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I am wondering whether there is a general statement of the sort "earlier layers in neural networks learn more concepts/features than later layers" or the other way around.

The output layer not being taken into account, as it should learn as many concepts as there are classes (in a classification task).

Are there any resources or papers which tackled this questions, maybe in image classification?

thanks

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  • $\begingroup$ If you consider each node in a neural network as defining a concept/feature, this will depend very much on the architecture of the network. If your earlier layers have more nodes, they will be able to detect more distinct features, but that will be flipped if your later layers have more nodes. $\endgroup$ Jan 21 '20 at 14:46
  • $\begingroup$ Define concept/feature. Twenty lvl1 Conv2D may learn an edge orientation, maybe local texture each; a single lvl 50 filter may learn a car, or a face. What's counts as learning more features? $\endgroup$
    – jkm
    Jan 21 '20 at 15:03
  • $\begingroup$ I would not consider each node/neuron as a feature, since many neurons just capture noise and some learn the same concepts. That's a good point @jkm, I guess maybe something like (number of not noisy neurons)/(total number of neurons), and compute that for each layer? this would represent the intrinsic dimension of a layer $\endgroup$
    – Tom
    Jan 21 '20 at 15:10
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    $\begingroup$ This question is very closely related. stats.stackexchange.com/questions/344498/… $\endgroup$
    – Sycorax
    Jan 21 '20 at 15:17
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Lots of work have been carried out in this area, and in general I'd say your simplification holds true. A very good visual guide with discussion on how to actually visualize different nets is this website by Chris Olah and co-authors, which also includes an overview of other methods.

A nearly 10 years old paper on this is this classic by Lee et al.:

enter image description here

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Although not fully answering your question, I recommend looking at the paper Identity Crisis: Memorization and Generalization under Extreme Overparameterization by Zhang et al., 2019. They discuss differences in behavior of fully connected layers and convnets in terms of inductive biases towards generalization and memorization, but also examine how much do different layers learn depending on the depth of the network, see e.g. Figure 15 in the supplementary material:

Visualization the intermediate layers of CNNs with different number of layers. The frst column shows a randomly initialized 20-layer CNN (random shallower CNNs look similar to the truncation of this). The rest of the columns show the trained CNNs with various number of layers.

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