We call these symbols "embeddings" or "representations" in a vector or tensor space... but these symbols may not have any known or readily interpretable human meaning. People who are uneducated in basic vector (and tensor) math may have difficulty understanding how this is possible, but it's a fact.
For example, the ELMo embedding of a particular word in a sentence is a symbol that represents the complex syntax, semantics, and polysemy of that word given its location and use in the text.[a] Similarly, a trained WaveNet model represents a sequence of text as a (fairly large) tensor embedding that encodes the information necessary for generating the corresponding speech; this embedding is a symbol too.[b] As a final example, the next-to-last layer's embedding of an image processed through a trained Detectron model contains representations of every identified object in the image; those representations are symbols too.[c]
Moreover, the kind of automatic differentiation that is necessary for training deep learning models with backprop reduces into manipulation of symbols in a tree, viewed through the right lens. Witness, for example, the recent work done by Mike Innes et al for the Julia language.[d] We could very well be in the early stages of adoption of "deep differentiable programming" for a growing number of cognitive tasks that might not be solvable via human manipulation of symbols.
The challenge for deep learning going forward, as Bengio says and Marcus quotes, is in figuring out how to "extend it to do things like reasoning, learning, causality, and exploring the world."[e] As far as I can tell, everyone in the field already agrees on these goals; many researchers are thinking about and wondering how it might be possible to pursue them.
Does Marcus understand this? His complaining about the "lack of symbols" is... misguided, I think.
[b] https://deepmind.com/blog/wavenet-generative-model-raw-audio...
[c] https://research.fb.com/downloads/detectron/
[d] https://julialang.org/blog/2018/12/ml-language-compiler
[e] https://twitter.com/GaryMarcus/status/1065280340669816832