Does Flatten or Reshape Precede a Keras Dense Layer with Multi-Dimensional Input?

Input Shape Error: Flatten vs. Reshape in Keras Dense Layer

In a typical Keras network, the Dense layer expects flattened input data with a single dimension. However, a common error arises when using the Dense layer with input data of higher dimensionality. This can lead to the following output:

<tf.Tensor 'dense_2/add:0' shape=(?, 2, 4) dtype=float32>

Understanding the Discrepancy

Contrary to the documentation, which states that high-dimensional input is flattened before applying the Dense layer, recent updates in Keras have changed this behavior. The layer is now applied independently to the last axis of the input tensor.

In the example above, the input shape is (2, 3). The Dense layer with 4 units is applied separately to each row, resulting in an output shape of (2, 4).

Implications and Considerations

This change has certain implications:

• Shared Weights: Each unit in the Dense layer is connected to the input with the same weights. This means that a Dense layer applied to multi-dimensional input effectively implements shared weights across rows.
• Equivalence with TimeDistributed: For time-series data, using TimeDistributed(Dense(...)) is now equivalent to Dense(...) for single-step prediction tasks.

A Visual Illustration

For a better understanding, consider the following illustration:

[Image of a diagram showing how a Dense layer is applied to a multi-dimensional input, with weights shared across rows]

Conclusion

To avoid the aforementioned error, ensure that the input to the Dense layer is flattened prior to application. Alternatively, embrace the new behavior of the Dense layer when dealing with multi-dimensional input, considering its implications and potential advantages for certain network architectures.

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