Learn an amazing programming language as you build a neural network from scratch.

This workshop inspired this YouTube video series on learning APL with neural networks.


The aim of this workshop is to introduce people to the APL programming language, with the first contact geared towards building a neural network from scratch. It helps if the audience has some programming knowledge (in no programming language in particular) and has heard of neural networks a bit, but that is not necessary.

There are two reasons why I use neural networks to introduce APL to newcomers in this workshop:

  • for one, it is better to learn a language and build something with it instead of just going through all the built-ins that APL has to offer;
  • secondly, neural networks can be built on top of matrix algebra and such operations lend themselves naturally to APL.


The objective of the workshop is to make incremental improvements to a namespace that eventually contains enough functionality to create a neural network that can be trained on the MNIST data (mnistdata.rar) and classify handwritten digits.

That is, the neural network will receive input images like the ones below and should be able to identify the digit in the image.

MNIST image examples
Image by Josef Steppan, CC BY-SA 4.0 license

For that matter, here is the standard order in which things get done in the workshop (this lines up almost perfectly with the order in which objects appear in NeuralNets.apln):

  1. defining a dfn and writing glyphs in APL;
  2. go over the intuitive basics on neural networks;
  3. build an array of arbitrary shape with normally-distributed real numbers;
  4. build the random parameters for the network:
    • build the weight matrices;
    • build the bias column vectors;
  5. build an activation function (e.g. leaky ReLU);
  6. implement the forward pass;
  7. implement loss function;
  8. implement derivatives for backprop algorithm:
    • for the loss function;
    • for the activation function;
  9. go over the details of the backpropagation algorithm;
  10. implement the backwards pass;
  11. check the backward pass is in the correct direction;
  12. read MNIST data from a file;
  13. display some data;
  14. train the network on the MNIST training data;
  15. test the network on the MNIST testing data;

The number of people attending the workshop, their previous knowledge of APL and neural networks and other related factors impacts how much we manage to accomplish.

If the list is exhausted within the time allotted for the workshop, here's a couple of follow-ups with little opportunity cost to start:

  • writing a small function that takes a network and prints some digits and their classifications;
  • changing the loss function to something more appropriate to the task at hand, e.g. the cross-entropy measure;
  • learning about student-teacher models;


By the end of the workshop, attendees will have a (close to finished) neural network written in a programming language they probably never dealt with, APL.

Attendees will have dabbled for the first time with a purely array-oriented programming language and built a popular, modern-day machine learning model from scratch.

Finally, their own implementation of a neural network can be trained in less than 2 minutes to recognise handwritten digits with 89% accuracy (timed on my laptop). Here is an example of some drawn digits and the neural network's guesses.

             @@@                                   @@@                                              
            @@@@                                @@@@@@@@                                            
           @@@@       @                       @@@@@@@@@@            @@                @       @@    
           @@@       @@@@@@@@                @@@@@@@  @@@       @@@@@@@              @@       @@    
          @@@        @@@@@@@@@@@@@           @@@@@   @@@        @@@@@@@@            @@@      @@@    
         @@@@         @@@@@@@@@@@@@          @@@     @@@      @@@@    @@@          @@@      @@@     
         @@@            @@@@@@@@@@@                  @@@      @@@      @@@        @@@       @@@     
        @@@                   @@@@                  @@@@     @@@        @@       @@@        @@      
        @@@   @@@@           @@@@@                 @@@       @@@        @@@     @@@@       @@@      
       @@@   @@@@@@          @@@@@                @@@@      @@@        @@@@     @@@@       @@@      
       @@@  @@@@@@@          @@@@                 @@@@      @@@@    @@@@@@@      @@@@@    @@@       
       @@@ @@@@  @@         @@@@@                @@@@@       @@@@@@@@@@@@@        @@@@@@@@@@        
       @@ @@@@   @@         @@@@                @@@@@@@@      @@@@@@@@ @@@          @@@@@@@@        
       @@@@@@   @@@        @@@@@             @@@@@@@@@@@@@      @@     @@@               @@@        
       @@@@@@ @@@@@        @@@@@            @@@@@@@@  @@@@@@           @@                @@@        
        @@@@@@@@@@         @@@@            @@@@@@@      @@@@          @@@                @@         
        @@@@@@@@           @@@@           @@@@@@@         @@          @@                @@@         
          @@@@             @@@@          @@@@@@                      @@@                @@@         
                           @@@@          @@@@                        @@@                @@          
                           @@@@          @@@                         @@@               @@@          
                           @@@@                                      @@@               @@@          
                           @@@                                       @@@               @@           

guessing 6          guessing 7          guessing 2          guessing 9          guessing 4          


Here is what some people had to say about the contents of the workshop and the way I led it:

It was amazing what we did in just 2 hours [...] In the end I was tired but satisfied with, and fascinated by what I had learned and built.” – João Afonso

The best thing was to have this hands-on approach to learning a new programming language” – Carlos

I really enjoyed the simple and accessible way in which it was taught” – Anonymous

Past sessions

  • Impromptu 2-part workshop organised with a mathematics student union from my university, on the 14th and 21st of October of 2020.

Additional resources

Other than the code with the reference implementation (available in this GitHub repository), here are some links that might be useful:

  • A pdf version of the "Mastering Dyalog APL" book, and its online version (the online version is a work in progress);
  • The APL Orchard is a chat room where people from any APL level get together to talk about, teach and learn APL;
  • The APL Cart is the go-to place whenever you have a question of the form "How do I ___ in APL?";
  • The APL wiki has articles on everything that has to do with APL.

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