In this work, the authors develop signaling models based on ideas from homology and discuss how to design a model of signal space which decomposes the incoming signals into classes of progressively higher levels of associative meaning. The tools needed are illustrated with a simple approach using standard linear algebra processing but this is just a simple point of departure into a more complex and potentially more useful signal processing toolbox involving computational homology. These ideas then lead to models of grammar for signals in terms of cascaded barcode signal representations.
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We discuss how to model the signals that come into a complex system which must then be parsed into an appropriate meaning so that the output of the system can be targeted appropriately. There are a lot of ideas about this in the world of complex biological systems and it is difficult to understand the process by which higher level meaning is extracted from raw signals. There are clearly specialized neural architectures in all biological organisms that have evolved to do this. By studying them, it is possible to gain valuable insights into how to design artificial systems that can perform associative learning better. Progress in a complicated problem like this often comes from looking at the problem in the proper abstract way. So that is what the focus is here: a fairly abstract vision of how to decompose a signal into interesting pieces is introduced and then over time, these ideas are tied into a framework for the design of engineering systems that are perhaps more capable at understanding how to handle a complex input and parse its meaning.
The problem of signal fusion is well known. A good example is how is speech understood? Raw auditory signals that a baby hears are not randomly organized. Instead, what the baby hears are short sounds separated at perhaps 10 millisecond intervals. The cortex in vertebrates is initially the same whether it is eventually going to become auditory, visual, motor or other. It is exposure to environmental signals that shapes how a particular cortical area processes information.
Hence, at first, the baby is exposed to patterns of sound separated by short amounts of relative silence. This exposure, in a sense, primes the cortical architecture responsible for processing auditory information to pay attention to this pattern of on and off. Effectively, the cortical processing tunes the time constants of the cortical neural architecture.
This is a network of computational nodes (here they are biological neurons) combined into a graph using edges which themselves perform various computations. The time constants then refer to the way in which the edges and nodes interact to focus on the signal. The specialized architecture of the cortex is organized as a series of stacked cans which are laid one on top of the other in a vertical chain. The tuning we have spoken of amounts to aligning the bottom most can in this chain to optimally notice the primary on and off sound patterns. The results of this computation are passed upward to the next can in the chain whose architecture is designed to notice the time constants associated with groupings of the first level of on and off patterns. If the first on patterns are called phonemes, the next level of processing focuses on groups of phonemes which might be called word primitives. It is posited that as the processing moves upward through the chain of cans, higher and higher levels of meaning in the signal are extracted. Of course, the cortex really consists of large sheets of chains of cans organized much like the springs in a mattress and there is also a lot of crosstalk between the chains. We discuss this a bit more in Section 6 and actually show some of neural circuits involved, but for now just retain the idea that the signals that come into a complex system, need to be analyzed and higher levels of associated meaning must be found so that the system creates an appropriate output or response to the environmental input received.
For example, suppose you embed approximately 106 sensors into the fuselage of an airplane all of which provide information on a millisecond level to control programs. How do you parse that vast array of information to make an intelligent decision about what the data is telling you? Statistical techniques are tricky as many times the important data is a rare event which is lost in averaging. The amount of computation to process the data is intense and most of the data being processed is not relevant to the operational state of the aircraft. There is a great need to extract higher level meaning from the complex signal the sensors are generating.