Classical Conditioning

You're probably familiar with classical conditioning. Ring bell, get food. Ring bell, get food. Before long, you get Ring bell -> salivate..

But how does it work, more precisely?

The rescorla wagner model is popular because it is an actual concrete model (kinda) even though it's wrong.

Blatently ripping off wikipedia:

and

where

• ΔVX is the change in the strength of association of X
• α is the salience of the CS (bounded by 0 and 1)
• β is the rate parameter for the US (bounded by 0 and 1), sometimes called its association value
• λ is the maximum conditioning possible for the US
• VX is the current associative strength
• Vtot is the total associative strength of all CS

I say "kinda", because it doesn't really specify what counts as "US" or "CS", and I say its wrong because, well... 

Wikipedia gives a list of failures of the model.

• Spontaneous recovery from extinction and recovery from extinction caused by reminder treatments (reinstatement)
• Extinction of a previously conditioned inhibitor
• Facilitated reacquisition after extinction
• The exclusiveness of excitation and inhibition
• Pairing a novel stimulus with a conditioned inhibitor
• CS-preexposure effect
• Higher-order conditioning
• Sensory preconditioning

As far as I can tell, all of these things can be fixed by adding a degree of freedom for inhibition as distinct from lack of excitation (the inhibition association has to decay faster than the excitation association), and clarification of what qualifies as US/CS. Checking this is left as an exercise for the reader ;-)

In addition, there appears to be a big difference between (Vn+1 = deltaV+Vn) and (Vn+1 = deltaV+fear experienced). That is, if you block the fear response with propranolol, the fear doesn't just come back.

As far as what counts as a US or CS, it looks like any recognizable stimuli works as either - anything for which there exists a node on the neural net (under some representation).  It looks like there's no real distinction (other than instinctual priors), as evidenced by higher order conditioning, as well as all the cognitive components involved in conditioning. 

The general neural net structure seems to allow it, hypnotists seem to make whatever associations they want, and the conditioning literature doesn't show any limitations either. It appears that we have do free reign to condition any two "concepts" together. Anything from the sensation of searing heat to thoughts about truffle hunting unicorns.

So I talked about modifying arbitrary connection strengths, and now we have a way to do it: Present them both at the same time when the US is "surprising" (low Vtot), and the CS is the most salient thing (high alpha).

More on how to do it quickly and purely cognitively later.