Softmax Function Explained In Depth with 3D Visuals

The softmax function is often used in machine learning to transform the outputs of the last layer of your neural network (the logits) into probabilities. In this video, I explain how the softmax function works and provide some intuition for thinking about it in higher dimensions. In addition to using the softmax function for classification, it’s also used in models that use attention, such as transformer models. The softmax function is very similar to the sigmoid function, except it’s generalized for higher dimensions, so if you’re also interested in learning more about the sigmoid function, check out my previous video about it linked below.

My previous video, "Why We Use the Sigmoid Function in Neural Networks for Binary Classification":
📼    • Why Do We Use the Sigmoid Function fo...  

My other video, "Derivative of Sigmoid and Softmax Explained Visually":
📼    • Derivative of Sigmoid and Softmax Exp...  

GitHub code for visualizing how the logit values that are passed into the softmax function change over time as the model is trained with SGD (stochastic gradient descent) or the Adam optimizer:
💻 https://github.com/elliotwaite/softma...

Desmos 2D graph of softmax for 4 classes:
📈 https://www.desmos.com/calculator/drq...

GeoGebra 3D graph of softmax for 2 classes (with derivatives and Gaussians):
📈 https://www.geogebra.org/classic/qhdd...

GeoGebra 3D graph of softmax for 3 classes (with derivatives):
📈 https://www.geogebra.org/classic/ps9g...

GeoGebra 3D graph of softmax with Gaussians for 3 classes:
📈 https://www.geogebra.org/classic/vgwa...

GeoGebra 3D graph of the shape of the softmax input space for 4 and 5 classes:
📈 https://www.geogebra.org/classic/emjn...

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