Inequalities has been a favourite Olympiad topic of mine, so this piqued interest. As I have limited experience with LSTMs, wanted to pass on a possible first angle of attack.
There is a Vietnamese book that advocates a very organic approach to solving inequalities through rewriting as sum of squares “Diamonds in Mathematical Inequalities”.
This could be used to attack a subset of the problem.
- Reformulate the problem to prove LHS(x, y, z, …) >= 0
- Generate a large set of expressions of sum of squares like so (a-b)^2, (a-2b+c)^2+b^2, etc.
- Calculate the expanded form of these expressions, e.g., a^2-2ab+b^2
- Train an LSTM to solve the inverse problem, e.g.,
- To see if an inequality is solvable with this approach, see if the neural network output expression is a sum of squares and expands to the original - if so => inequality proved.