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Edited by: Yoram Burak, Hebrew University, Israel

Reviewed by: Athena Akrami, Princeton University - Howard Hughes Medical Institute, USA; Daniel Martí, École Normale Supérieure, France

*Correspondence: Tim N. Palmer, Department of Physics, University of Oxford, Oxford, OX1 3PU, UK

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution and reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

How is the brain configured for creativity? What is the computational substrate for ‘eureka’ moments of insight? Here we argue that creative thinking arises ultimately from a synergy between low-energy stochastic and energy-intensive deterministic processing, and is a by-product of a nervous system whose signal-processing capability per unit of available energy has become highly energy optimised. We suggest that the stochastic component has its origin in thermal (ultimately quantum decoherent) noise affecting the activity of neurons. Without this component, deterministic computational models of the brain are incomplete.

Problems that are computationally complex can be routinely solved by the nervous system with remarkably little expenditure of energy. Consider for example the Travelling Salesman task. Computationally this is notoriously difficult to solve because the number of candidate “shortest routes” increases exponentially with the number of destinations and purely deterministic algorithms can take an unacceptably long time to reach solution. And yet bumblebees foraging on arrays of flowers optimise their flight distances and rearrange their flower visitation sequences dynamically as new sources of food are presented (Lihoreau et al.,

Our proposal for an energy-optimised hybrid stochastic/deterministic computational model for the operation of the brain is inspired by the development of a new type of energy-optimised computer which operates in both probabilistic and conventional bit-reproducible mode (Palem,

A particular example of a problem class which can benefit from such hybrid computation, with potential links to understanding the nature of human creativity, is that of finding the global minimum of some objective function. Purely deterministic heuristic algorithms risk converging to some local minimum. This risk is reduced in partially stochastic schemes (such as simulated annealing) which can jump randomly from one local basin to another. More generally, adding an element of stochasticity to an otherwise deterministic heuristic can help prevent the occurrence of problem instances where the time to solution becomes unacceptably long, thus improving the overall performance of the heuristic (Gomes et al.,

In the brain, information is transmitted in the temporal pattern of action potentials (spikes or nerve impulses). But the brain is susceptible to a variety of sources of noise which affect the reliability of the information contained in spike trains (White et al.,

The miniaturisation of the brain’s wiring permits a significantly larger number and density of signal-processing elements (i.e., neurons) than would otherwise be possible (Faisal et al.,

We are not the first to propose a constructive role for stochasticity in simulating the brain (see e.g., White et al.,

More recently the phenomenon of ‘Stochastic Resonance’ or SR has been cited as a mechanism by which noise in sensory systems enhances sensitivity (Wiesenfeld and Moss,

Could a model which combines stochasticity and determinism in some synergistic hybrid operation which is optimised for energy efficiency, be relevant to the human brain? Certainly as the brain is an energetically “expensive” organ (Laughlin et al.,

Continually switching between Mode 1 and 2 is reminiscent of the way a stochastic heuristic algorithm (such as discussed above) tackles the problem of finding the global minimum of an objective function: stochasticity allows some jumping between local “potential wells”, and minimises the chance that the heuristic does not “get stuck” near some local minimum. By analogy, in trying to find the solution to a problem which requires creative thinking (for example, proving that the square root of 2 is either rational or irrational) the human brain might start in Mode 1, randomly selecting a candidate line of enquiry (e.g., properties of the geometry of circles—representing a local region in some abstract space of mathematical concepts), and exploring the logical developments in Mode 2. Influenced by a first unsuccessful attempt to find the solution (c.f. failing to find the global minimum) a second candidate line of enquiry can again be randomly chosen in Mode 1 (e.g., properties of even numbers) and the required solution found through further analysis in Mode 2.

Consistent with this, it is a familiar experience that taking a break in concentration from some difficult problem, i.e., switching from Mode 2 to Mode 1, can provide unexpected new angles on a problem at hand, ultimately leading to its solution. The mathematical physicist Roger Penrose (Penrose,

We conclude with some comments about links to artificial intelligence. Firstly, from a theoretical point of view, our hybrid probabilistic/deterministic computing system provides a novel way to understand the implications of Gödel’s Theorem. Gödel’s theorem is essentially a statement about the incompleteness of algorithmic reasoning: no matter how complex a formal logical system might be, there are always logically sound propositions that cannot be proven by deductive reasoning using the rules of the system. By definition, Gödel’s Theorem would be meaningless to an artificial intelligence that operates by deterministic computational (and hence algorithmic) rules. That Gödel’s theorem is not meaningless to us humans is suggestive of the fact that we do not operate entirely by such computational rules. Penrose argues that because of Gödel’s theorem, the human brain cannot be emulated by a conventional digital computer, no matter how big (Penrose,

However, the Penrose argument is readily accounted for by our hybrid probabilistic/deterministic proposal for the operation of the brain, precisely because the ultimate source of neuronal noise at the molecular level is quantum decoherence. The term “decoherence” describes the random nature by which a quantum system reveals its properties when interacting with its environment. Here the word “random” encompasses the notion that, under repeated preparation and measurement, the fluctuations in the measured properties of a quantum system do not appear to be representable with any finite algorithm (Calude et al.,

From the perspective of the hybrid probabilistic/deterministic proposal, it is reasonable to suppose that the more random and more constant the source of noise, and the less energy needed to access it, the more effective it will be for complex problem solving. In computational science, stochastic search algorithms are often driven by integrating low-order chaotic systems over extended periods of time (Hoos and Stützle,

These remarks are relevant for attempts to emulate the brain on next-generation exascale computers. Notwithstanding the fact that such computers may require in excess of 50MW to operate (Kogge,

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.