A Neural Network in 10 lines of CUDA C++ Code

Purpose: For education purposes only. The code demonstrates supervised learning task using a very simple neural network.

Reference: inspired by Andrew Trask‘s post.

The core component of the code, the learning algorithm, is only 10 lines:

The loop above runs for 50 iterations (epochs) and fits the vector of attributes X to the vector of classes y. I am going to use 4 records from Iris flower dataset. The attributes (X) are sepal length, sepal width, petal length, and petal width. In my example, I have 2 (Iris Setosa (0) and Iris Virginica (1)) of 3 classes you can find in the original dataset. Predictions are stored in vector pred.

Neural network architecture. Values of vectors W0, W1, layer_1 and pred change over the course of training the network, while vectors X and y must not be changed:

The size of matrix X is the size of the batch by the number of attributes.

Line 3. Finding the values of the hidden layer:

In order to calculate the hidden layer, first of all, we will need to multiply a 4 x 4 matrix X by a 4 x 4 matrix W0. Then, we will need to apply an activation function; in this case, we will use a sigmoid function.

A subroutine for matrix multiplication:

A subroutine for the sigmoid function:

Sigmoid function (red) and its first derivative (blue graph):
desmos-graph

Line 4. Finding the matrix with predictions pred. In order to do so, we will need to multiply a 4 x 8 matrix l1 by a 8 x 1 matrix W1. Then, we will need to apply an activation function:

 

Line 5. Determine the vector of prediction errors pred_d. First, subtract pred from y. Then, calculate sigmoid( pred ) and, finally, multiply (elementwise) the result of these two operations.

CUDA kernel which finds the difference between two matrices:

Elemetwise multiplicaton of two vectors:

Line 6. Back propagate the prediction errors to l_1_d. First, multiply pred_d by transposed W1. Then, calculate sigmoid( l1 ) and, finally, multiply (elementwise) the result of these two operations.

A subroutine that multiplies matrix by transposed matrix:

 

Line 7. Update weights W1 with the result of matrix multiplication of transposed l1 and pred_d:

This line computes weight updates. In order to do that, we need to perform matrix multiplication of transposed matrix X by matrix pred_delta.

 

Line 8. Update weights W0 with the result of matrix multiplication of transposed X and l_1_d:

 

Complete code:

Output:

Compile…

… and run

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How to install NVIDIA CUDA 8.0, cuDNN 5.1, TensorFlow, and Keras on Ubuntu 16.04

Please follow the instructions below and you will be rewarded with Keras with Tenserflow backend and, most importantly, GPU support.

The latest version of CUDA Toolkit you can download from here. It is also clear from that page which versions of Ubuntu are supported.

screen-shot-2017-07-10-at-1-02-15-am.png

The latest version of cuDNN you can download from here. TensorFlow, however, requires cuDNN 5.1 and GPU card with CUDA Compute Capability 3.0 or higher.

Step 1. Linux

Update apt repositories and install the linux -image-extra-virtual package.
This package includes the kernel module that’s required by the NVIDIA drivers.

sudo apt-get update
sudo apt-get install -y linux-image-extra-virtual

Install the version of the headers that matches the freshly installed kernel from the previous step.

sudo apt-get install linux-source linux-headers-`uname-r`
sudo reboot

Step 2. Python

Download (from here) and Install Anaconda Python 3.6 64 bit

chmod +x Anaconda3-4.4.0-Linux-x86_64.sh
sudo ./Anaconda3-4.3.1-Linux-x86_64.sh

Step 3. NVIDIA Drivers and CUDA

Blacklist Noveau which has a conflict with the NVIDIA Drivers

echo -e "blacklist nouveau\nblacklist lbm-nouveau\noptions nouveau modeset=0\nalias nouveau off\nalias lbm-nouveau off\n" | sudo tee /etc/modprobe.d/blacklist-nouveau.conf

Disable the Kernel Nouveau

echo options nouveau modeset=0 | sudo tee -a /etc/modprobe.d/nouveau-kms.conf
sudo update-initramfs -u
sudo reboot

Download the Installer and make it executable

chmod +x cuda_8.0.61_375.26_linux.run

Hit Ctrl + Alt + F1

Kill X server

sudo systemctl stop lightdm.service
sudo init 3

Run the Installer and accept the license agreement and install samples

sudo sh cuda_8.0.61_375.26_linux.run

Enable NVIDIA Driver

sudo modprobe nvidia

Restart X server

sudo service lightdm restart

Compile and run the deviceQuery sample from the CUDA distribution to validate the NVIDIA driver installation was successful.

cd /home/evg/NVIDIA_CUDA-8.0_Samples/1_Utilities/deviceQuery/
make ./deviceQuery

valid-results-from-sample-cuda-devicequery-program.png

Step 4. cuDNN v5.1 for CUDA 8.0

Download cuDNN

Unzip the .tar archive

tar -xzf cudnn-8.0-linux-x64-v5.1.tgz

Copy the cuDNN libraries and header file to the CUDA folders

sudo cp cuda/lib64/libcudnn* /usr/local/cuda/lib64
sudo cp cuda/include/cudnn.h /usr/local/cuda/include/
sudo chmod a+r /usr/local/cuda/lib64/libcudnn*

Add some environment variables

gedit ~/.bashrc

Insert the following lines and save the changes

export CUDA_HOME="/usr/local/cuda"
export LD_LIBRARY_PATH="/usr/local/cuda-8.0/lib64"
export PATH="/usr/local/cuda-8.0/bin:$PATH"

Enable changes in bashrc

source ~/.bashrc

Check if the environment variables contain the paths from the previous step

echo $CUDA_HOME
echo $PATH
echo $LD_LIBRARY_PATH

alias sudo='sudo env PATH=$PATH'

Step 5. Tensorflow

Create a conda environment named tensorflow to run a version of Python by invoking the following command:

conda create -n tensorflow

Activate the conda environment by issuing the following command:

source activate tensorflow

Issue a command of the following format to install TensorFlow inside your conda environment:

sudo pip install –ignore-installed –upgrade TF_PYTHON_URL where TF_PYTHON_URL is the URL of the TensorFlow Python package. For example, the following command installs the CPU-only version of TensorFlow for Python 3.6:

sudo pip install --ignore-installed --upgrade https://storage.googleapis.com/tensorflow/linux/gpu/tensorflow_gpu-1.1.0-cp36-cp36m-linux_x86_64.whl

Test Tensorflow

Invoke python from your shell as follows:

python

Enter the following short program inside the python interactive shell:

import tensorflow as tf
hello = tf.constant('Hello, TensorFlow!')
sess = tf.Session()
print(sess.run(hello))

Exit python interactive shell

exit()

Step 6. Keras

sudo pip install keras