Interest in neural networks was renewed with Werbos's (1975) backpropagation algorithm. There was continued progress in ANNs all this time.

I think the aversion to ANNs during the 90s was more philosophical and aesthetic - ANNs math is indeed "ugly" compared to symbolic logic, bayesian inference, SVM (in the 00's), and many other traditional AI methods.

https://en.wikipedia.org/wiki/History_of_artificial_neural_n...