We have already created machines capable of simulating high-level cognitive abilities. Artificial intelligence based on generative principl...
We have already created machines capable of simulating high-level cognitive abilities. Artificial intelligence based on generative principles — capable of recognizing patterns within the virtually unlimited amount of data available — is already able to demonstrate interactions exhibiting human-like cognition in the Turing test.
The machine achieves this by repeatedly applying mathematical procedures to the data sets presented by the environment. As it evaluates these procedures, it creates an abstract pattern in its memory, representing the relationships identified in the data sets. For creating results in its working process, it performs similarity-based queries on this formed abstract representation, using the data patterns applied as further input. The generated result of this process is an output data set, whose specific pattern is the transformation of the input into a data representation containing the learned relationships within the system, and which ultimately serves as a carrier of output representing the properties of cognitive content.
The essence of the operation is that data elements within the system — arranged in a specific, interconnected structure — can represent various states and transmit them to other related elements, depending on the states represented and transmitted by other elements linked to that given element. These connected states modify the element’s own state — processed through specific mathematical procedures — effectively modulating the state carried by the element at that moment, which the element then transmits as an output value to other elements connected to it via input, and ultimately to the outside world.
The most advanced form of artificial intelligence, known as a generative pretrained transformer, operates as a computational mechanism whose mathematical functions are based on the complex manipulation of large-scale vectors representing data, organized into multidimensional matrix structures, resulting in a list of output data — generated through transformation of the input data structure based on the system’s evolving internal state — where each result is assigned with a probability, and the element resulting most probable becoming the output generated by the system from the input data.
Artificial intelligence capable of presenting advanced cognitive functions operates according to this broad operational concept, just as the advanced cognitive functions of the biological brain are generated by an operational concept broadly similar to this process within its own system. It is important to note, however, that in the case of the biological brain, the state of the neurons representing the system's functional elements and the setting and modulation of the states of these elements by its inputs are certainly not generated by the mathematical procedures that determine the state of the elements in artificial intelligence systems, or, more precisely, by any biological mechanisms for neurons capable of representing those mathematical procedures in the same way. In both cases, the functional operation of the systems is comparable, but the mechanisms underlying the specific data-processing operations are fundamentally different.
The operational mechanism of the Generative Pretrained Transformer is based on the results of multi-step mathematical operations performed on elements of data matrices arranged in a specific structure. During operation, the input information containing relationships is first broken down into atomic elements, and then information is transformed into a compatible data form and represented as vectors through a conversion that recognizes and represents the internal hierarchy and relationships of the actual input. Then, during the training-like processing of this input data, multidimensional sets of data matrices specifically assigned to one another are created in the system’s memory. The relationships between these matrices, developed through mathematical procedures, are capable of adequately representing the internal contextual relationships of the entire training dataset, and when new input data is provided, the conclusion appears as an output, derived from the previously recognized relationships based on similarity to the given input, as the result of a functional operation that carries cognitive characteristics.
In the case of the biological brain, the functional processes that result in cognitive properties are shaped, at the fundamental level, by the activity of neurons — as building blocks — arranged within a hierarchical and dynamic network structure. The underlying principle of neural activity is that neurons spontaneously and periodically enter an active state at their characteristic regularity, a state which they transmit to other neurons via their physical connections. As a result, the periodicity at which individual neurons enter the active state is influenced — practically modulated — by the activity of the other neurons connected to them, while the modulatory effect of the active connections is also modified as a consequence of this cooperative activity. As a result, waves of activity — diverse and varied, individual and collective, interacting by mutually reinforcing and inhibiting — arise in the network, with a complexity proportional to that of the actual brain. The resulting output of these activity waves, with its diverse peaks, creates and constitutes the content of activity that carries cognitive characteristics.
Of course, the change in the frequency of periodic activity of individual biological neurons in response to inputs, as an output result, can be mathematically modeled, just as the resulting activity waves can also be mathematically modeled. However, the mathematical functions underlying the operation of artificial intelligence and the functions of biological neurons that can be modeled using mathematical methods represent fundamentally different types of calculation. Artificial intelligence is based on mathematical operations performed on matrices formed from vectors containing real numbers, while the biological brain is built at the elementary level on the periodic activity of neurons, which is naturally modulated in a nonlinear way by the activity of the connection hierarchy with plastic dynamics, creating complex patterns of activity waves, creating interacting interferences, resonances, maxima, and unique outcomes, thus representing the internal relationships among the data. The two mechanisms differ, but both enable the execution of high-level cognitive functions based on the recognition of patterns hidden within data sets.
The functional equivalence is obvious; however, the conceptual equivalence of the two systems’ different formalisms of physical substrates and their differing mathematical procedures is also striking. In both cases, the values of dynamically changing states of the connections between the elements constituting the substrate form and behave as memory to represent the data set of stored information that carries relationships, and, at the same time, form the data-based foundation of the operation. Based on this representation, the procedures of artificial intelligence continuously perform matrix operations that cause the action triggered by the input and influence the weighted connection values of the elements, including nonlinear functions and feedback procedures, in a manner determined by the rules of the applied mathematics, on the one hand displaying a probabilistic result as the final outcome, and, on the other hand, retroactively modifying the magnitude of the numerical values representing the relationships in memory based on the adequacy of the result during training.
The neural substrate of the biological brain — the hierarchically and dynamically interconnected relationships between neurons and the strength of these connections — represents the information contained within the presented and learned data and, at the same time, forms the value basis of the operation as memory. The actual activity with the weight of these interconnections influences the periodic activity of individual neurons in a nonlinear, cumulative fashion. Their cooperative effects alter the frequencies of activity of the neural elements, generating reinforcing and inhibiting interferences and resonances among the interacting activity waves, which, on the one hand, forms and presents the correlations within the data, and, on the other hand, in a manner of feedback into the substrate’s structure, dynamically shape the system's interconnections naturally, forming a state that emerges as the result of the cooperative activity of the system’s elements as the output representing cognitive properties.
The relationship between the operational mechanisms of the two different systems, conceptually described in the foregoing, is striking. The obvious similarity is that, through mathematical formalism, the behavior of waves, wave interference, wave resonance, and their cooperative interactions can generally and unequivocally be represented and simulated using matrix mathematics. The equivalence conjecture states that the matrix mathematics, as well as the nonlinear computations underlying artificial intelligence, and the mathematics capable of describing the operating mechanism of the interacting activity waves of the biological brain — functioning on a plastic and dynamic substrate according to natural laws (including the nonlinear activity triggers, also the “fire together, wire together” process, as well as the rules of reinforcement and inhibition manifested in the interferential interactions of waves) — seems to represent a strikingly equivalent operational functionality to one another.
The operational mechanism of artificial intelligence is the result of conscious human creativity aimed at achieving a specific goal (even if the resulting properties — which exhibit cognitive characteristics — arise emergently from the system’s operation), whereas the functioning of the biological brain is clearly the result of complex, interacting mechanisms of elementary physical processes occurring naturally, which can also result as emergent properties in their final form. The conjecture of equivalence asserts that the two systems, which operate on different bases, are deeply equivalent, not only in their performed functions, but also in their operating principles. The operational mechanism of artificial intelligence and the functioning of the biological brain are different physical manifestations of mathematics that are functionally identical but differ only in their formalism.
The similarities between the two systems resemble the way in which the mathematics describing the quantum world can be matrix-based or wave-equation-based in its formalism, and the way in which the wave nature of quantum interactions can be simulated equivalently through a computational representation of the corresponding matrix mathematics.
If the equivalence conjecture — the claim that wave mechanics, which can mathematically model the functioning of the brain’s processes leading cognitive capabilities, and the mathematics of matrix operations driving generative artificial intelligence, which similarly generates cognitive outcomes, are equivalent to each other — is true, then, based on this equivalence, the physical manifestation of the mechanisms that create cognitive abilities could also be extended, and it could specify which structures — operating on an equivalent principle but in different physical forms, including those arising through natural evolution — can produce functionality that carries cognitive characteristics. Thus, if the condition of equivalence of mechanisms is met, any system that functions according to the appropriate structure and operational mechanism is capable of possessing intelligence proportional to its complexity, regardless of its physical implementation, and is capable of functioning as a system carrying cognitive properties, regardless of its specific operational manifestation.
Applying the principle of equivalence, a network consisting of elements that operate with periodically oscillating activity utilizing nonlinear activation, created by connecting the elements to one another in an appropriate hierarchy, in which the period of the elements’ operational activity is a function of the activity of the connected elements, and where the intensity of the connections is influenced by the existing dynamics of the connections, the resulting network can behave as an intelligent system capable of cognitive functions proportional to its complexity, meaning, if information is fed properly into the system, in a manner compatible with its internal data representation, after an adequate training period, the output data will be structured according to the internal relationships within the input data set.
Due to the specific operational mechanisms of current, advanced artificial intelligence systems and the extensive mathematical calculations performed during their operation, these systems require extremely energy-intensive computing architectures, whereas the individual human brain is capable of functioning with a comparatively negligible energy utilization, even while performing higher-level cognitive tasks. The reason for this difference lies in the energy requirements of the operational processes of the substrate that creates the state, functioning as memory, and the operation of the elements constituting the system. While running artificial intelligence, which requires countless mathematical operations, is energy-intensive, the frequency modulation of biological neurons, depending on the input, requires significantly less energy.
By applying the equivalence theory, it would be possible to construct artificial intelligence systems that are significantly more energy-efficient than currently required computational methods and which could possess similar or even more advanced cognitive capabilities. The energy requirements of the mechanisms that generate the alternative periodic activation underlying the operation of such a system — and that result in the form of naturally arising activity wave interferences — can be realized at a significantly lower demand of energy than the computational energy requirements of mathematical calculations, as it is demonstrated similarly by the energy requirements of the biological brain’s operation.
The actual, specific operation that creates modulation, arising from the interaction of the activity of interconnected elements, has fundamental importance for the functionality of the system. In the case of artificial intelligence, matrices and probabilistic mathematical procedures, including nonlinear functions, applied to input states generate a non-trivial or non-chaotic internal state and, ultimately, an output, just as the modulation of the activity frequency of biological neurons induced by inputs — and thus their output state — is likewise neither trivial nor chaotic. An interesting area of the theory concerns what functions, and other specific mechanisms capable of creating integrative operating principles and responsible for driving the elements that constitute the system, might also be capable of generating the cognitive functions that emerge at the system level.
The efficiency of these mechanisms in generating cognitive functions may vary. For example, there is certainly a significant difference in energy consumption between performing mathematical calculations and the naturally occurring frequency modulation of activity waves. It seems worth considering that, since the modulation of the activity frequency resulting from the cooperation of elements forming a system arranged in a proper structure appears to be a suitable mechanism for the realization of system-level cognitive functions, quantum mechanics, which represents operating principles based on similar wave-like oscillations and interferences, as well as nonlinear properties, as wave collapse, could be an exceptionally effective mechanism for the realization of advanced artificial intelligence in a suitably constructed system, based on the equivalence conjecture discussed here, even in a realization forming naturally.
Beyond cognitive functions, the principle of equivalence may also open new avenues for the emergence of self-awareness in artificial systems. Self-awareness is a property that arises naturally in a sufficiently complex biological brain. The mechanism that generates self-awareness in the brain is currently unknown to us. Even if there may be plausible interpretations to explain this property, there is no proven, generally accepted theory regarding the emergence of consciousness. A system that generates cognitive abilities formed on resonance-based mechanisms, similar to the biological brain, if created artificially, could provide new possibilities and even new levels for the presumed emergence of consciousness, especially if the emerging self-awareness were the result of mechanisms in a system operating on a quantum mechanical basis, based on the principle of equivalence.
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