C++ Implemntation of MNIST

Here we describe a C++ implementation of the neural network (with hidden layer) for the MNIST digits.

• matrix.H

  This builds on the previous Matrix class by implementing additional operators, including an element-by-element multiplication (using the % operator) and multiplication by a scalar.

  Note

  This is the same operator that the armadillo library uses for element-by-element multiplication.

  The Matrix class also implements addition and subtraction of matrices and element-by-element addition / subtraction of a scalar, and the compound operators += and -=.

  Finally, an apply() method can be used to apply a function to a matrix on an element-by-element basis.

  For example:

  Matrix B{{1, 2}, {3, 4}};
  
  B.apply([](double x) -> double {return 2*x+1;});
  

• mnist.H

  This provides functions for reacting the test and training data sets (CSV files) as well as a MNISTDigit class that manages the data and representation for a single digit.

  For example, we the training set and look at the first digit as:

  auto training_set = mnist::read_training_set();
  training_set[0].display();
  

  This will display:

  
  
  
  
  
  
                  ▒▒▓ ▓██▒
            ░▓▓██████▓██▓░
         ░██████████░░░░
          ██████▓▓██
          ░▓▒███   ▓
             ▓█░
             ▒█▓
              ▓█░
               ██▓▒
               ░███▒
                 ▓██▒
                  ░██▓
                   ███░
                 ▒▓███
               ▒█████▓
             ▒█████▓░
           ░█████▓░
         ▓█████▓░
      ░▓██████▒
      ▒████▒▒
  
  
  

• neural_network.H

  This is the main network, which provides a NeuralNetwork class that manages the weights (including a single hidden layer).

• test_nn.cpp

  This is a test driver that first trains the network using the training set and then evaluates how we do by reporting the fraction of the test set we get correct.

  It will also display the first 10 digits we get wrong, along with our prediction and the right answer.

  Note

  This requires C++23, and should be compiled with optimization like:

  g++ -O3 -DNDEBUG -std=c++23 -o test_nn test_nn.cpp
  

  Note

  To run, the unzipped CSV files need to be in the same directory as the executable.