Exploring the Softmax Function. Developing Intuition With the Wolfram Language

In machine learning, classification problems are often solved with neural networks which give probabilities for each class or type it is trained to recognize. A typical example is image classification where the input to a neural network is an image and the output is a list of possible things that image represents with probabilities.

The Wolfram Language (WL) comes with a large library of pre-trained neural networks including ones that solve classification problems. For example, the built-in system function ImageIdentify uses a pre-trained network that can recognize over 4,000 objects in images.

Image by the author using a photo by James Sutton on Unsplash

*Side note: Because of the unique typesetting capabilities of the Wolfram notebook interface (such as mixing code with images), all code is shown with screen captures. A notebook with full code is included at the end of this story.*

You can use the underlying neural network directly to access the probabilities for each of the 4,000+ possible objects. Clearly “domestic cat” wins hands down in this case with a probability of almost 1. Other types of cat follow with lower probabilities. The result for “shower curtain” is probably because of the background of the image. Summing up all the 4,000+ probabilities gives the number 1.0.

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