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This phrase is from the "Rethinking the Inception Architecture for Computer Vision" paper. it says :

  1. Higher dimensional representations are easier to process locally within a network. Increasing the activations per tile in a convolutional network allows for more disentangled features. The resulting networks will train faster.

What does the phrase

  1. Higher dimensional representations are easier to process locally within a network"

mean?

Does it simply mean, a higher representation is achieved more easily by having more feature-maps in a layer? again indicating, having lots of feature-maps per layer, (more width) is more beneficial?
If so, does the next part indicate the same thing where it says :

Increasing the activations per tile in a convolutional network allows for more disentangled features.

what does disentagled features mean in that regard?

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"Higher dimensional representation" refers to having more feature maps like you suggested (check the inception module proposed in figure 7).

As to what disentangled features mean, I believe they mean decorrelated: the more features (with different filters) the inception module extracts, the more and the faster the network learns. Because the network will have access to more information leading to detecting which features are salient earlier in the training.

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