambridge (2017)
Capone, F., Paolucci, M., Assenza, F., Brunelli, N., Ricci, L., Florio, L., Di Lazzaro, V.: Canonical cortical circuits: current evidence and theoretical implications. Neurosci. Neuroeconomics 1–8, (2016)
Markov, N.T., Vezoli, J., Chameau, P., Falchier, A., Quilodran, R., Huissoud, C., Lamy, C., Misery, P., Giroud, P., Ullman, S., Barone, P., Dehay, C., Knoblauch, K., Kennedy, H.: Anatomy of hierarchy: feedforward and feedback pathways in macaque visual cortex. J. Comp. Neurol. 522(1), 225–259 (2013)
Fuster, J.M.: Upper processing stages of the perception-action cycle. Trends Cogn. Sci. 8(4), 143–145 (2004)
Marcus, G.: Kluge: the haphazard evolution of the human mind. Houghton MIfflin Company, Boston (2008)
Werner, G.: Fractals in the nervous system: conceptual implications for theoretical neuroscience. Front Physiol. 1, 1–28 (2010)
Anderson, R.B.: The power law as an emergent property. Mem. Cogn. 29(7), 1061–1068 (2001)
Bastos, A.M., Vezoli, J., Bosman, C.A., Schoffelen, J.-M., Oostenveld, R., Dowdall, J.R., De Weerd, P., Kennedy, H., Fries, P.: Visual areas exert feedforward and feedback influences through distinct frequency channels. Neuron 85(2), 390–401 (2015)
Palva, S., Palva, J.M.: Roles of brain criticality and multiscale oscillations in temporal predictions for sensorimotor processing. Trends Neurosci. 41(10), 729–743 (2018)
Joglekar, M.R., Mejias, J.F., Yang, G.R., Wang, X.-J.: Inter-areal balanced amplification enhances signal propagation in a large-scale circuit model of the primate cortex. Neuron 98(1), 222–234 (2018)
Kinouchi, O., Copelli, M.: Optimal dynamical range of excitable networks at criticality. Nat. Phys. 2(5), 348–352 (2006)
Rao, R.P.N., Ballard, D.H.: Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. Nat. Neurosci. (1999)
Arnal, L.H., Giraud, A.-L.: Cortical oscillations and sensory predictions. Trends Cognit. Sci. 16(7), 390–398 (2012)
Izhikevich, E.M.: Dynamical Systems in Neuroscience. MIT Press, Cambridge (2007)
Dayan, P., Abbot, L.F.: Theoretical Neuroscience. Computational and Mathematical Modeling of Neural Systems. MIT Press, Cambridge (2005)
Razi, A., Friston, K.J.: The connected brain: causality, models, and intrinsic dynamics. IEEE Signal Proc. Mag. 33(3), 14–35 (2016)
Friston, K., Ao, P.: Free energy, value, and attractors. Comput. Math. Methods Med. 5, 1–27 (2012)
Bogacz, R.: A tutorial on the free-energy framework for modelling perception and learning. J. Math. Psychol. 76, 198–211 (2017)
Wiiliam, T.: Powers. Living Control Systems. Selected Papers, CSG (1989)
MacKay, D.J.C.: Information Theory. Inference and Learning Algorithms. Cambridge University Press, Cambridge (2003)
Friston, K., Stephan, K., Li, B., Daunizeau, J.: Generalised filtering. Math. Probl. Eng. 2010(3), 1–34 (2010)
MacKay, D.J.C.: Free energy minimisation algorithm for decoding and cryptanalysis. Electron. Lett. 31, 446–447 (1995)
Friston, K.: The free-energy principle: a unified brain theory? Nat. Rev. Neurosci. 11(2), 127–138 (2010)
Gu, S., Pasqualetti, F., Cieslak, M., Telesford, Q.K., Yu, A.B., Kahn, A.E., Medaglia, J.D., Vettel, J.M., Miller, M.B., Grafton, S.T., Bassett, D.S.: Controllability of structural brain networks. Nat. Commun. 6, 8414 (2015)
Schmidt, M., Bakker, R., Hilgetag, C.C., Diesmann, M., van Albada, S.J.: Multi-scale account of the network structure of macaque visual cortex. Brain Struct. Funct. 223(3), 1409–1435 (2018)
Ballard, D.H.: Brain Computation as Hierarchical Abstraction. MIT Press, Cambridge (2015)
Fox, K.: Barrel Cortex. Cambridge University Press, Cambridge (2008)
Sayood, K.: Information theory and cognition: a review. Entropy 20(9), 1–19 (2018)
Deco, G., Kringelbach, M.L.: Hierarchy of information processing in the brain: a novel ‘Intrinsic Ignition’ framework. Neuron 94(5), 961–968 (2017)
Valverde-Albacete, F.J., Peláez-Moreno, C.: The Rényi entropies operate in positive semifields. Entropy 21(8) (2019)
Gondran, M., Minoux, M.: Graphs, Dioids and Semirings. New Models and Algorithms. Operations Research Computer Science Interfaces series. Springer, Berlin (2008)
Renyi, A.: Probability Theory. Courier Dover Publications, Mineola (1970)
Pap, E.: g-calculus. Zbornik Radova Prirodno-Matematichkog Fakulteta. Serija za Matematiku. Review of Research. Faculty of Science. Mathematics Series 23(1), 145–156 (1993)
Grossman, M., Katz, R.: Non-Newtonian Calculus. Lee Press, Pigeon Cove (1972)
Mesiar, R., Pap, E.: Idempotent integral as limit of g-integrals. Fuzzy Sets Syst. 102(3), 385–392 (1999)
Palva, J.M., Palva, S.: Roles of multiscale brain activity fluctuations in shaping the variability and dynamics of psychophysical performance. Prog. Brain Res. 193, 335–350 (2011)
Siegel, M., Donner, T.H., Engel, A.K.: Spectral fingerprints of large-scale neuronal interactions. Nat. Rev. Neurosci 13(2), 121–134 (2012)
Zhigalov, A., Arnulfo, G., Nobili, L., Palva, S., Palva, J.M.: Modular co-organization of functional connectivity and scale-free dynamics in the human brain. Netw. Neurosci. 1(2), 143–165 (2017)
Valverde-Albacete, F.J., Peláez-Moreno, C.: The case for shifting the Renyi entropy. Entropy 21(1) (2019)
Butkovič, P.: Max-linear Systems. Theory and Algorithms. Monographs in Mathematics. Springer, Berlin (2010)
Kato, S., Kaplan, H.S., Schrödel, T., Skora, S., Lindsay, T.H., Yemini, E., Lockery, S., Zimmer, M.: Global brain dynamics embed the motor command sequence of caenorhabditis elegans. Cell 163(3), 656–669 (2015)
Kaplan, H.S., Thula, O.S., Khoss, N., Zimmer, M.: Nested neuronal dynamics orchestrate a behavioral hierarchy Across timescales. Neuron 105(3), 562–576.e9 (2020)
Gleeson, P., Lung, D., Grosu, R., Hasani, R., Larson, S.D.: c302: a multiscale framework for modelling the nervous system of Caenorhabditis elegans. Philos. Trans. R. Soc. Lond. Ser. B Biol. Sci. 373(1758), 20170379 (2018)
Liu, Q., Kidd, P.B., Dobosiewicz, M., Bargmann, C.I.: C. elegans AWA olfactory neurons fire calcium-mediated all-or-none action potentials. Cell 175(1), 57–70.e17 (2018)
Pradhan, S., Quilez, S., Homer, K., Hendricks, M.: Environmental programming of adult foraging behavior in C. elegans. Curr. Biol. 29(17), 2867–2879.e4 (2019)
Estévez-Albuja, I., Valverde-Albacete, F.J., Peláez-Moreno, C.: Replication of two computational models of locomotion of Caenorhabditis elegans in Brian 2. In: Neuromatch Conference (2020)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Valverde-Albacete, F.J., Peláez-Moreno, C. (2021). The Case for Quantifying Artificial General Intelligence with Entropy Semifields. In: Pap, E. (eds) Artificial Intelligence: Theory and Applications. Studies in Computational Intelligence, vol 973. Springer, Cham. https://doi.org/10.1007/978-3-030-72711-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-72711-6_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-72710-9
Online ISBN: 978-3-030-72711-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)