Why Does the Keras Dense Layer Preserve Dimensionality?

Keras Dense Layer Input Shape Conundrum

This question explores an apparent contradiction between Keras documentation and the behavior of its Dense layer. The documentation states that the Dense layer flattens its input before applying the dot product with its kernel. However, as the provided code snippet demonstrates, the output shape of the Dense layer does not seem to be flattened.

Understanding the Behavior

The key to resolving this discrepancy lies in understanding how the Dense layer is applied in Keras. Contrary to the documentation, the Dense layer actually operates on the last axis of the input tensor. Therefore, in the example code snippet, the Dense layer is applied to each column of the (2,3) input tensor, resulting in an output shape of (2, 4).

Implications and Side Notes

This behavior has significant implications:

• TimeDistributed(Dense(...)) and Dense(...) Equivalence: TimeDistributed(Dense(...)) and Dense(...) are now equivalent, as both apply the Dense layer to the last axis of the input tensor.
• Shared Weights Effect: Each unit in the Dense layer is connected to every element on the last dimension of the input with the same weights, resulting in a lower number of parameters compared to flattening.

Visual Illustration

The following visual illustration clarifies the behavior of the Dense layer:

[Image of a tensor with (2,3) shape and a Dense layer with 4 units applied to the last axis]

Each unit in the Dense layer is connected to every element in a column of the input tensor with the same set of weights. The result is an output tensor with a shape of (2, 4).

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