Tsang's Brain Fractal Theory: The ultimate algorithm for AGI

In this chapter I will discuss how Tsang's Fractal Brain Theory describes a way to implement the evolutionary algorithm of intelligence in a computer environment to generate Artificial General Intelligence.

Background

In my previous book "Is Intelligence an Algorithm?" I described an algorithm that evolution follows to generate complexity. To my great surprise I found the same ingredients back in the book "Fractal Brain Theory", although differently presented. This chapter is the first of a series of a sequel to my previous book.
I described how when a (living) system encounters a problem such as a lack of resources, this gives the system a stimulus to start to probe for a variety of alternatives or other solutions.
Quote from my previous book:

Nature will now generate a plethora of alternatives by combining elements from the environment with the system. 

This includes changes such as mutations.
In Tsang's book an equivalent is found in that the system differentiates or diverges.
From the probing or testing of these alternatives by the system, the system abstracts patterns. (Screening of relational “Syntheses”.) From these the most successful alternative strategies can be selected. (Elimination, Pruning of Syntheses and Emergence of new “Theses”.)
This plays a role in what Tsang calls "intersection", which I will discuss later in this chapter.
Quote from my previous book:

This can be repeated on a heterarchical level between groups of entities or (living or non-living) systems (such as bacterial colonies or animal societies). When contending groups encounter each other, this gives a stimulus to start a so-called “Intergroup tournament”. The tournament can lead to a mutual probing of the distinctions between the groups. Nature will screen which elements from the contender can be copied and integrated and which ones should be discarded. This can result in the formation of 1) a “niche” (each group specialises in a niche such that it does not poach on the contender’s preserves); 2) a “symbiosis”: the groups learn to cohabitate peacefully together and provide each other with a service, resulting in a transactional scenario of a win-win situation); or 3) an exchange of those features which are different between the groups (“mimicking”). Thus the system adapts itself to its environment.

The most promising strategies ideally result in symbiosis, a unification of features toward which the system will strive. 

In Tsang's book I found an equivalent which he calls convergence.
Quote from my previous book:

The system will try to resonate “morphogenetically” (i.e. in form, as dictated by its genetic make-up) with its new environment and thereby adapt to it. This is Nature’s way of continuously striving for more complexity and incorporation of mutual features, as this assures more adaptability to and integration with the environment and hence increased chances for survival. In other words Nature’s intelligence algorithm is essentially integrative: It tries to unite, to combine apparent opposites.

Now one of the most interesting points I found in Tsang's book was the way he described the selection process (which I called the screening and pruning), which he calls the intersection of the convergence and divergence. This is one of the points that I will discuss in more detail in this chapter.
The other point is that Nature is a system performing mapping. I discussed this in my essay: "Is structure fossilised sense". Likewise I find that Tsang describes mapping as the unifying process underlying all natural processes.
Finally, Tsang speaks about a recursive self-modifying process, in which the process takes itself as an object and maps this. This is Yoneda embedding, which I also discussed in my article on structure being fossilised sense. Moreover, in my article on sentience I suggested that this form of self-representation is the very ontogenetic process of reality generation.

Mapping

Tsang convincingly shows that nature both on the genetic as well as the brain level cunningly exploits the process of making binary trees to arrive at an ontogenetic process which observes rules of symmetry and symmetry breaking, recursive self-modification and warranting self-similarity over different scales. The brain maps its experiences, its sensory data observing a hierarchical process involving binary trees, and these are reflected in the generation of corresponding structures at the neuronal level in the form of axonal and dendritic branching  (but also at the genetic level: e.g. epigenetic markers). Moreover, this forward chaining process is mimicked by a backward chaining process in the motor neurons. Both the structural modifications and the motor neuron actions can be considered as mappings of the sensory process: (s)ensing translates into (r)econstruction in terms of Tsang. From (s)timulus to (r)esponse.

Amplification, Reproduction and seed.

Nature has found both at the neuronal and genetic level a system to reproduce itself, which is a special kind of recursive mapping which takes itself as object to generate isomorphic structures, we could call this amplification. At the same time, there is a kind of randomisation process going on allowing for mutations and changes, a differentiation can occur in the copies. At the level of DNA this is obvious in the form of point mutations, deletions and insertions, but at the brain level as well plasticity is rewarded allowing for morphological differentiation and asymmetric linking up of the neurons. Moreover, a Yoneda type mapping process occurs in that the mapping process itself becomes the object of the mapping process. We can reflect on how we reflect and this is reflected in new links being created at the neuronal level. Now that we understand that this type of reflecting is a Yoneda-type of mapping we are actually doing this very thing in situ. The process which maps and creates our neuronal links is mapped to itself. You have now created a mapping of the recursive process by the recursive process. You have done so by creating a hierarchical binary tree. You have crystallised (or fossilised) sensing and function into structure. This is what nature does, it evolves evolvability by a process which Tsang calls recursive self-modification. A hierarchical binary tree generation process which is the unifying process in our ontogenesis.
Tsang moreover shows that the brain is like a fractal structure as every idiosyncratic aspect of the brain can be mapped to a structure or function at the genetic level. After all our genome encodes precisely how our brain's architecture should be formed. Our genome in a certain sense is a brain in seed form.
Interestingly, Stephen King a computer scientist (not the horror writer), called this process of self-generation the generation of a null-representation, a self-representation or a seed, which can grow out into a full blown new entity.

Divergence and Differentiation

And Tsang adds the modifying and divergence or symmetry breaking aspect to it. Some branches will get more attention than others. Neurons have a kind of background random spiking activity, which can be rewarded if an interaction is generated and a connection is built. This creates a divergence. If a cell would simply undergo a doubling process by division without any differentiation, all you would get is a homogeneous essentially spherical blob of cells. Fortunately, nature has invented a way to differentiate by employing so-called morphogens (special chemicals that cells produce), the presence of which tells the cell to differentiate, by silencing certain parts of the DNA and switching on other parts. These morphogens form a gradient, so that not every cell is differentiated, but only the ones where the morphogen concentration is high. Even on the neuronal level there is a differentiation in type, there are activating and inhibitory neurons; there are also spindle cells for long distance information transfer.

Screening, Pruning, Intersection and Selection

I described how nature has to screen and prune the variety of alternatives it has generated to select the most promising ones. Darwin's survival of the fittest. But how does it pull off this trick if a mapping process underlies the ontogenesis? It is here that I found Tsang's description most elegant and inspiring. It employs a combination of forward chaining and backward chaining, just like certain type of heuristics in artificial intelligence. In a literal sense the sensory  motor neurons expand and branch until they meet each other and only those who meet are selected, because they form a link! Just like  a forward chaining heuristic starting from the problem meets a backward chaining heuristic starting from the solution. Tsang describes this as Bayes inverse probability Rule in action. Bayesian probability can be expressed as the chance that B occurs when A is present  P(B ¦ A) being equal to the chance that A occurs multiplied by the chance that A occurs when B is presented and divided by the chance that B occurs: P (B ¦ A) = P(A)*P(A ¦ B)/P(B).
The chance that B occurs when A is present is like the forward chaining heuristic and the chance that A occurs when B is present as the backward chaining heuristic. Where the branches meet a connection is formed and metaphorically an intersection is formed. This is how neurons select. Neurons that wire together fire together. Enhanced flow through a neuron attracts the attention of other neurons, which will then also benefit from enhanced flow. This is like publicity. This is what Howard Bloom calls the "Matthew" principle: To those who have it shall be given, from those who have not it shall be taken away. There is a mutual rewarding going on, which is rather exclusive. Only really new ontologies to be created may be able pull off the trick of including the previously excluded neurons.
But only those who can create a proper linkage create a connection, and Tsang here uses the lock and key metaphor. The conjugation or linking up at every level can only occur if the key of the backward chaining heuristic fits the lock of the forward chaining heuristic. In order to select which ones can link up, a scoring system is needed. Tsang proposes that the lock comes before the keys otherwise we wouldn't have anything to score the keys with. The female precedes the male, in this chicken-and-egg problem.

Convergence and Integration

This shows that ontogenesis is more than differentiation and selection only. The parts must also start to work together, they must be integrated into a whole. A meta-system transition must occur for the cells to group into an organ. And again this trick is pulled off by mapping. Yes, mathematical category theory is a very powerful concept, for describing reality as we know it. Here we employ linking up of the various  mapped elements. This is the cooperative symbiotic part of the evolutionary search engine, allowing the mapped conjugated entities to map into a convergent hierarchical tree. And this new entity can then be submitted to a new round of recursive self-modification, giving rise to the steps I described as intergroup tournament, distinction probing and (further) symbiosis.

Artificial Intelligence

Tsang believes that the ingredients of symmetry, self-similarity and recursion resulting in a simple self-modifying recursive algorithm, which creates binary trees, may be the key to unlocking the secret of Artificial general Intelligence: Creating AI which is context independent and which can achieve or surpass the human level of intelligence. Provided that Tsang in his endeavours in AI includes the elements of selection and integration he has described, this may indeed be a promising novel avenue in this field. But we must not forget that it took nature billions of years to arrive at the complexity we presently have. The different layers and structures in the brain (cerebellum, hypothalamus, pituary gland, hypophysis, hippocampus, amygdala, cerebral cortex etc.) have a very special fine-tuned architecture, which employs a great variety of neurotransmitters. If Tsang's future algorithm is successful it will take quite some cycles and extensive pruning and selection, before a human  level AGI evolves from it. On the other hand the ever increasing speed at which this can occur and the ever increasing resources in terms of memory and miniaturisation according to Moore's law, may pull-off this trick faster than we think. Because it has the very notion of representation and recursive self-modification at its heart.
Noteworthy, Dr Joe Tsien has recently shown that intelligence indeed follows a “neural network” type algorithm (not a traditional von Neumann style algorithm). The more thought, the more cliques join in, Tsien says. The basis of Tsien’s Theory of Connectivity is the algorithm, n=2ⁱ-1, which defines how many cliques are needed for a “Functional Connectivity Motif” to arise. This enabled the scientists to predict the number of cliques needed to recognise options in their testing of the theory. The  2ⁱ in this formula represents the number of neurons that join in, which follows exactly the binary tree indicated by Tsang!

Conclusion

We have seen that Tsang's brain fractal theory can be mapped quite accurately to my "intelligence algorithm" and "structure is fossilised sense" ideas. We have seen that Tsang provides serious improvements thereof in terms of binary trees, an intersection selection and connection process and a recursive self-modifying process. We have also seen that this may be a serious candidate to create human level AGI which may perhaps one day herald the advent of the technological singularity. Thus Tsang lifts the veil of the underlying algorithm of existence as a whole, a process, which the Greek called Apokalypsis. The Fractal Brain Theory by Wai H.Tsang, wholeheartedly recommended.