gradient_notes

just +/* semiring, where the gradietns are getting multiplied together as it is going back
then it is adding the different cases where it appears in the progrma

stop gradient???
     - if want to limit backpropagating through a particular operation?
       I suppose that this could just be overriding the gradient to a given operation, so it could use something like
       $gradient with := operator, then it could just override what the input for a particular gradient's accumulator is defined as


transformation based learning
- start with sentences and the starting tags, can then update which takes are selected, and what the respective change is for a given value.  It would want to update the parameters with


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When it comes to representing the problem using a jacobian and then sovoling


If we consider an equation like `a * 2 = b, a + 1 = b` for when `a == 1`, then it is not 100% clear what the gradient should be in this case.  There are two different ways in which teh gradient could be computed.  Also if either of the equations was to change, then it would likely eleminate the rule in this case, meaning that the gradient is likely wrong due to the filtering.
   - current systems which are computing the gradient are basically ignoring the gradient wrt



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This just needs to find /some/ mode which is supported by all of the operations.
In which case, this can use the safety planning, and then identify the different
possible modes of every expression.  From that point, it can just construct the
computation circuit such that the flow from the different inputs to the output
follows the backwards graph of the modes.  Anything that is not involved in the
moded computation of the result, is just directly attached to the computation as
a side condition.  Those operations still need to get checked, but those
operations are just