Embeddings

Imagine you're developing a food-recommendation application, where users input their favorite meals, and the app suggests similar meals that they might like. You want to develop a machine learning (ML) model that can predict food similarity, so your app can make high quality recommendations ("Since you like pancakes, we recommend crepes").

To train your model, you curate a dataset of 5,000 popular meal items, including borscht, hot dog, salad, pizza, and shawarma.

Figure 1. A set of illustrations of five food items. Clockwise from top-left: borscht, hot dog, salad, pizza, shawarma.
Figure 1. Sampling of meal items included in the food dataset.

You create a meal feature that contains a one-hot encoded representation of each of the meal items in the dataset.

Figure 2. Top: a visualization of the one-hot encoding for borscht. The vector [1, 0, 0, 0, ..., 0] is displayed above six boxes, each aligned from left to right with one of the vector numbers. The boxes, from left to right contain the following images: borscht, hot dog, salad, pizza, [empty], shawarma. Middle: a visualization of the one-hot encoding for hot dog. The vector [0, 1, 0, 0, ..., 0] is displayed above six boxes, each aligned from left to right with one of the vector numbers. The boxes have the same images from left to right as for the borscht visualization above. Bottom: a visualization of the one-hot encoding for shawarma. The vector [0, 0, 0, 0, ..., 1] is displayed above six boxes, each aligned from left to right with one of the vector numbers. The boxes have the same images from left to right as for the borscht and hot dog visualizations.
Figure 2. One-hot encodings of borscht, hot dog, and shawarma. Each one-hot encoding vector has a length of 5,000 (one entry for each menu item in the dataset). The ellipsis in the diagram represents the 4,995 entries not shown.

Pitfalls of sparse data representations

Reviewing these one-hot encodings, you notice two key problems with this representation of the data.

  • Number of weights. Large input vectors mean a huge number of weights for a neural network. With M entries in your one-hot encoding, and N nodes in the first layer of the network after the input, the model has to train MxN weights for that layer. A large number of weights causes further problems:
    • Number of datapoints. The more weights in your model, the more data you need to train effectively.
    • Amount of computation. The more weights, the more computation required to train and use the model. It's easy to exceed the capabilities of your hardware.
    • Amount of memory. The more weights in your model, the more memory that is needed on the accelerators that train and serve it. Scaling this up efficiently is very difficult.
    • Difficulty of supporting on-device machine learning (ODML). If you're hoping to run your ML model on local devices (as opposed to serving them), you'll need to be focused on making your model smaller, and will want to decrease the number of weights.
  • Lack of meaningful relations between vectors. The vector values in the one-hot encodings for food don't provide any meaningful information about the similarity of food items. Mathematically, index 1 ("hot dog") is closer to index 2 ("salad") than to index 4999 ("shawarma"), even though a hot dog is more similar to shawarma (both contain meat and bread) than to salad.

In this module, you'll learn how to create embeddings, lower-dimensional representations of sparse data, that address both these issues.

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Translating to a lower-dimensional space (15 min)