On the Spatiotemporal Behavior in Biology-Mimicking Computing Systems

Abstract

Both the growing demand to cope with "big data" (based on, or assisted by, artificial intelligence) and the interest in understanding the operation of our brain more completely, stimulated the efforts to build biology-mimicking computing systems from inexpensive conventional components and build different ("neuromorphic") computing systems. On one side, those systems require an unusually large number of processors, which introduces performance limitations and nonlinear scaling. On the other side, the neuronal operation drastically differs from the conventional workloads. The conduction time (transfer time) is ignored in both in conventional computing and "spatiotemporal" computational models of neural networks, although von Neumann warned: "In the human nervous system the conduction times along the lines (axons) can be longer than the synaptic delays, hence our procedure of neglecting them aside of the processing time would be unsound" [1], section 6.3. This difference alone makes imitating biological behavior in technical implementation hard. Besides, the recent issues in computing called the attention to that the temporal behavior is a general feature of computing systems, too. Some of their effects in both biological and technical systems were already noticed. Instead of introducing some "looks like" models, the correct handling of the transfer time is suggested here. Introducing the temporal logic, based on the Minkowski transform, gives quantitative insight into the operation of both kinds of computing systems, furthermore provides a natural explanation of decades-old empirical phenomena. Without considering their temporal behavior correctly, neither effective implementation nor a true imitation of biological neural systems are possible.

Towards Generalizing the Information Theory for Neural Communication

“…Given that the internal operation of the neuron membrane needs time (the neuron membrane is not isopotential [ 36 , 37 ]), the result of a neural computation depends not only on its inputs but also on the neuron’s internal state (a spike arriving during the relative refractory period finds a membrane potential above the resting level, leading to spike generation at an earlier time). One can easily interpret the effect using the temporal behavior [ 38 ], seen experimentally as nonlinear summing of synaptic inputs [ 34 ]: the changed time of charge arrival (due to changes in the presynaptic spiking time, conduction velocity, and synapse’s joining location). This time role suggests that biological computation results in changes in neurons’ temporal behavior, instead of spike signal amplitude, as expected from the parallel with technical systems.…”

On the Role of Speed in Technological and Biological Information Transfer for Computations

“…As the technology develops, it becomes evident that the classic paradigm cannot describe real-world implementations, neither technological (electronic) nor biological (neural) ones. Furthermore, in technology, it leads directly (Végh 2021) to the idea of unlimited computing capacity and workload-independent processing time. In electronics, mainly the issues experienced in connection with building so-called neuromorphic computers led the researchers to the idea that "More physics and materials are needed.…”

“…In some sense, hundred years after inventing the Minkowski-mathematics, it is still a scandal (Walter 2008) to consider that the theory of technological implementation of computing must also include some modern physics. The important consequences include (but are not limited to) inefficient processor chips (Hameed et al 2010), enormous power consumption (Waser 2012), the experience of "dark silicon" (Esmaeilzadeh et al 2012), the stalled supercomputer performance (Végh 2020;Simon 2014), the stalled Artificial Intelligence (AI) development (Hutson 2020;Végh 2021) and failed brain simulation (Abbott 2020). The at that time "disciplinary analysis of the reception of Minkowski's Cologne lecture reveals an overwhelmingly positive response on the part of mathematicians and a decidedly mixed reaction on the part of physicists" (Walter 2008) has turned to its exact opposite.…”

Revising the Classic Computing Paradigm and Its Technological Implementations

“…Although he explicitly mentioned that the propagation speed of electromagnetic waves limits the operating speed of the electronic components-until recently-that effect was not admitted in computing (except introducing clock domains and clock signal skew). In contrast, in biology, the "spatiotemporal" behavior [57] was recognized very early. In both technical and biology-related computing, the recent trend has been to describe computing systems theoretically and model their operations electronically using the time-unaware computing paradigm proposed by von Neumann, which is undoubtedly not valid for today's technologies.…”