Apart from deep wagging contests this might become less relevant if we go by the notion "poly time == solved". The reason why this is so is that 3 layer Neural

Apart from deep wagging contests this might become less relevant if we go by the notion "poly time == solved". The reason why this is so is that 3 layer Neural Networks are uniform approximators of smooth functions. I have to read the paper carefully for assumptions made, but if the result holds true for the entire class of 3 layer NNs, or a class that is big enough not to sacrifice uniform approximation then this would be Big Deal. Of course for practical applications, poly-time may not mean that it is a solved problem, or that the poly-time algorithm is the best algorithm to use on a typical instance. The exponent or the leading constant could be very high, and deeper networks may well offer more conducive properties.