Backpropagation is a leaky abstraction

1. Neurons, or more specifically, connections between neurons ("synapses"), absolutely do have weights, and the "strength" of synapses can be adjusted by a variety of properties that act on a scale of seconds to hours or days. At the "semi-permanent" end of the spectrum, the location of a synapse matters a lot: input arriving far from the cell body has much less influence the cell's spiking. The number (and location?) of receptors on the cell surface can also affect the relative impact of a given input. Receptors can be trafficked to/from the membrane (a fairly slow process), or switched on and off more rapidly by intracellular processes. You may want to read up on long-term potentiation/depression (LTP/LTD), which are activity-dependent changes in synaptic strength. There are a whole host of these processes, and even some (limited) evidence that the electric fields generated by nearby neurons can "ephaptically" affect nearby neurons, even without making direct contact, which would allow for millisecond-scale changes.

2. While you can start by dividing neurons in excitatory and inhibitory populations, there's a lot more going on. On the glutamate (excitatory) side, AMPA receptors let glutamate rapidly excite a cell and make it more likely to fire. However, it also controls NMDA channels that, under certain circumstances, allow calcium into a cell. These calcium ions are involved in all sorts of signaling cascades (and are involved--we think--in tuning synaptic weights). GABA typically hyperpolarizes cells (i.e., makes them less likely to fire) and is secreted by cells called interneurons . However, there's a huge diversity of interneurons. Some seem to "subtract" from excitatory activity, others can affect it more strongly in a divisive sort of way or even cancel it completely. Furthermore, there's a whole host of other neurotransmitters. Dopamine, which is heavily involved in reward, can have excitatory or inhibitory effects, depending on whether it activates D1 or D2 receptors

3. While the textbook feed-forward neural networks certainly have "instant" signal propagation, there are lots of other computational models that do include time. Time-delay neural networks are essentially convnets extended over time instead of space. Reservoir computing methods like liquid state machines also handle time, but in a much more complicated way.

4. I chuckled at the idea of finding a biological correlate analog for reinforcement learning, since reinforcement learning was initially inspired by the idea of reinforcement in psychology/animal behavior. People have shown that brain areas--and individual neurons within them--encode action values, state estimates, and other building blocks of reinforcement learning. Clearly, we have a lot to discover still, but the general idea isn't at all implausible.

Finally, some people are fairly skeptical that the fields have much to learn from each other; Jürgen Schmidhuber said this a lot at NIPS last year. However, other, equally-smart people (e.g., Geoff Hinton) seem to think that there may be a common mechanism, or at least a useful source of inspiration there. But, if you want to work on something like this (and it is awesomely interesting), it really helps to have a solid grounding in both.

hmm, I did the cs231n homework and had the opposite experience. It was really easy to complete it by ignoring numpy's provided matrix methods (just write a bunch of for loops in python) but that solution was really slow. If you could use numpy's matrix methods, however, the code executed a lot faster (the loops and control flow now run in C instead of python, so to speak). The hard part of the assignments was expressing my python code, with all its ad-hoc mixture of nested loops and conditionals, in numpy.

At that level, they assume you are pretty smart and capable of figuring out something like an API on your own time as needed. They'd rather you know what all these funky things in these APIs are doing at a core level so that you can employ them in an effective manner.

This is not as good. There's a lot of evidence from neuroscience that this leads to an illusion of competence. I.e. it's much easier to follow along through a sample solution than to craft a solution yourself. Until you craft the solution yourself, the knowledge won't actually be chunked as firmly in your brain.

I've seen this time and again, as a teacher, and it was mentioned explicitly in Coursera's Learning How To Learn course: https://www.coursera.org/learn/learning-how-to-learn

NOTE: watching someone is a good way to get started, but until you do it on your own, you haven't learned it deeply, and it may be difficult to recall in a real situation.