Continuing this blog’s recent focus on categorization, one possibility of how new items are classified has been hypothesized as either assimilitaion (adding the item to an existing schema in the feature space) or accomodation (addition of a new schema around the item in the feature space). We’ll leave aside the newly introduced concept of Restructuring for this particular discussion.

Schemata, it is to be remembered, are conceptualized as nothing but a named cluster in the feature space. If we become a bit more audacious, we can posit that the clustering in the feature space is mimicked by the actual clustering/ connectivity of neurons in the Hippocampus (or the appropriate semantic memory brain module), with each neuron representing a particular item- say a neuron being a Halley Barry neuron. These neurons would not be randomly distributed- they form a small-world model with local clustering and bistability. whenever a group of neurons get activated together (and also belong to a cluster or clique), we can say that the memory of that category is activated.

Further suppose that learning and memory are crucially dependent on Neurogeneisis and new learning (of concepts ) happens by insertion of a new node (neuron in the small-world network of brain) and connecting it appropriately with other neurons.

As an example consider that all face recognition cells cluster together in the brain and the concept of face is activated by simultaneous activation of all cells of this cluster. The fact that a new visual stimulus (a novel human face of a stranger) is a face is determined by calculating the stimulus features and their difference from the prototypical/ exemplar face neurons and their features. A match so determined not only enables us to say that this new stimulus is a face (as this input would activate the face clique) , but would also give us an idea of where to place a new neuron that may encode for this new face and how to connect this with other neurons and with which other neurons.

Now whenever we encounter a novel stimulus we have two possibilities. If it matches some existing cluster / category, we encode this new memory by placing a new neuron coding for this in the region of that category in the feature space and (crucially) following preferential attachment attach it in a manner such that the probability of its linking to any other neighboring neuron is in proportion of the links that old neuron already has. (This can be readily implemented in brains as axonal connections will whither if not much functional activity happens at the synapse formed between the new neuron and the older one) . This is akin to assimilation of a new memory/ learning neuron. this method of insertion still keeps the neural net a small-world network.

Now consider the second case when the novel stimuli matches no older categories but necessitates that we form a new category if we have to represent that new item in the feature space. We need accommodation here. On the neural level this is still accomplished by inserting a new neuron, but this time the new node is not peripheral- the new neuron is a hub (category) neuron. So we use the method of copy to insert the new element. We copy the links (partially) of a neighboring hub (cluster center/ category label neuron) and use that link structure to link the newly introduced neuron in the small-world network. the network still remains scale-free and we have introduced a hub or a new category in this case.

All this seems very exciting. Some snippets from wikipedia article on scale -free networks are very relevant.

The mostly widely known generative model for a subset of scale-free networks is Barabási and Albert’s (1999) rich get richer generative model in which each new Web page creates links to existent Web pages with a probability distribution which is not uniform, but proportional to the current in-degree of Web pages.

A different generative model is the copy model studied by Kumar et al. (2000), in which new nodes choose an existent node at random and copy a fraction of the links of the existent node. This also generates a power law.

Recently, Manev and Manev (Med. Hypotheses, 2005) proposed that small world networks may be operative in adult brain neurogenesis. Adult neurogenesis has been observed in mammalian brains, including those of humans, but a question remains: how do new neurons become functional in the adult brain? It is proposed that the random addition of only a few new neurons functions as a maintenance system for the brain’s “small-world” networks. Randomly added to an orderly network, new links enhance signal propagation speed and synchronizability. Newly generated neurons are ideally suited to become such links: they are immature, form more new connections compared to mature ones, and their number but not their precise location may be maintained by continuous proliferation and dying off.

I am excited, what about you?

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