I don't think this is quite right. I've done some work around the edges of this space (not solving, more making sure predictions were explainable by combining

I don't think this is quite right. I've done some work around the edges of this space (not solving, more making sure predictions were explainable by combining deep nets and Bayesian models). The deep nets handle the object (and language) recognition, and build the vector representation (so comparisons are possible; ie, your lossy continuous space). But then you - somehow - build a mapping to symbolic space. Then when confronted with unmapped data the net can measure similarities to previously known examples, and use them to translate via similarity measures. I'm not entirely sure if this is the approach taken (I haven't read their paper) but my impression is that the "turn it into a symbolic program" means that the symbolic program itself is a traditional solver (whether it be a theorem solver or something like Prolog/Datalog is unclear)