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barrista   - a Python interface to Berkeley Caffe.
Berkeley Caffe   - a framework for convolutional neural network algorithms
BigDL   - Distributed Deep learning Library for Apache Spark
Caffe 2   - a Lightweight, Modular, and Scalable Deep Learning Framework
Catalyst   - High-level utils for PyTorch DL & RL research. It was developed with a focus on reproducibility, fast experimentation and code/ideas reusing.
Chainer   - Flexible neural network (NN) framework. See, also the main website.
cuda-convnet   - a fast C++/CUDA implementation of convolutional (or more generally, feed-forward) neural networks. It can model arbitrary layer connectivity and network depth.
DeepLearn toolbox   - Matlab/Octave toolbox for deep learning.
deeplearning4j: Deep learning for Java  
DIGITS: an interactive training system from NVIDIA  
DJL   - Amazon's deep Java library
DSSTNE   - Amazon DSSTNE (pronounced "Destiny") is an open source software library for training and deploying deep neural networks using GPUs.
DyNET   - Dynamic neural network library
Gorgonia   - deep learning package for GoLang.
H2O   - Open Source Fast Scalable Machine Learning Platform For Smarter Applications: Deep Learning, Gradient Boosting & XGBoost, Random Forest, Generalized Linear Modeling (Logistic Regression, Elastic Net), K-Means, PCA, Stacked Ensembles, Automatic Machine Learning (AutoML), etc.
Keras  Theano-based Deep Learning library
Lasagne  a lightweight library to build and train neural networks in Theano.
Microsoft CNTK   - (Computational Network Toolkit by Microsoft Research) a unified deep-learning toolkit that describes neural networks as a series of computational steps via a directed graph. It implements stochastic gradient descent (SGD, error backpropagation) learning with automatic differentiation and parallelization across multiple GPUs and servers.
MXNET   - Lightweight, Portable, Flexible Distributed/Mobile Deep Learning with Dynamic, Mutation-aware Dataflow Dep Scheduler; for Python, R, Julia, Scala, Go, Javascript and more.
NEON   - NErvana's pythON based Deep Learning Framework.
Neural Network Libraries by Sony   - Efficient and flexible C++ neural net libraries (dynamic graphs are supported)
NeuralTalk2   - contains Python+numpy source code for learning Multimodal Recurrent Neural Networks that describe images with sentences.
NNVM   - Open Compiler for AI Frameworks.
OpenSeq2Seq   - Toolkit for efficient experimentation with various sequence-to-sequence models.
probtorch   - Probabilistic Torch is library for deep generative models that extends PyTorch.
Pyro   - Deep universal probabilistic programming with Python and PyTorch
Pytorch   - Tensors and Dynamic neural networks in Python with strong GPU acceleration.
Pytorch Ignite   - a high-level library to help with training neural networks in PyTorch.
tensorflow   - Open source software library for numerical computation using data flow graphs.
Veles   - Distributed platform for rapid Deep learning application development from Samsung.