The case against synaptic plasticity

Any attempt to research AI requires knowledge of both philosophy and mathematics in such great detail that one so easily forgets that it is ‘the little grey cells’ that came first. Philosophy (incl. formal logics, linguistics) and mathematics (incl. automata theory, computability) may represent the organised attempts by civilised society to reveal the secret inner life of these cells but they are just means to an end. When they stop being useful as powerful tools to uncover important natural truths, they should be replaced with better ones. The very existence of maverick genii (eg Copernicus, Newton, Turing) over the centuries refutes the notion that only large, powerful institutions like science and mathematics can find nature’s secret truths. That was the mistake that organised religion made, and is not one that contemporary science wishes to repeat. The mob may decide on matters of high street fashion, but it is not a deep thinker, even when that mob is a cloistered moneyed elite such as the ‘Vienna Circle’ or the MIT media lab. If one presents a theory of mind which is ‘insufficiently philosophical‘ or contains ‘too few‘ mathematical formulae, one’s publications struggle to achieve academic credibility. No one will say so out loud, or to one’s face, but everyone understands this to be the truth of the situation. Academia is not just big business, but it is a highly personal one. One person’s success is another person’s fall from favour. Moreover, these are not just Wikipedia entries, they are people you have met at international conferences, perhaps even shook hands with, then struggled to stay awake while they delivered the fruits of their labours to the assembled intelligentsia. Moreover, you were happy to do so, knowing that when your time comes, it is they who will patiently listen to you. When considered in this context, science and fashion don’t seem so different after all. When mini skirts were big, in the 1960’s, all fashion designers included them in their work, even if they privately thought them tasteless, or sexist. Inevitably, men liked minis just a bit more than women did. That was just how things worked.

So what has this got to do with neuroscience? Quite a lot, unfortunately. We humans, like the ‘higher’ animals we evolved from, consist of a core set of instincts which labor under the weight of a huge developmental superstructure, stuff we learn from infancy as individuals acting within a group context. Language use is the poster child in this regard. No baby needs to be taught to walk, they crawl until one day they get up on two legs and take their first unsteady steps. Incredibly, the same thing is true of speaking. No one teaches a baby to walk, and no one teaches a baby to talk. This reality then begs the question - what are the changes in neurons or their interconnections which are responsible for each individual‘s growth in both skills and knowledge over their lifetime. 

We know a lot about using pharmaceuticals to change certain behaviours and perceptions. These substances seem to mimic the role of the endogenous ‘neurotransmitters‘ that transmit signals across the synapses between neurons. Antagonists like nerve agents just block their function, then you die. Agonists (incl. reuptake inhibitors) like antidepressants lock into the same locations in the neuron cell membrane as neurotransmitters, pressing the same buttons but in slightly different ways, then you get better. Neuroscientists could be forgiven for believing that it is changes in the ability of the synapse to conduct signals which also encode an individual’s growth in knowledge over time. Software engineers who observed these apparent successes lost no time in inventing artificial neural networks (ANN’s) based on the same principles of synaptic variation. After overcoming a small glitch (the so-called XOR problem) in a type of ANN called perceptrons, the ANN industry surged forward in leaps and bounds, powered by the invention of ‘backpropagation’, the first practical learning algorithm for multilayer perceptrons. 

This was a critical feature which enabled the widespread use of ANNs, since it seemed to solve the issue of how to turn external (global) teaching signals into internal (local) changes in synaptic conductance. However, backprop had problems. Consider a pair of fully interconnected feedforward layers, each composed of 100  neurons. Between these layers there are 100 x 100 = 10,000 synapses. How do teaching signals (external errors produced by labelled data sets) get translated into so many tiny incremental variations. Also remember that a neural layer with 100 neurons is small beer, a mere toy in the context of brains which have tens of millions of neurons per cortical layer. The conclusion is inevitable- backpropagation may be a successful tool in industrial applications of AI, but it fails hopelessly when faced with the hypernumerical complexity of brains.

Unfortunately, belief in the synapse theory of behavioural plasticity is much larger than warranted by the scientific evidence. It has morphed from a popular theory into a fashion trend, just like the miniskirt, if you will. Just because it is possible to change neural function in one way, eg by modifying synaptic parameters, doesn't necessarily mean that nature does it like that. There is a considerable body of evidence pointing away from the synapse theory. As early as 1943, AI pioneers McCulloch & Pitts suggested that circuit loops should be used to encode state in neural networks.

Using Cybercircuits to implement neural plasticity

The term 'cybernetics' refers to a system of regulation which triggers corrective action whenever the actual value of any given biovariable differs from its desired value, or ‘setpoint‘ by a sufficiently large amount. The modulus (a.k.a. ‘absolute value’ or magnitude) of this difference is often shortened to  the greek letter 'delta'. While the mathematical details of the corrective action taken depends on the context, the basic meaning is always the same- cybernetics involves doing something to reduce the absolute size of the delta.

The neural circuits in the brain are cybernetic. Every somatic and cognitive variable has an instinctive 'setpoint' associated with it. This genetic parameter represents the idealised value of the biovariable; it is the value that it 'should' be maintained at. Most engineers associate the term ‘setpoint’ with thermostats, ie we use the term to describe the desired temperature (a process variable, one that varies constantly). Biosystems tend to use use setpoints for another class of roles - to maintain structural integrity. Setpoints are local parameters which regulate structural integrity.

If we wish to expand cybernetics to do feedforward engineering as well as feedback science, it must incorporate offsets, in addition to setpoints. Figure 1a depicts a generalised cybercircuit (a.k.a. servostat, cyberstat or unistat) in which a setpoint is complemented by an offset. It may be helpful to visualise a concrete example, such as a human elbow joint, whose flexure under external load ('curls') is controlled by the biceps muscle - see Figure 1b. 

Under zero or small load, there is little or no muscle stretch, so the input sensor neuron has little or no output. The sensor neuron's axon meets the motoneuron(sic) at the bushy dendrites which cover most of its (ie the motoneuron's) cell body. The dendrites help to minimize signal loss by maximizing contact area between pre-synaptic and post-synaptic neurons. Since the sensor neuron output at the moment is low and positive (ie excitatory), and the motoneuron's resting membrane potential is large, and negative, the motoneuron is insufficiently stimulated to trigger a signal transmission. Without a signal from the motoneuron, the muscle remains at its current length. If external load is added, eg a gym buddy puts some barbells into the subject’s hand/s, the elbow joint is extended, stretching the muscle (ie increasing its length). This will cause the stretch sensor neuron to fire, therefore bringing the motoneuron closer to its self-triggering threshold. Depending on the size and number of the other inputs to the motoneuron, this may cause the motoneuron to fire, thereby causing the muscle to contract.

In simpler models of triggered threshold neural networks, the output of each neurode is either ‘on’ (ie firing) or ‘off’ (quiescent), depending on the sign of the difference between threshold T and sum of inputs Sigma(p). In reality, the greater the delta, the higher the frequency of neuronal discharging. This mechanism works because of the variable length of the refractory period between firings. The greater the sum of inputs, the less the refractory period (the time it takes for the neuron to be recharged by the membrane’s anionic influx). The quotient of the refractory period and the firing period equals a kind of mark-space ratio, controlling axonal current in precisely the same manner as switch-mode dimmers in domestic lighting.

There is a simple mechanical equivalent (or 'analogue') to this situation, which consists of a jointed lever ( representing the forearm) whose angular range is limited by a spring (representing the biceps muscle). Offset is a bipolar variable- it can be negative, when it is called 'slack'/'dead-zone', or positive, when it is sometimes referred to as 'preload' or 'preset'.

Crucially, offset represents the solution to two requirements -
(i) how to use a top-down neural signal to command the arm to flex;
(ii) how to store behavioural adaptations (ie consolidate local learning states).

In the case of the biceps muscle, a top-down signal (eg from the brain's motor centers) added phasically at a spinal ganglion, is able to get the muscle to contract or relax (governing motion via varying the offset signal*).  Exactly the same signal delivered tonically serves as a non-synaptic mechanism for musculoskeletal adaptation (storing new learning as offset states). 

*McCulloch, W.  & Pitts, W. (1943) A logical calculus of the ideas immanent in nervous activity.  Bulletin of Mathematical Biophysics, Vol. 5, pp. 115-133.  The authors specifically describe 'circular paths' and persistent state via regeneration of neural inputs - "The nervous system contains many circular paths, whose activity so regenerates the excitation of any participant neuron that reference to time past becomes indefinite, although it still implies that afferent activity has realized one of a certain class of configurations over time. Precise specification of these implications by means of recursive functions, and determination of those that can be embodied in the activity of nervous nets, completes the theory."

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