This is a concise sigmoid nn over mnist in c for illustration/education purposes. 
Note that it's single core and doesn't have some basic features such as minibatch.

The only dependancies are libc. Assumed to be for x86 for loading mnist.

Fetch the MNIST dataset:
 curl -O http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz -O http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz -O http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz -O http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz
 gunzip *.gz

Compile:
  For optimized, use:
  gcc -lm -O3 -std=c99 -Wall -DNDEBUG sigmoid_mnist.c -o sigmoid_mnist

  For debug, use:
  clang -lm -DDEBUG -g -std=c99 -Wall sigmoid_mnist.c -o sigmoid_mnist_dbg

Run:
  ./sigmoid_mnist