If we solve computer vision… If we solve computer audition,…. If we solve computer olfaction,…
If we solve computer vision… If we solve computer audition,…. If we solve computer olfaction,… If we solve computer vision, how can we build computers that can prove Fermat’s last theorem?
Invariances Invariances in audition. We can recognize a tune invariantly with respect to: intensity, speed, tonality, harmonization, instrumentation, style, background. Invariances in olfaction. We can recognize an odor invariantly with respect to: concentrations, humidity, pressure, winds, mixtures, background.
Non-Invariances Invariances evolution did not care about (although we are still evolving!...) – We cannot recognize faces upside down. – We cannot recognize tunes played in reverse. – We cannot recognize stereoisomers as such. Enantiomers smell differently.
Origin of Invariances Weight sharing and translational invariance. Can we quantify approximate weight sharing? Can we use approximate weight sharing to improve performance? Some of the invariance comes from the architecture. Some may come from the learning rules.
Learning Invariances E Hebb symmetric connections w ij =w ji 111 11-1 1-11 Acyclic orientation of the Hypercube O(H) Isometry Hebb O(H) H I(O(H)) I(H)
Deep Learning ≈ Deep Targets Training set: (x i,y i ) or i=1,..., m ?