... current analytic approaches in neuroscience may fall short of producing meaningful understanding of neural systems ...
[Jonas and Kording]
When trying to understand a complex system about which nothing is known it is best to begin with general principles that are known to be true, while at the same time excluding anything that is ‘intuitive’. Neural systems are practical systems and therefore these principles need to be useful in building practical systems. Moreover, complex natural systems are known to have evolved from much simpler systems and therefore elements of a general theory has to fit within the specific evolutionary history of natural systems.
All natural neural systems can be described as systems which take input from a set of sensors and which produce output that drives a set of motors. Whatever the inner complexity of the system, the complexity of its function is constrained purely to its input and its output. Both input and output are strictly numerical; a value between a minimum and a maximum, representing the strength of sensor input or a motor output. It follows from this simple observation that the function of any neural system must be inherently numerical; beginning with its primary role, which is to transmit numerical values between sensors and motors. The role of any natural neural system is to modulate a motor function by specific sensor input. But yet this most basic function is rarely mentioned in the literature on the neuron. This is in spite of the neural code that is used to transmit the numerical values being an all-or-none unary code; a code which is ideally suited to repetition. The simplest of all neural systems is one in which the numerical values produced by a sensor neuron are simply repeated until they reach a motor neuron. This transmission of a numerical value may be defined as a signal . Repeating a signal is fundamental to all natural neural system, being used to transmit sensor and motor values to distant sensor and motor neurons. Furthermore, there exist a wide variety of very simple organisms whose nervous system consists of little more than sensor values being sent to drive the motor function, and indeed neural systems that mimick the activity of very simple organisms can be designed using just repetition.
Traditional approaches to neural coding characterize the encoding of known stimuli in average neural responses. Organisms face nearly the opposite task-extracting information about an unknown time-dependent stimulus from short segments of a spike train.
[Bialek et al]
Incorrect thinking is the primary hindrance in developing a useful understanding of neural systems. The principle that neural activity is strictly numerical is well established and well accepted. Nevertheless, many researchers cannot accept this well established principle at face value and feel it necessary to introduce axioms that go on to pollute further deduction. Neural sensors do not “encode ... stimuli” and neither do neural systems extract information about an “unknown time-dependent stimulus from short segments of a spike train”. This is simply wishful thinking rather than strictly relying on facts that can be shown to be true. We perceive things in the external environment and give it the label stimulus to give the impression of rigourous scientific thinking. In fact nothing is gained by doing this. Perception and sensor input have no necessary relation. Perception is an internal state of the neural system, most likely several levels of abstraction away from the underlying hardware. Nevertheless, we are naturally predisposed to feeling that the perceptual world is the external physical world rather than an internal abstract representation of it. This natural bias is what leads researchers to assume that the objects of perception somehow have an independent existance in the external physical world. This implicit assumption leads to an entire chain of mistaken reasoning about how the objects of the physical world somehow imprint themselves onto the sensors or the information flow that they produce.
The fact that natural neural systems are necessarily numerical systems leads immediately to the first important step in reasoning that natural neural systems are either systems of calculation or systems of computation. By the Church-Turing thesis, computation is universal (with calculation being a simplifed form of computation) and therefore the function of an unknown numerical system can always be expressed in terms of a numerical systems that are known.
The simplest of natural neural systems merely modify the sensor-motor flow of information. They are in effect feed-forward-systems.
The same inductitive methods used to sketch out the details about neural function can be used to determine how the neural system as a whole must function.
Having established with certainty that natural neural systems are purely numerical systems and are therefore equivalent to any system capable of general computation (referred to as Turing-complete) there are two general approaches that can be made to understand how these systems function. The first is a bottom-up investigation of how the underlying hardware supports the fundamentals of computation, and the second is an attempt to discover general principles from known facts. The former requires a detailed investigation of the atomic units of function of natural neural systems; which is the neuron, and this is explored in some detail in the section on this subject. Making this distinction is important because many researchers confuse the high-level functionality of neural systems with the underlying abilities of neurons. Neural systems often seem to be capable of functionality that appears intractable to the systems of computation which we are accustomed to, and there is a temptation therefore to ascribe this ability to neural ability. It is often claimed that it is ‘neurons’ that
It is sometimes claimed that natural neural systems have the ability to recognize ‘things’ and at the same time it is suggested that ‘artificial’ neural networks are able to usefully replicate this ability. This is amost entirely a product of fallacious thinking. Natural neural systems do indeed have the ability to recognize specific objects in their environment, but this ability is as a part of the ability to see things. One cannot have the former without first having the latter. This is demonstrated by a study of the visual system in human subjects who were are able to see but who have lost (in part) the ability to recognize. The ability to recognize without the ability to see is simply a misunderstanding how visual systems work. This is demonstrated by the fact that the performance of those systems which claim to perform recognition invariably fall to zero when they are tested outside of their ‘training’ data set. Recognition may appear promising, but a performance of zero is not often useful. Even if an oracle could somehow be constructed which had the ability to ‘recognize’ common everyday objects such as cats and grandmothers, it would apart from its novelty not be especially useful. It is not useful because it does not in any meaningful way build a representation of a cat or grandmother, or other real-world objects. Real-world objects are often recursively defined (consisting of sub-components such as hair, eyes, faces and so forth) and a simple act of recognition is it itself not very useful. Applied to a more simple environment, an oracle that, for example, ‘recognizes’ triangles in a two-dimensional perceptual world that consists of just the simplest possible geometrical object would be of little use because what a perceptual system needs to know would be the parameters of specific triangle (such as the location of its vertices), rather than simply recognition that something is a triangle (which in a world of only triangles would be trivial). Even if we were to imagine an oracle capable of both recognizing triangles and providing the essential information about them, the parameters alone of the triangles ‘recognized’ would not be enough. This is, among other things, because a triangle is a representation that can be defined recursively, as illustrated by Figs 1-3. A simple minded algorithm that divides raw bit-map images up into ‘regions of interest’, and then downsamples that region to a handful of pixels, simply demonstrates a misguided approach. The complex recursive structure of even simple objects can never be recognized, but must be understood and represented before it can be seen. Representatation necessarily preceedes recognition; and specifically with systems that represent things by things within things. These types of systems can achieve great complexity from an underlying simplcity. Indeed, it may be that recognition is simply a part of building complex representations from simple elements.
While researchers have focused a great deal of effort on visual processing, it is unclear how recognition would work for even the most simple of geometries. What is unclear are the underlying principles of how this system would work. The primary hindrance in understanding visual perception is the complexity inherent to vision. On the other hand, the perception of language is much simpler and much better understood. The processing of language has for some time now been understood as a product of a generative grammar. While this linguistic theory has not yet been universally recognized, it is widely accepted and is most certainly true. This establishes an important known fact about the function of natural neural systems. The underlying principle of a generative grammar is predicate logic and induction. A generative grammar is inherently a system of induction and therefore it follows that natural neural systems are very likely to employ induction for language processing. If induction can be shown to be necessary for processing natural language, it is likely that induction may well be more broadly used. It is possible, therefore, that induction may be one of the fundamental organzational principles of complex natural neural systems. Indeed, an informal indicator of this is that games that rely on logic and induction (such as crosswords or sudoku) are very popular past-times for human leisure activity.
The underlying ‘geometric’ elements of language are the phonemes, which are represented formally by the letters of a phonetic language. Letters form words, which is an act of ‘recognition’ so trivial that it often not even remarked upon. While induction is not necessary for this simple step, it is nevertheless important. An alphabet of basic symbols is used to form more complex objects – words. Words then go on to form sentences, and the set of rules for producing valid sentences is the generative grammar. The defining feature of this type of system is that it works effectively with sparse and incomplete information. The process of induction is best illustrated by a logic puzzles such as crossword or sudoku, where induction will find a solution if there is logical necessity. What language demonstrates quite clearly is that statistical methods are of little use in recognizing words and sentences. The application of a statistical pattern recognizer such as a deep learning neural network to solving crosswords or sudoku demonstrates not only that this approach will fail to find solutions but that it is almost self-evident that the approach is unsound for this type of application. Sudoku probably demonstrates this most clearly in that solutions can only be found step-by-step by working through the dependencies. When the puzzle difficulty is at its lowest then a statistical approach might work, but at its most difficult the puzzle is mostly empty space and can be solved only by resolving possible dependencies and critically by making and testing hypotheses. Sudoku grids can be solved with as few as 17 ‘clues’, which means the grid is about 80% empty. Testing hypotheses is a speculative step, where an empty space is simply given an arbitrary value and the whole game space is tested to see if that value leads to contradiction. If a contradiction cannot be found then the hypothetical value is a part of the potential solution space. The power of induction lies in that a hypothetical ‘fact’ can be introduced and the same system can then be used as if the hypothetical fact were a known fact. If a purely hypothetical fact leads to necessity then that fact can be considered just real as known facts.
The difference between a recognition system and an induction system is a philosophical difference that is little remarked on in the literature. A recognition system implicitly assumes that things exist in the external world and the role of a perception system is simply to detect them. It is assumed that the properties of the object in the external world impresses itself onto the perceptual system. There are indeed a wide variety of natural organisms whose neural systems take that simplistic approach. This sometimes lead to an unwieldly proliferation of sensors, each with a specific purpose. This is analagous to the ubiquitous automobile proximity sensor which can detect nearby objects and warn the driver of an imminent collision. While these systems can be effective the limitations are demonstrated by the evolutionary history of natural organisms, where seeing has proven to be more effecting than detecting. The big shift between a system which sees and a system which detects is that the assumption that things have an independent existence in the external world is removed. Sensors are no longer independent feature detectors, but are instead integrated into a fact driven information system. The sensors provide the initial facts and the system hypothesises and proves what can be shown to be true from those initial facts. This is not explicitly a system of representation or modelling, but a fact processing system which takes the initial facts provided by the sensors and transforms these facts by a set of rules. Representation and models emerge from this system of rules, but do not necessarily need to be defined explicitly. With this type of system what is and what might be is strictly a product of this information processing system and not necessarily related to what exists in the external physical world. For a natural organism, hundreds of millions of years of evolution have of course led to systems which are functionally consistent with the external environment. Nevertheless, it is important to draw the distinction between how the system sees things and how things really are.
This type of system does not require an elaborate set of sensors, and neither does it require particularly sophisticated sensors because it is able to work with very sparse information. It does, however, require a sophisticated cognitive structure which is capable of performing the complex processing necessary. It is in this cognitive structure in which the ability to perceive lies, in the same way as the ability to process language resides in the generative grammar. Language indicates that while the individual rules of the grammar can be learned, the structure of the grammar itself is fixed.
A game of sodoku can be defined very compactly by just a handful of rules. Natural language (in simplified form) can be defined by a few pages of rules. Vision, however, does not appear to lend itself readily to the same type of system. The success of digital imaging has led to a paradigm of image processing rather than perception. This is because the information in the digital image is so precise and regular that the external world appears to be imprinted directly into the information contained in the image. This is mistaken thinking. A digital image merely contains the information needed to present the stimuli of perception. It is our perceptual system which sees and a photograph simply reproduces what we need to see, rather than what we do see or how we see. In the simplest sense, the ability to produce light to stimulate our visual sensors in a way that appears to reproduce what we see does not inform us about how our perceptual system works. Accordingly, when we examine the sensor array of a digital camera we find that it is a highly regular array of light sensors, arranged onto a two-dimensional surface. In principle, it is no different than a pin-hole camera where the light projects directly onto a two-dimensional surface and an image of the external environment may be seen from the light reflected. Digital imaging consists of little more than placing a sensor array onto the two-dimensional surface and measuring the amount of light at each position. The sensor array is then replaced with an array of lights and the image can be reproduced, mimicking the image produced by the light passing through the pinhole. A regular array over the entire surface of the image is essential for reproducing images, but when we investigate the visual sensor array of the human visual system we find that it is arranged very differently than the sensor array of a digital camera. Both systems use very similar sensors to measure light levels at a specific position on the sensor array, but the digital sensor array is designed to provide as much information as possible. Even a single sensor failure would lead to a defective image. The sensor system of the human visual system on the other produces information that is as sparse as possible. Each sensor produces a measurement, but they are organized into opposing pairs, and a value is produced only when there is a difference. Not only is this method inherently sparse, but it also results in measurements that have only local validity. Moreover, the visual sensors are not arranged systematically but rather randomly, with some areas being having more sensors and other areas having fewer sensor. In addition, not all opponent pairs have the same resolution; some consist of single sensor pairs but others cover more broad regions and consist of groups of sensors. Individual sensors may be part of a number of different groupings. Together these produce a sparse set of luminance difference measurements that is very different from highly regular information rich images produced by digital imaging technology. This way of organizing information is much more suitable for inductive processes.
An object composed of illusory contours such as a Kanizsa triangle cannot be recognized by an oracle because it exists only in the mind of perceiver and an oracle has no mind to perceive with.
The study of dreams indicates that while visual perception is relatively invariant and fixed function (as indicated by REM sleep) most functions must be separate from the underlying hardware. The episodic memory of dreams is actively erased once a period of REM sleep has completed and this indicates the speed by which memory can be formed and then subsequently erased. The study of subjects suffering from multiple personality (or the more common phenomenon of alcohol-linked “black-outs”) indicates that memory, skills and individual preferences are not fixed but can be arbitrarily installed in the same way that an individual program can be read from the storage system into active memory and then run.