The neurostat is proposed as a cybernetic building block for brains and minds in response to the failure of the synapse theory to provide a compelling account of brain plasticity (ie neural adaptation). It is a deceptively simple canonical neural circuit that represents a novel approach to governance based on the interplay between two cybernetic variables, setpoint (representing structure, the 'what' stream, and local integrity) and offset (representing process, the 'where' stream, and global governance).
If the sum total of excitatory and inhibitory inputs to any given neuron exceeds its membrane threshold, it fires, ie a highly localised region of reversed membrane voltage travels rapidly down the axon from hillock to button*. This is the simplest form of neural action, which is exemplified by the biceps muscle/elbow joint circuit depicted in Figure 1 and is mathematically described in Equation(1) below-
s.t. Σ(p[i]) > T[j] .............Eq(1)
The inputs p[i] to the neurostat don't always come from external sensors. In fact, most neuronal inputs come from other 'internal' neurons. In the cortex, these interconnecting bundles of axons form the 'white matter', which are located inside the 'grey matter' (the neurostats' cell bodies). Figure 2.1 depicts some of these neurons. There are two shared or 'ganged' offset lines. The red one (conscious) carries phasic command signals. The blue one (unconscious) carries tonic learning signals, which maintain memory state.
All the neurons in this group can be brought closer to threshold simultaneously (ie synchronously) by means of the ganged inputs. The most important part of offset inputs is that they cause the neuron/s to fire 'sooner' (ie at a lower summed total value of the inputs) and with greater intensity than would otherwise be the case. This is precisely the way that (so-called 'top-down') command signals work, like a kind of 'accelerator pedal', or 'amplifier gain control' if you will. Neurons with top-down offset command lines can even be made to fire without any external sensory input at all.
If the range of individual neural thresholds T[j] follows some distribution R[j] (eg the familiar bell-shaped 'normal') then that distribution will be preserved in the pattern of outputs, because all that is changing is applying the same offset value Θ (theta) to each one.
s.t. Σ(p[i]) + Θ > R[j] .............Eq(2)
Figure 2.1
There is no direct participation of synaptic conductances a[i] in this model. This is deliberate, since the aim of this analysis is to demonstrate that changing membrane threshold values is a much more viable method of controlling neuronal gating than changing synaptic conductance. While conductances affect the shape of the distribution R[j], acting as a multiplying factor for each dendritic input, linking them in a reproducible manner to external command or learning signals is impractical, overly complex and problematic, violating Occam's Razor.
The actions of the ascending and descending reticular activation system (ARAS & DRAS) in vertebrates can be mimicked by varying the signal levels in a reticulum of shared input links. Increasing the reticulum signal value (++Θ) increases the chance that sensory input patterns present in the environment will cause many neurons in the layer to fire. Conversely, reducing the shared signal (--Θ) will reduce the collective response of the neural layer to external stimuli. This model suggests there may be a simple, single mechanism which drives the fundamental neural changes in our brains during periods of waking or sleeping.
s.t. Sigma(a[i]p[i]) > R[j] - Θ.............Eq(3.1)
then averaged A[j] for each neurode, as overall dividing factor
s.t. Sigma(p[i]) > ( R[j] - Θ )/A[j] ...........Eq(3.2)
*the normal membrane polarity is when the outside is positive and the inside negative. Molecules which span the membrane act like trapdoors, snapping open in response to a specific trigger. Na+ ions rush in, and cause temporary polarity reversal. Almost instantly, Mg+ ions respond by rushing out, restoring the usual negative internal polarity. Later, other spanning molecules pump the sodium ions out again, while also letting magnesium ions back in due to ion concentration differential (osmotic pressure) between inside and outside.
Figure 2 depicts a generic memory matrix built from layers, each one a (one or two dimensional) sheet of neurostats. Every neurostat in the (n+1)th layer receives inputs from each and every one of the previous (ie nth) layer outputs. That is, the net layers are 'completely connected'. The inputs at the zeroth (bottom) layer comprehensively sample the total output from all of the available sensory input devices. Now when the organism whose memory is formed in this manner is switched on, a wave of abstract activation will immediately fill the matrix, starting from the most concrete inputs at the zeroth layer, and moving upward through the layers, an extra set of abstraction features (ie descriptive categories) being added each new layer. At lower layers, the features detected by each category will be familiar, such as roundness or whiteness, but at higher levels specific object categories (ie 'types') will appear like 'eggness' (= ovality + whiteness) or 'tableness' (=flattopness + fourlegness).
Analyses very similar to the one in the paragraph above appear in most if not all neural network texts. Most of them arrive at the same endpoint- the 'grandmother cell'- a single neuron so utterly specialised from the many layers of abstraction processes below it, that it will only fire when Grandma appears. Of course, there will be a cell for Grandad too, &c.
In a network constructed from layers of neurostats, something different happens. Instead of producing extreme specialisation from the repeated layers of abstractness, the neurostat produces the opposite effect, extreme generalisation. In other words, at some middle layer, all the activation signals present in a given situation (ie informational environment /context) will merge and form a peak of maximum activity. This zenith will not move, even when the organism moves around and perceives different parts of the space in which it has been placed. The reason for this is that the network responds only to the combinations of percept categories in each situation. For example, two classrooms may contain completely different groups of students, with different stuff written on the blackboard, but all classrooms contain many students and some blackboards and one teacher. If the organism is then placed in a more complex environment, we expect the same spectrum of categories with a single peak, but at a higher layer with more categories available to define the situation.
The network's ability to form higher-order categories is an emergent property, not a deliberate design feature, since it is just a network made from layers of identical neurostats. If we reflect on our use of words, we realise that words (eg nouns) do not have fixed meanings. Instead, all words are category labels, ie each one defines a set of exemplars, or 'true' members. When we combine words in a sentence, we must somehow combine these sets mentally, like Venn Diagrams perhaps, in order to find the exemplar which satisfies all criteria. But this exemplar is a member of all the semantic sets defined by the words in the sentence. The situation itself seems to be a member of an imaginary supercategory defined by the sentence as a whole.
This network seems to have a single focus point, no matter what kind of perceptual situation it is placed in. This metaspectral peak seems to represent a contradiction in terms, a maximally generic exemplar! Perhaps this is what happens in our brains when we are conscious of entire situations, as opposed to paying attention to specific things.
In the first network ‘A’, there was nothing preventing simultaneous membership of broad percept categories. An entity at a particular abstraction level could be (say) white and round and leathery to touch and...so forth. What if the same net of neurostat layers is connected to a different set of input devices? This time, instead of feeding in disparate groups of inputs, the devices contain detectors which 'span' a space because they are physically adjacent-eg the measurement of robot joint angles, divided up into adjacent buckets which each cover 5 degrees of rotation. Pixel density is another case- an object can not be both black and white. In these cases, the categories that the zeroth layer detects (ie the dimensions of the sensory space covered by the device) are mutually exclusive, ie independent. For example, when the limb angle is in the second 'bucket', ie between 5 and 10 degrees, it cannot be in any other 5-degree-wide bucket.
What will happen at the higher abstraction layers in network ‘B’ which is fed by mutually exclusive percept categories? In this case, we do find grandmother cells, or their kinematic equivalent. If this network ‘B’ is fed by devices made from arrays of mutually exclusive space and motion detectors, the spectral peak acts just like our focus of attention with a sharp focus and constantly shifting around.
This second ‘B’ kind of net also produces a spectral super-category at its zenith, but this is a peak that moves around. If we combine the first kind of net, type ‘A’, ie one that categorizes entire situations, with the second kind, type ‘B’, ie one that reacts to regions of maximum informational change, we obtain a hybrid (‘B’ over ‘A’ = ‘C’ ) model in which both tonic (incumbent/occupied) and phasic (intensional/observational) features of conscious experience occur as a combination of emergent features. This neural network ‘C’ is clearly agnostic as regards any kind of a priori theory. Rather, it consists of unified informational opposites.