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Convolutional neural networks

2017-11-10 — 2021-11-20

quality 3.2

Wherein Convolutional Neural Networks Are Presented as a Topology Whose Layers Are Constructed With Finite-Impulse-Response Filters and Pooling, Receptive Fields Are Computed for Analysis, and Activations Are Visualised as High-Rank Tensors With Exploitable Regularity.

machine learning
neural nets
signal processing
Figure 1

The network topology that more or less kicked off the current revolution in computer vision and thus the whole modern neural network craze.

Convolutional nets (convnets or CNNs to the suave) are well described elsewhere. I’m going to collect some choice morsels here. Classic signal processing baked into neural networks.

There is a long story about how convolutions naturally encourage certain invariances and symmetries, although AFAICT it’s all somewhat hand-wavey.

Generally uses FIR filters plus some smudgy “pooling”.

1 Visualising

Figure 2

Here is a visualisation of convolutions: vdumoulin/conv_arithmetic

Visualising the actual activations of a convnet is an interesting data visualisation challenge, since intermediate activations often end up being high-rank tensors, but they have a lot of regularity that can be exploited, so it feels like it should be feasible.

Figure 3: Terence Broad’s convnet visualizer

2 Connection to filter theory

TBC. For now, work it out from other signal processing link material.

3 Resnets

Interesting, and they pop up in fun places like Dynamical models of neural nets. TBD.

Figure 4

4 References

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Gonzalez. 2018. “Deep Convolutional Neural Networks [Lecture Notes].” IEEE Signal Processing Magazine.
Gu, Johnson, Goel, et al. 2021. “Combining Recurrent, Convolutional, and Continuous-Time Models with Linear State Space Layers.” In Advances in Neural Information Processing Systems.
Kipf, and Welling. 2016. “Semi-Supervised Classification with Graph Convolutional Networks.” In arXiv:1609.02907 [Cs, Stat].
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