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The Neuro-Symbolic Brain

Neural networks promote a distributed representation with no clear place for symbols. Despite this, we propose that symbols are manufactured simply by training a sparse random noise as a self-sustaining attractor in a feedback spiking neural network. This way, we can generate many of what we shall call prime attractors, and the networks that support them are like registers holding a symbolic value, and we call them registers. Like symbols, prime attractors are atomic and devoid of any internal structure. Moreover, the winner-take-all mechanism naturally implemented by spiking neurons enables registers to recover a prime attractor within a noisy signal. Using this faculty, when considering two connected registers, an input one and an output one, it is possible to bind in one shot using a Hebbian rule the attractor active on the output to the attractor active on the input. Thus, whenever an attractor is active on the input, it induces its bound attractor on the output; even though the signal gets blurrier with more bindings, the winner-take-all filtering faculty can recover the bound prime attractor. However, the capacity is still limited. It is also possible to unbind in one shot, restoring the capacity taken by that binding. This mechanism serves as a basis for working memory, turning prime attractors into variables. Also, we use a random second-order network to amalgamate the prime attractors held by two registers to bind the prime attractor held by a third register to them in one shot, de facto implementing a hash table. Furthermore, we introduce the register switch box composed of registers to move the content of one register to another. Then, we use spiking neurons to build a toy symbolic computer based on the above. The technics used suggest ways to design extrapolating, reusable, sample-efficient deep learning networks at the cost of structural priors.

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