hgm wrote: ↑
Wed Oct 23, 2019 12:58 pm
But a NN is nothing but a set of expressions...
A quick comparison of NN training with generating expressions and fitting them to a classification problem using linear prgramming. NN offers the following advantages:
1. You can download a software library like TensorFlow and, if you know what you're doing, you're good to go
2. Proven way of getting a good learning system for many problem types
3. Being used right now for chess position evaluation in many chess engines (some of them free and open source, and they mostly play very well)
4. If you want a classifier that fits the given data using Linear Programming (LP), and which would hence output a set of expressions, then right now you're building it yourself
LP generated expressions would offer the following advantages:
1. IMO LP will be more able to fit a complex shape like the solution to chess than a NN will
2. Could fit the data to the mathematical limit - the best possible fit (it may be necessary to use some LP tricks like symmetry breaking in such a large model space)
3. Having found the best fit, you could then turn the achieved fit into a model condition, and then do another optimisation to maximise the number of expressions for which the weight is zero, resulting in a smaller set of expressions
4. Having got a set of expressions and weights, it would be easy to translate this into a computer language for a program that would run on any computer - with or without a graphics card
5. If it turns out to be possible to make smallish set of expressions which can correctly classify most chess positions, it might be possible to articulate this expression in English language
Btw - if classification by LP turns out to be viable, you'll then have another optimisation problem: selection of position/evaluation pairs. The 7 piece tablebase alone has 423,836,835,667,331 positions in, which is infeasibly large for an LP model with today's technology - by many orders of magnitude. If you couldn't find a selection of around a million of them which could enable most of the others to be solved by the classifier, then the quest to solve "known chess" this way would likely be out of reach.