Do wide and deep networks learn the same things? | Hacker News Reader

Do wide and deep networks learn the same things?

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107 pointsMindGods22 comments

For more context to people, we have the universal approximation theorem for neural nets that basically says if a network is wide enough it can approximate anything (with at least 2 layers). So a lot of stuff was really wide. Then VGG[0] came out and showed that deep networks were very effective (along with other papers, things happen in unison. Leibniz and Newton). Then you get ResNets[1] with skip connections and move forward to today. Today we've started looking more at what networks are doing and where their biases lie. This is because we're running into some roadblocks with CNNs vs Transformers. They have different inductive biases. Vision transformers still aren't defeating CNNs, but they are close and it is clear they learn different things. So we're seeing more papers doing these types of analyses. ML will likely never be fully interpretable, but we're getting better at understanding. This is good because a lot of times picking your model and network architecture is more art than science (especially when choosing hyper parameters).

[0] https://arxiv.org/abs/1409.1556

[1] https://arxiv.org/abs/1512.03385

I would say AlexNet [1], rather than VGG, was the landmark paper that got the computer vision community to pay attention to deep learning, specifically by winning the 2012 imagenet competition by a large margin. Not that there weren't successes before (specifically, deep nets had also been getting traction in speech processing), and of course deep learning itself is much older than alexnet. But I think most people, specially in vision, would say the 2012 imagenet competition was the watershed moment for DL. By current standards it's not very deep, but at the time it was definitely "deeper"than the popular models at the time (which were mostly not neural networks).

VGG is also super influential of course -- it reinforced the trend towards ever deeper networks, which ResNet also took to another level.

[1] https://papers.nips.cc/paper/4824-imagenet-classification-wi...

AlexNet really highlighted the importance of convolutions (especially with respect to vision). I'm not disagreeing with you, but there's of course nuance. I thought VGG better highlighted the depth vs breadth argument whereas AlexNet was more CNN vs Linear.

Deep networks have also been shown to be universal, just FYI,

Oh yes, sorry if it gets interpreted otherwise. It is too late to edit for that clarity but thanks for the note.

Those are very interesting empirical results. This lecture explains the deeper vs shallow tradeoff theoretically: https://www.youtube.com/watch?v=qpuLxXrHQB4. He's an amazing lecturer; wish I didn't need subtitles!

(If you're too lazy to watch, it turns out that there exist functions that a shallow network can never approximate)

At first I thought this had something to do with the classic "breadth vs. depth" notion on learning stuff -- if you're preparing for the MCAT it is better to have breadth that covers all the topics than depth in one or two particulars for the exam, but this is actually just about the dimensions of the neural network used to create representations. Naturally, one would expect a "sweet spot" or series of "sweet spots."

From the paper at https://arxiv.org/pdf/2010.15327.pdf

> As the model gets wider or deeper, we seethe emergence of a distinctive block structure— a considerable range of hidden layers that have very high representation similarity (seen as a yellow square on the heatmap). This block structure mostly appears in the later layers (the last two stages) of the network.

I wonder if we could do similar analysis on the human brain and find "high representational similarity" for people who do the same task over and over again, such as play chess.

Also, I don't really know what sort of data they are analyzing or looking at with these NN, maybe someone with better scansion can let me know?

Haven't read thoroughly but it seems they are investigating ResNet models [0] trained for image classification.

> We apply CKA to a family of ResNets of varying depths and widths, trained on common benchmark datasets (CIFAR-10, CIFAR-100 and ImageNet)

[0] https://arxiv.org/abs/1512.03385

iirc, the human neocortex is only 6 layers deep with some interesting vertical connection structures, perhaps similar to skip connections in NN.

It would be interesting to see where the deep vs wide analysis ends up when many problem types are used. Can a single network be trained on multiple problems at once and perform well on all?

Each cortical area has six layers, but most behaviors require interactions between many cortical areas, so "input" passes through many more than six layers before it produces an output.

Felleman and Van Essen is a classic paper on the organization of the visual system. Figure 2 (p. 4) might give you good sense for how much of the brain it occupies and Figure 4 (p. 30) is the well-known "wiring diagram.

In the 30 years since that paper was written, we've found a few more boxes and a lot more wires! We've also come to appreciate that there are lots of recurrent loops. V1 -> V2 is one of the biggest connections in the brain, V2 -> V1 is a near runner up.

https://cogsci.ucsd.edu/~sereno/201/readings/04.03-MacaqueAr...

Indeed, there are many "horizontal" and recurrent connections and simply thinking of it as a 6 layer feed forward network is a gross oversimplification. It's more like a complex network of complex networks... of the spiking variety

Yup, and that’s just the “classical” synaptic transmission.

Mixed in with that, there is also slower signaling via neuromodulators (dopamine, norepinephrine etc), neuroendocrine system, and God only knows whatever the astrocytes are doing. Every neuron has its own internal dynamics too, over scales ranging from milliseconds (channel inactivation) to hours or days (receptor internalization).

There’s even the possibility of “ephaptic coupling”, wherein the electric fields produced by some neurons affect the activity of others, without making any sort of direct contact. We’ve collected some of the stronger data in favor of that possibility and yet I remain firmly in denial because it would make the brain so absurdly complicated.

Did you see the FPGA which had an "ineffectual" circuit created while using Evolution Algo to optimize design for calculating integrals? Turns out it wasn't ineffectual but had EM effects between circuits that the calculation required!

I would not be surprised if the brain did similar things, especially given that light and magnets are causing effects in various studies.

Yes! It's wild!

That's sorta what might be happening in the brain. I do brain stimulation experiments where we generate electric fields in the brain by passing currents across the scalp: 0.5 V/m or so (which you get by putting 1-2 mA across the scalp) is enough to do some really wild things to neurons, even in a big primate head. This is cool, and potentially useful for various kinds of rehab/neuroprosthetics/etc.

The crazier thing is that the neurons themselves generate much stronger electric fields themselves (~10x stronger, in some parts of the brain). Whether those fields are actively used or merely "tolerated" is hard to say but....woah.

There's a lot of differences between the mainstream CNNs and biological NNs though. For one, inference in most CNNs is just feed-forward, whereas in the brain the information flow is a lot more complex, modulated by all sorts of feedback loops as well as a dynamic state given by memory, expectation, attention, etc. Biological neurons are also a lot more complicated (and diverse) than the artificial ones. So those six layers aren't really very comparable to six layers in a typical modern CNN.

Of course, I'm talking about just the typical current day CNN. There's a lot of ongoing work in recurrent neural nets, memory for neural nets, attention (though the idea of "attention" that is hot right now is quite simplified compared to what we usually call attention), etc.

I'm not sure what skip connections are, but I think I have a good guess as to what they are.

I've wanted to try a neural network where the output of every layer goes into every subsequent layer. Each layer would thus provide a different perspective to subsequent layers.

Anyone know if this has been tried?

Densely Connected Convolutional Networks (https://arxiv.org/abs/1608.06993) use the idea you're talking about quite effectively.

Yeah. That seems like exactly what I was describing. Thanks.

Have a look at AlphaStar, it's a pretty interesting network of networks that has some skip functionality.

The DeepMind lecture series on YouTube is pretty great.

You'd likely overdue it with skips everywhere, too many connections to learn and backprop on that learning would likely be difficult

That sounds fascinating. When talking about something as complex and interconnected as a human neocortex, what does "only 6 layers deep" mean?

If you look at a slice of cortex under the microscope, there appear to be six physical layers (like a cake), owing to the different types, numbers, and arrangement of neurons in each.

Canonically, the cortex is built out of columns, each of which repeat the same motif. Within a cortical column, signals enter a cortical region through layer IV, 'ascend' to other cortical areas via Layers II and III, and project elsewhere in the brain via Layer V/VI. Layer I mostly contains passing fibers going elsewhere. There are also "horizontal" or lateral connections between and within columns.

This is sort of an abstraction though. It's often hard to clearly delineate the boundary between Layer II and III. Layer IV of primary visual cortex has many small sublayers (4C alpha), but it's very very small in others.

So, it seems like the "blocks" they're talking about are basically redundancies, duplicated logic. It makes sense to me that since they provide the same functionality, how or how these duplicates exist doesn't matter. But I'm an amateur

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