Google search popped out quite a few open source deep learning frameworks. Here is a collected list
Google TensorFlow
Theano
mxnet
keras
Pylearn2
Blocks
Lasagne
chainer
scikit-neuralnetwork
theano-lights
deepy
idlf
reinforce.js
opendeep
mxnet.js
CGT
Torch
Caffe
scikit-cuda
cuda4py
Which one can be implemented in a straight-forward way with Hadoop streaming and MapReduce?
Python is prefered, other languages can also be considered.
EDIT:
Currently I am mainly interested in Deep Reinforcement Learning and LSTM.
Deeplearning4j claims to be scalable on Hadoop and Spark: