Gary Marcus

GQ1. DL is part of the solution GQ2. "vectors, not symbols” is false dichotomy diff functions: yes, in part Operations a la logic, we do need (contra your view) GQ3. Outputs of deep learning may serve as input to reasoning; symbolic techniques needed for some inferences.

Most humans don't actually do much that resemble your answer to GQ3, except a small number of humans using pen and paper, and only in the last couple of millennia. Right now, we need to get machines to the level of a house cat. Never mind symbolic mathematics and formal logic.

I don’t argue that people can’t use formalisms that involve derivatives just because most people can’t explicitly explain what a derivative is. I think you are confusing formal, conscious use of a certain kind of machinery with what brain does unconsciously.

If you see the reasoning engine as *separate* (and qualitatively different) from the deep learning system that provides it with inputs, then we disagree. Unless this reasoning "system" is a pen and paper to do math/logic. And much of human intelligence functions without it.

That may distill a second point of disagreement; I see nothing wrong with (for some purposes) having separate systems for (eg) image classification vs reasoning. Certainly it is possible in principle to engineer systems that way; what’s your objection? Efficiencies of training?

I wonder if we are mixing different methodological questions here. If I need to build a robust and reliable system today, I would mix deep learning, probabilistic programming, and symbolic methods. 1/

But at the same time, I think it is critically important to see if we can push DL methods to provide a unified solution to perception, reasoning, and action (with robustness and safety). 2/

Deep learning, in principle, provides grounding for the semantics of internal representations that current symbolic methods lack. Other learning approaches might do this too. 3/