Dr. Neurosymbolic, or: How I Learned to Stop Worrying and Accept Statistics

The symbolic AI community is increasingly trying to embrace machine learning in neuro-symbolic architectures, yet is still struggling due to cultural barriers. To break the barrier, this rather opinionated personal memo attempts to explain and rectify the conventions in Statistics, Machine Learning, and Deep Learning from the viewpoint of outsiders. It provides a step-by-step protocol for designing a machine learning system that satisfies a minimum theoretical guarantee necessary for being taken seriously by the symbolic AI community, i.e., it discusses "in what condition we can stop worrying and accept statistical machine learning." Some highlights: Most textbooks are written for those who plan to specialize in Stat/ML/DL and are supposed to accept jargons. This memo is for experienced symbolic researchers that hear a lot of buzz but are still uncertain and skeptical. Information on Stat/ML/DL is currently too scattered or too noisy to invest in. This memo prioritizes compactness and pays special attention to concepts that resonate well with symbolic paradigms. I hope this memo offers time savings. It prioritizes general mathematical modeling and does not discuss any specific function approximator, such as neural networks (NNs), SVMs, decision trees, etc. It is open to corrections. Consider this memo as something similar to a blog post taking the form of a paper on Arxiv.