What is the difference between an Embedding Layer and a Dense Layer?

Question

The docs for an Embedding Layer in Keras say:

Turns positive integers (indexes) into dense vectors of fixed size. eg. [[4], [20]] ->

Answer 1

An embedding layer is faster, because it is essentially the equivalent of a dense layer that makes simplifying assumptions.

Imagine a word-to-embedding layer with these weights:

w = [[0.1, 0.2, 0.3, 0.4],
     [0.5, 0.6, 0.7, 0.8],
     [0.9, 0.0, 0.1, 0.2]]

A Dense layer will treat these like actual weights with which to perform matrix multiplication. An embedding layer will simply treat these weights as a list of vectors, each vector representing one word; the 0th word in the vocabulary is w[0], 1st is w[1], etc.

---

For an example, use the weights above and this sentence:

[0, 2, 1, 2]

A naive Dense-based net needs to convert that sentence to a 1-hot encoding

[[1, 0, 0],
 [0, 0, 1],
 [0, 1, 0],
 [0, 0, 1]]

then do a matrix multiplication

[[1 * 0.1 + 0 * 0.5 + 0 * 0.9, 1 * 0.2 + 0 * 0.6 + 0 * 0.0, 1 * 0.3 + 0 * 0.7 + 0 * 0.1, 1 * 0.4 + 0 * 0.8 + 0 * 0.2],
 [0 * 0.1 + 0 * 0.5 + 1 * 0.9, 0 * 0.2 + 0 * 0.6 + 1 * 0.0, 0 * 0.3 + 0 * 0.7 + 1 * 0.1, 0 * 0.4 + 0 * 0.8 + 1 * 0.2],
 [0 * 0.1 + 1 * 0.5 + 0 * 0.9, 0 * 0.2 + 1 * 0.6 + 0 * 0.0, 0 * 0.3 + 1 * 0.7 + 0 * 0.1, 0 * 0.4 + 1 * 0.8 + 0 * 0.2],
 [0 * 0.1 + 0 * 0.5 + 1 * 0.9, 0 * 0.2 + 0 * 0.6 + 1 * 0.0, 0 * 0.3 + 0 * 0.7 + 1 * 0.1, 0 * 0.4 + 0 * 0.8 + 1 * 0.2]]

=

[[0.1, 0.2, 0.3, 0.4],
 [0.9, 0.0, 0.1, 0.2],
 [0.5, 0.6, 0.7, 0.8],
 [0.9, 0.0, 0.1, 0.2]]

---

However, an Embedding layer simply looks at [0, 2, 1, 2] and takes the weights of the layer at indices zero, two, one, and two to immediately get

[w[0],
 w[2],
 w[1],
 w[2]]

=

[[0.1, 0.2, 0.3, 0.4],
 [0.9, 0.0, 0.1, 0.2],
 [0.5, 0.6, 0.7, 0.8],
 [0.9, 0.0, 0.1, 0.2]]

So it's the same result, just obtained in a hopefully faster way.

---

The Embedding layer does have limitations:

• The input needs to be integers in [0, vocab_length).
• No bias.
• No activation.

However, none of those limitations should matter if you just want to convert an integer-encoded word into an embedding.