I am wondering what (qualitative) sense one can make from PCA and t-SNE plots of weights in a neural network.

I'm training a neural network that regresses five different control values, including a position (X, Y) and an angle (sin, cos), from an image - think of it as trying to determine how to orient a robotic arm. The last layer maps 64 weights to these five values (2x 2D, 1x 1D). In case it matters: No dropout is used for the network, the activations are ReLU-like (MPELU to be exact).

Since I'm working with TensorFlow, I can use TensorBoard's Embeddings view to display these weights using either PCA or t-SNE. Both variants end up mapping the weights sort-of spherical, so PCA to three dimensions results in a sphere and t-SNE to two dimensions results in a disc - it looks like this:

The PCA with three principal components, describing 70% of the total variance (it looks similar from all perspectives):

3D PCA, variance described: 70%

The PCA with two principal components, describing 50% of the total variance:

2D PCA, variance described: 50%

The t-SNE embedding (30k iterations, perplexity 5, learning 0.01), describing whatever t-SNE describes:

t-SNE embeddings

Now in the regressed results there are two pairs of values (X/Y and sin/cos) that do tend to be correlated and in earlier versions of the network, when I was regressing angles only, approximately half of the values were close to each other, while both halves (one for the sine, one for the cosine) were dissimilar in both PCA and t-SNE. Given this, I would expect to see a hint of three or five clusters of values. Instead, the values appear to be well distributed across the embedding space.

Given that t-SNE tries to move points close together in low-dimensional space that are close together in high-dimensional space, seeing it sort-of form a circle over all the iterations appears to indicate that all the values are indeed somewhat related.

Can you give me an idea of what can be read out of these graphs? Is there some qualitative judgement that can be made?



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