I think one of the best things to learn from Schmidhuber is that progress involves a lot of players and over a lot of time. Attribution is actually a difficult game and usually we are only assigning credit to those at the end of some milestone. It's like giving a gold medal to the runner in the last leg of a relay race or focusing only on the lead singer of a band. It's never one person that does it alone. Shoulders of giants, but those giants are just a couple of dudes in a really big trenchcoat.

Another important lesson is that often good ideas get passed over because of hype or politics. We often like to pretend that science is all about the merit and what is correct. Unfortunately this isn't true. It is that way in the long run, but in the short run there's a lot of politics and humans still get in their own way. This is a solvable problem, but we need to acknowledge it and create systematic changes. Unfortunately a lot of that is coupled to the aforementioned one.

  > I do respect the extent to which he continues his credit-attribution crusade even to his own reputational detriment.

> That said, I do respect the extent to which he continues his credit-attribution crusade even to his own reputational detriment.

Lol, I still used to notice him before covid when he was railing against Bengio, Hinton, and LeCun. Can't believe he's still going.

That's a cool paper. Super interesting to see how work was progressing at the time, when Convex was the machine everybody wanted on (or rather next to) their desks.

For residual networks with an infinite number of layers it is absolutely correct. For a residual network with finite layers, you can get away with any non zero constant weight as long as the weight chosen appropriately for the fixed network depth. The problem is simply c^n gives you very big or very small numbers for large n and large deviations from 1.

Now let me address the other possibility that you are talking about: what if residual connections aren't necessary? What if there is another way? What are the criteria necessary to avoid exploding or vanishing gradient or slow learning in the absence of both?

For that we need to first know why residual connections work. There is no way around calculating the back propagation formula by hand, but there is an easy trick to make it simple. We don't care about the number of parameters in the network, we only care about the flow of the gradient. So just have a single input and output with hidden size 1 and two hidden layers.

Each layer has a bias and a single weight and an activation function.

Let's assume you initialize each weight and bias with zero. The forward pass returns zero for any input and the gradient is zero. In this artificial scenario the gradient starts vanished and stays vanished. The reason is pretty obvious when you apply back propagation. The second layer clips the gradient of the first layer. If there was a single layer, the gradient would be non zero and yield a non zero gradient, rescuing the network out of the vanishing gradient.

Now what if you add residual connections? The forward pass stays the same, but the backward pass changes for two layers and beyond. The gradient for the second layer consists of just the second layer activation function multiplied by the first layer activation of the forward pass. The first layer gradient consists of the second layer gradient where the first layer activation is substituted by the gradient of the first layer but because it is a residual net, you also add the gradient of just the first layer.

In other words, the first layer is trained independently of the layers that come after it, but also gets feedback from higher layers on top. This allows it to become non zero, which then lets the second layer become non zero, which lets the third be non zero and so on.

Since the degenerate case of a zero initialized network makes things easy to conceptualise, it should help you figure out what other ways there are to accomplish the same task.

For example, what if we apply the loss to every layer's output as a regularizer? That is essentially doing the same thing as a residual, but with skip connections that sum up the outputs. You could replace the sum with a weighted sum where the weights are not equal to 1.0.

But what if you don't want skip connections either, because they are too similar to residual networks? A residual network has one skip connection already and summing up in a different way is uninteresting. It is also too reliant on each layer being encouraged to produce an output that is matched against the label.

In other words, what if we wanted to let the inner layers not be subject to any correlation with the output data? You would need something that forces the gradients away from zero but also away from excessively high numbers. I.e. weight regularization or layer normalisation with a fixed non zero bias.

Predictive coding and especially batched predictive coding could also be a solution to this.

Predictive coding predicts the input of the next layer, so the only requirement is that the forward pass produces a non zero output. There is no requirement for the gradient to flow through the entire network.

Surely they wrote some papers in English even if they wrote their dissertation in German? Most people don’t go straight to dissertations anyway, it’s more of a place to go after you read a much shorter paper.

I think what you're referring to is also known as Stigler's law of eponymy [1], which is interestingly self-referential and ironic in its own naming. There's also the related "Matthew effect" [2] in the sciences.

[1] https://en.wikipedia.org/wiki/Stigler's_law_of_eponymy

[2] https://en.wikipedia.org/wiki/Matthew_effect

Perhaps then inventors of promising ideas should make multiple attempts at popularizing their ideas if they care about association, multiple attempts at explaining why the idea is important and demonstrations of killer applications.

Einstein published his relativity papers originally in German.

That's how all/most science normally works.

Conversely, a huge amount of science is just scientists going "here's something I found interesting" but no one can figure out what to do with it. Then 30 or 100 years go by and it's a useful in a field that didn't even exist at the time.