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Differential Transformer

arxiv.org

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Re: Differential Transformer

#141

Post by sigmoid10 »

Imnimo wrote: post #108

I feel like I'm missing a key insight here. I understand the problem that regular softmax attention struggles to approach assigning zero attention to irrelevant stuff. And I get that having this subtraction formula makes it possible to assign exactly (or near) zero attention weight without having crazy outlier activations. But it seems like it also makes it very easy to have negative attention weight (which is equiva…

>I'm just struggling to build a picture of how exactly the network accomplishes this.

I mean, intuitively it would be trivial for the model to just optimise lambda to zero during training. Then you essentially have built a vanilla transformer with an overcomplicated parameter pruning mechanism. Pruning is already pretty well established in the literature as something that works surprisingly good for reducing parameter counts up to (hold on to your papers)... about 40%. In practice the model probably doesn't work exactly like that, but I wouldn't be surprised if it just approximates the normal transformer in the end anyways.

Re: Differential Transformer

#142

Post by kridsdale3 »

pizza wrote: post #53
freeqaz wrote: post #49

Earlier quoted context omitted.

I'm able to follow most of what you're saying. It's unclear to me what "convex hull" means though. Also, where is each softmax happening here? For each attention head?

O_i = softmax(...) * V_i and softmax is between 0 and 1, so O_i = alpha * V_i for some alpha between 0 and 1 so that makes it convex, and it makes the O_i just a shrunken version of V_i. Whereas if you have the diff of softmaxes, you get O_i = (alpha - beta) * V_i, which can range from -V_i to +V_i, so its output could rescale /or/ flip V_i. And yes this is happening in every head in parallel, then they get summed.

By simply inputting your comment in to 4o, with no other context about the paper, I was able to get a pretty good analysis of the dual-head concept's implications.

https://chatgpt.com/share/67058973-ba94-8008-bed7-c7f9d08dc5...

Re: Differential Transformer

#143

Post by blackbear_ »

nyrikki wrote: post #103
blackbear_ wrote: post #43

Earlier quoted context omitted.

With a single softmax you cannot predict exactly 0, but only very small numbers. When you have a large number of values to add up, this "poisons" the output with a lot of irrelevant stuff (the noise mentioned in the paper). To make things worse, low attention values will have very low gradient, thus needing a lot of weight updates to undo that kind of mistakes. On the other hand, subtracting the output of two softmax…

While I don't discount the value of this, can you expand on the meaning of your claim that it makes the model 'more expressive' Everything I am seeing in this paper is related to reduced size and noise, which implies a reduction in expressiveness. The improvement in needle and a haystack, benchmarks on multi-hop questions of in corpus data and multishot in-context learning points to this. This is a wonderful thing if…

What I meant is that by changing lambda each attention head is able to put its outputs in a subspace that is different than that of the other heads. This means that the outputs of different heads do not mingle with each other, and it's easier for the following layer to pick them apart. So I was thinking at increased expressiveness because the attention output can in principle cover a larger volume.

Maybe expressiveness is not the right term, or not the main consequence. I could imagine that having different subspaces like that also introduces a degree of robustness to out-of-distribution inputs, as this would make it harder for the outputs of one attention head to shift towards the in-distribution outputs of another head, and thus for the following layer to confuse them.

Re: Differential Transformer

#145

Post by kridsdale3 »

WithinReason wrote: post #87

We empirically find that the setting λᵢₙᵢₜ = 0.8 − 0.6 × exp(−0.3 · (l − 1)) works well in practice I wonder about the story behind that formula...

A whole lot of things are tuned optimally by rotating an analog dial until things look / sound right.

Re: Differential Transformer

#146

Post by mota7 »

pxdm wrote: post #45

What's the comparison with conventional attention using a more aggressive (lower temperature) softmax? I can imagine that for the multi-needle retrieval test this may also give a performance boost, although at some cost other more creative tasks.

I had the same thought: Just eye-balling the graphs, the result of the subtraction looks very close to just reducing the temperature.

They're effectively doing softmax with a fixed temperature, but it's unclear that this work is going to do better than just learning a per-head temperature parameter.

c.f. https://arxiv.org/abs/2010.04245 which shows an improvement by learning per-head temperature.

The other way to think about this is that it looks like a hacked-up kinda-sorta gated attention. If that's the case, then doing softmax(alphaq_1k_1^T - log_sigmoid(betaq_2k_2^T)) might be better? (where alpha,beta are learned temperatures).

Re: Differential Transformer

#147

Post by stellalo »

WithinReason wrote: post #87

We empirically find that the setting λᵢₙᵢₜ = 0.8 − 0.6 × exp(−0.3 · (l − 1)) works well in practice I wonder about the story behind that formula...

Looks like this makes (at least initially in training) the “negative” attention term smaller in the early layers (smaller l) compared to later layers (larger l). Which I guess makes sense: you probably want to attend a little bit to everything before concluding that it’s really a few spots you should look at.

(Although it seems the author do not discuss this choice anywhere in the paper?)

Re: Differential Transformer

#149

Post by michalsustr »

slashdave wrote: post #114

I don't get it. Arbitrary linear combinations are already accommodated via feed forward. What am I missing?

My hunch is that this effectively creates a differentiable minimax “search” “tree” that can be backpropagated through. Not a tree — a dag really — and not search, but learning. :)

Re: Differential Transformer

#150

Post by impossiblefork »

Grosvenor wrote: post #139
Imnimo wrote: post #108

I feel like I'm missing a key insight here. I understand the problem that regular softmax attention struggles to approach assigning zero attention to irrelevant stuff. And I get that having this subtraction formula makes it possible to assign exactly (or near) zero attention weight without having crazy outlier activations. But it seems like it also makes it very easy to have negative attention weight (which is equiva…

Regular softmax (and attention) has an error in it. softmax should be exp()/1+∑exp() Notice the 1 added to the denominator. The difference is at the negative limit, softmax can be 0, instead of some epsilon. The same could be done by adding an extra zero value in x. Downside is, you have to retrain your model from scratch to fix this.

I've tried that in a small transformer that I trained from scratch and it didn't really make any difference. I also made a version where I made this trainable somehow, probably by replacing the 1 with a constant associated with the layer, and that didn't make any difference either.

I didn't follow Miller's proposal quite as he wrote it though and I put the mechanism in all the layers rather than avoiding it at the end.

My test doesn't absolutely rule out usefulness-- there's always different ways of applying something, but I saw no indication of it.

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