(cont)
I probably should have lead with this, but there's been a lot of interest in backprop-like algorithms in the brain
* Geoff Hinton has a talk (and slide deck) about how back-propagation might be implemented in the brain. (Slide deck: https://www.cs.toronto.edu/~hinton/backpropincortex2014.pdf Video: http://sms.cam.ac.uk/media/2017973?format=mpeg4&quality=720p )
* As always, the French part of Canada has its own, slightly different version of things, care of Yoshua Bengio (slide deck from NIPS 2015: https://www.iro.umontreal.ca/~bengioy/talks/NIPS2015_NeuralS... preprint: https://arxiv.org/abs/1502.04156 )
* Here is another late 2015 take on back-prop in the brain by Whittington and Bogacz (http://biorxiv.org/content/early/2015/12/28/035451) This one is interesting because they view the brain as a predictive coding device which is continuously estimating the future state of the world and then updating its predictions. (I think the general predictive coding idea is cool and probably under-explored).
* There's a much older paper by Pietro Mazzioni, Richard Andersen, and Michael I. Jordon attempting to derive a more biologically plausible learning rule (here: http://www.pnas.org/content/88/10/4433.full.pdf) This work is particularly neat because it builds on earlier work by Zipser and Andersen (https://www.vis.caltech.edu/documents/54-v331_88.pdf), who trained a three-layer network (via back-prop) to transform data from gaze-centered ('retinotopic') to head-centered coordinates, and noticed that the hidden units performed transforms that look a lot like the work done by individual neurons in Area 7A. The Mazzioni paper then replaces the backprop with a learning procedure that is more biologically plausible.
For backprop, you need some sort of error signal. Wolfram Schultz's group has done a lot of work demonstrating that dopamine neurons encode something like "reward prediction error." (e.g., this: http://jn.physiology.org/content/80/1/1, but they have lots of similar papers: http://www.neuroscience.cam.ac.uk/directory/profile.php?Schu...). For reinforcement learning, you might also want to maintain some sort of value estimate. There are tons of studies looking at value representation in orbitofrontal cortex (OFC), using mostly humans and monkeys, but occasionally rats. Here's a review from Daeyeol Lee and his postdoc Hyojung Seo describing neural mechanisms for reinforcement learning (http://onlinelibrary.wiley.com/doi/10.1196/annals.1390.007/f... ) The Lee lab has done a lot of interesting value-related things too.
Switching gears slightly, there is also considerable interest around unsupervised learning and related methods for finding "good" representations for things. This is potentially interesting because it would allow for improvements within individuals and even across individuals (e.g., by evolution).
Olshausen and Fields kicked this off by demonstrating that maximizing the sparseness of a linear code for natural images produces a filter bank that resembles the way neurons in primary visual cortex process images. (http://courses.cs.washington.edu/courses/cse528/11sp/Olshaus...)
Michael Lewicki has done similar things in a variety of sensory modalities. Here's a recent paper from him looking at coding in the retina (http://journals.plos.org/ploscompbiol/article?id=10.1371/jou...) but he has similar work in the auditory system and building on the Olshausen and Fields paper linked above to explain complex cells (and more!) in visual cortex. Bill Geisler has also done a lot of work looking at the statistics of natural scenes and how the brain (and behavior) appears to be adapted for them.