Can a biological neural network solve an optimization problem?
In the previous article Metrics in machine learning of complex systems, algorithm and program code formula proposed for the signal-to-noise ratio in complex nonlinear systems with a tendency to self-organization. Experienced in processing electrocardiogram and earthquake data. A biological neural network is also a complex system.
Artificial neural networks emerged as an attempt to model the organization and functioning of biological neural networks—networks of nerve cells in a living organism. In existing artificial intelligence algorithms, the key link is solving the optimization problem, and the question remains: does a biological neural network solve the optimization problem? The optimization problem is finding the extrema of the objective function in the process of designing system parameters. A functional approach has been formed for the optimization problem, which involves considering an object as a complex of functions it performs, and not as a set of elements and their relationships.
The key condition in the formulation of the optimization problem is the presence of control factors or specified external rules. For example, choosing the optimal move according to the rules of a game of chess or in a teapot, water turns into steam and the controlling factor is temperature, where the formulation of optimization problems is applicable. When explosives detonate, liquid turns into gases in the absence of control factors. There are no external control factors in avalanche-like processes.
The absence of control factors and the scale invariance of self-organized criticality (SOC) processes are not intuitive and familiar. The obvious reaction of some readers will be “I don’t understand anything,” although we are talking about the activity of our brain.
The SOC approach was proposed to describe brain activity, and the first power-law distributions of neural avalanches were discovered: M. Usher, M. Stemmler, and Z. Olami, Phys. Rev. Lett. 74, 326 (1995).
The most powerful neural network has been experimentally discovered in infants (Mostafa Jannesari, Alireza Saeedi, Marzieh Zare, Silvia Ortiz-Mantilla. (2020) Stability of neuronal avalanches and long range temporal correlations during the first year of life in human infants. Brain Structure and Function 225:1169–1183), facilitating the adaptation of infants in an unstable external environment. Infant intelligence or herd intelligence refers to the task of numerical modeling of intelligence in the traditional experiment-model approach of physics, in the absence of external control factors. Characteristic is the manifestation of herd intelligence in interspecific and intraspecific conflicts, in an extremely unstable external environment and in the absence of any externally established rules, in contrast to the existing concept of artificial intelligence with an optimization algorithm.
Important experiment: When brain function is disrupted during epileptic seizures, a biological neural network loses its nonlinear avalanche characteristics and becomes Gaussian (Meisel, C., Storch, A., Hallmeyer-Elgner, S., Bullmore, E. & Gross, T. (2012) Failure of adaptive self-organized criticality during epileptic seizure attacks. PLOS Computational Biology 81–8.). When the characteristics of an avalanche are lost, data processing approaches existing Gaussian artificial intelligence algorithms with the formulation of an optimization problem. In existing artificial intelligence algorithms, an increase in control factors and established rules will inevitably lead to “epilepsy attacks” in a complex system.
When processing ECG data, I came across an interesting observation: each heartbeat is unique and will not be repeated either in the ECG or in life, most likely. Just as no two snowflakes are identical, but thanks to the uniqueness of snowflakes, scale-invariant snow avalanches arise.
The mathematics of existing artificial intelligence algorithms in the formulation of the optimization problem does not take into account avalanche-like processes.
Due to the absence of control parameters in a complex system with a tendency to self-organization, the question arises about the implementation of the principle of causality in the vicinity of criticality. The principle of causality is one of the most general physical principles that sets acceptable limits for the influence of events on each other. An empirically established principle, the validity of which is irrefutable today, but there is no evidence of its universality. In this case, the existence of a functional approach itself (a set of some mathematical functions) is implicitly assumed, capable of at least in principle describing the influence of events on each other.
Thus, the complex of intuitively incomprehensible aspects of self-organized criticality that describe brain activity includes:
· Resetting control factors;
· Scale invariance;
· Violation of the principle of causality.
The inclusion of the “Research in IT” hub justifies consideration in publications:
1. The original formula for the signal to noise ratio (SNR) in complex systems;
2. Limitations of the artificial intelligence algorithm in the formulation of the optimization problem for a complex system, a biological neural network.
At the economic forum in Davos, IT was given the ambitious task of replacing parliamentarians with artificial intelligence. But then the question is the choice of AI concept: individual optimization according to given rules in a stable external environment or herd self-organization in a world without rules and without the choice of personal optimization.
