Here are the big ones as covered in a survey article:
- Tensorflow. The newest one from Google. The biggest issue seems to be how this scales as Tensorflow is a single machine solution now. Google Brain is the a closed source scaled system.
- Torch. A great chance to learn lua and Facebook has open sourced their Torch tools
- Theano and it's libraries. This is the oldest framework and is in Python.
- Caffe. Focused on computer vision and recognition.
- DL4J. Deep learning for java also work in Scala
There a zillion tutorials out there as well:
- MSDN on Machine learning and computer vision