It looks like the basic meta-algorithm is: 1) Notice a pattern in the mathematics 2) Device a neural network that leverages structural properties of the space

It looks like the basic meta-algorithm is: 1) Notice a pattern in the mathematics 2) Device a neural network that leverages structural properties of the space you wish to investigate 3) Encode relationship in a manner allowing use of supervised learning and see if the net can learn a pattern. 4) If it failed, rethink pattern and go back to step 2 or give up; else use attribution and explainability tools to try and extract human understandable concepts. Go back to step 2 until human converges 5) Use the extracted concepts to generate a conjecture or aid a proof. 6) Profit In a way it's like AlphaZero in that a nnet is helping the searcher prune a highly branching decision space. Deepmind recently published another paper [for chess](https://arxiv.org/abs/2111.09259 https://arxiv.org/abs/2111.09259) which again was about extracting hidden knowledge from a neural network. Authors hope this can be an avenue through which machine learning can be useful to mathematics research. But even in the cases where their meta-algorithm works, I think they underestimate the difficulty of having expert neural network practitioners on hand, without which I expect step 3 failures will be massively inflated. ---------- Choice extracts: > In each of these cases, the necessary models can be trained within several hours on a machine with a single graphics processing unit > Further, in some domains the functions of interest may be difficult to learn in this paradigm. However, we believe there are many areas that could benefit from our methodology. > The Bruhat interval of a pair of permutations is a partially ordered set of the elements of the group, and it can be represented as a directed acyclic graph. For modelling the Bruhat intervals, we use a message-passing neural network. We add two features at each node representing the in-degree and out-degree of that node. > First, to gain confidence that the conjecture is correct, we trained a model to predict coefficients of the KL polynomial from the unlabelled Bruhat interval. We were able to do so across the different coefficients with reasonable accuracy giving some evidence that a general function may exist, as a four-step MPNN is a relatively simple function class. We trained a GraphNet model on the basis of a newly hypothesized representation and could achieve significantly better performance, lending evidence that it is a sufficient and helpful representation to understand the KL polynomial. To understand how the predictions were being made by the learned function f^, we used gradient-based attribution to define a salient subgraph SG for each example interval G