[adonovan]

“Formulas that update backwards” is the main idea behind neural networks such as LLMs: the computation network produces a value, the error in this value is computed, and then the error quantity is pushed backward through the network; this relies on the differentiability of the function computed at each node in the network.

[big-chungus4]

"Formulas that update backwards" isn't really the main idea behind neural networks. It's an efficient way of computing gradients, but there are other ways. For example forward propagation would compute a jacobian-matrix product of input wrt output with an identity matrix. Backpropagation is similar to bidi-calc to the same extent as it is similar to many other algorithms which traverse some graph backward.

I think you should be able to use bidi-calc to train a neural net, altough I haven't tried. You'd define a neural net, and then change it's random output to what you want it to output. However as I understand it, it won't find a good solution. It might find a least squares solution to the last layer, then you'd want previous layer to output something that reduces error of the last layer, but bidi-calc will no longer consider last layer at all.

[uoaei]

All those words and you forget to provide people the breadcrumbs to learn more for themselves.

The term of interest is "backpropagation".

[Towaway69]

Won’t another breadcrumb be Prolog and “declarative programming”[1].

Wasn’t Prolog invented to formalise these kinds of problems of making the inputs match what the desired output should be.

[1] https://en.wikipedia.org/wiki/Declarative_programming