I like "machine perception". We're not much past the point of sensory-motor development.
I have heard it called computer vision.
That's different. Some deep learning models are used for computer vision, and some computer vision involves deep learning. Neither is an essential part of the other.
"linear transformations with soft thresholds sandwiched in between"
LT-STIB = Linear Transformations w/ Soft Thresholds In Between
How about "long skinny networks" over "short and fat networks". Deep maps to profound in my mind rather than just talking about lots of layers.
I prefer "just throwing cycles at the problem".
You can throw cycles in various ways (like with regular algorithmic code that implements various heuristics or something). So, "just throwing cycles at statistics"