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Both S. L. Thaler and R. Hecht-Nielsen have set forth neural-based theories of "confabulation" applicable to machine learning.

The essential mathematics of Hecht-Nielsen is set forth in his paper "Cogent Confabulation". Briefly it is an inversion of Bayesian inference. Bayesian inference is P(x|a&b&c&d...) where one is estimating the probability of x assuming a, b, c, d, etc. Its inversion is P(a&b&c&d...|x), which RHN calls the "cogency" of x given the assumptions.

I haven't seen a similarly succinct description of Thaler's mathematics that would permit comparison to see if the theories are isomorphic. Are they?

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I don't think they map onto each other, aside from RHN's brief discussion of thalamo-cortical loops, the inspiration for SLT's so-called "Creativity Machines." In SLT's architectures, compelling/cogent solution patterns are sought within a stream of novel activation patterns (i.e., confabulations) driven by various forms of internal disturbances to biological neural nets. RHN's definition of cogency is obviously not the same. The mathematics of SLT's model are scattered over several patents and papers, but the following might provide an overview: Predicting ultra-hard binary compounds via cascaded auto- and hetero-associative neural networks, Journal of Alloys and Compounds, 279(1998), 47-59, Synaptic Perturbation and Consciousness, International Journal of Machine Consciousness, 6(2):75-107, 2014, Cycles of Insanity and Creativity within Contemplative Neural Systems, Medical Hypotheses, 94:138-147, Elsevier, 2016, and Pattern Turnover within Synaptically Perturbed Neural Systems, Procedia Computer Science, 88, Elsevier, 2016.

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To further elaborate using Bowery’s explanation, Thaler developed the chaotic neural network methodologies to predict the pattern $(a, b, c, d)$ that could result in $x$, without concern for probabilities. While doing so, he proposed that ideas were false memories or confabulations nucleating from noise, subsequently recognized for their novelty, utility, or value by monitoring neural nets that could then elect to reinforce them as memories. Bayesian probabilities would likely not apply in a system so awash in chaos.

For more math, see Pattern Turnover within Synaptically Perturbed Neural Systems, Procedia Computer Science, 88, Elsevier, 2016 and Cycles of Insanity and Creativity within Contemplative Neural Systems, Medical Hypotheses, 94:138-147, Elsevier, 2016.

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Actually, there is overlap between the two theories, but Thaler’s model is much more general.

RHN’s 2005 theory pertains only to the co-activation of intact memories, but SLT’s model allows for the inclusion of false or degraded memories (i.e., confabulations). So in terms of the prior comments, not only can a, b, c, and d activate in the context of x, but also a’, b’, c’, d’, and d’’, for example, making the probability calculation all the more daunting. That’s why SLT discussed the formation of ideational chains that are a mixture of memories and confabulations in his 1996 paper, A Proposed Symbolism for Network-Implemented Discovery Processes, In Proceedings of the World Congress on Neural Networks, (WCNN'96), Lawrence Erlbaum, Mawah, NJ. So, in what RHN describes as a winner-take-all horse race, the thoroughbreds are not only mutating at the starting gate, but also during the race itself. SLT attributes such ongoing mutations and hybridizations of memories to the injection/withdrawal of synaptic perturbations (e.g., 1998, J. Alloys and Compounds, above) by the limbic system in the form of volume neurotransmitter release (e.g., 2014, IJMC above).

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  • $\begingroup$ From the onset, SLT’s model has considered the temporal evolution of cognition an important indicator of the microscopic processes underlying cognition. (See for example, A quantitative model of seminal cognition: the creativity machine paradigm, Proceedings of the Mind II Conference, Dublin, Ireland, 1997). Based largely upon volume neurotransmitter release, SLT predicts the frequency and tentativeness of ideation in his limbo-thalamo-cortical model (e.g., 2016, Medical Hypotheses). $\endgroup$ – user63732 Dec 26 '16 at 16:59
  • $\begingroup$ SLT has also extended his model to include hysteretic effects in which idea formation (i.e., cognition) takes place over multiple cycles of synaptic chaos and relaxation (e.g., 2016, Medical Hypotheses, above) in a process that emulates the well-known process of incubation. This process is not part of RHN’s ‘comprehensive’ model of thought. Along these same lines, SLT’s theory predicts the many psychopathologies that accompany the mind’s self-induced stress as cognition turns creative. $\endgroup$ – user63732 Dec 26 '16 at 17:01
  • $\begingroup$ Welcome to the site! Rather than extending your answer by comments, please use the edit link to incorporate that material into the answer itself. $\endgroup$ – David Richerby Dec 26 '16 at 21:45

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