https://en.wikipedia.org/wiki/Perceptrons_(book)
Neural nets fell out of favor in the 1970's but came back and became hot in the early 1980's with work by John Hopfield and others that addressed the objections.
https://en.wikipedia.org/wiki/John_Hopfield
Practical and commercial successes were limited in the 1980's and 1990's which led to a reasonable decline in interest in the method. There were some commercial successes such as HNC Software which used neural nets for credit scoring and was acquired by Fair Isaac Corporation (FICO).
https://en.wikipedia.org/wiki/Robert_Hecht-Nielsen
I turned down a job offer from HNC in late 1992 and neural nets were still clearly hot at that time.
Some people continued to use neural nets with some limited success in the late 1990's and 2000s. I saw some successes using neural nets to locate faces in images, for example. Mostly they failed.
AI research is very faddish with periods of extreme optimism about a technique followed by disillusionment. One may wonder how much of the current Machine Learning/Deep Learning hype will prove exaggerated.
Also, traditional Hidden Markov Model (HMM) speech recognition is not rule based at all. It uses a maximum likelihood based extremely complex statistical model of speech.