— Context —

Speaking about the transformer architecture, one may incorrectly talk about an encoder-decoder architecture. But this is *clearly* not the case.
The transformer architecture is an example of encoder-predictor-decoder architecture, or a conditional language-model.
The classical definition of an encoder-decoder architecture is the autoencoder (AE). The (blue / cold / low-energy) target y is auto-encoded. (The AE slides are coming out later today.)
Now, the main difference between an AE and a language-model (LM) is that the input is delayed by one unit. This means that a predictor is necessary to estimate the hidden representation of a *future* symbol.
It's similar to a denoising AE, where there is a temporal corruption.
We also saw how a conditional predictive energy based model includes an additional input x (in pink). The input x can be considered as “context” for the given prediction.
Now, putting the two things together, we end up with a 2×encoder-predictor-decoder type architecture.
This is what was going on in my mind when I was just trying to explain how the “encoder-decoder transformer architecture” was supposed to work. Well, it didn't make any sense. 🙄
For the part concerning the attention, you can find a summary below.
In addition to which, I've added the explicit distinction between self-attention (thinking about how to make pizza) and cross-attention (calling mom, asking for all her pizza recipes) slide.

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More from @alfcnz

23 Nov 20

Coming from engineering, I'm a former @MATLAB user, moved to @TorchML and @LuaLang, then to @PyTorch and @ThePSF @RealPython, and now I'm exploring @WolframResearch @stephen_wolfram.
For learning, one would prefer knowledge packed frameworks and documentation.
In that regard, @MATLAB and @WolframResearch are ridiculously compelling. The user manuals are just amazing, with everything organised and available at your disposal. Moreover, the language syntax is logical, much closer to math, and aligned to your mental flow.
In Mathematica I can write y = 2x (implicit multiplication), x = 6, and y will be now equal 12. y is a variable.
Or I can create a function of x with y[x_] := 2x (notice that x_ means I don't evaluate y right now). Later, I can execute y[x] and get 12, as above.
Read 7 tweets
31 Oct 20
This week we went through the second part of my lecture on latent variable 👻 energy 🔋 based models. 🤓

We've warmed up a little the temperature 🌡, moving from the freezing 🥶 zero-temperature free energy Fₒₒ(y) (you see below spinning) to a warmer 🥰 Fᵦ(y).
Be careful with that thermostat! If it's gonna get too hot 🥵 you'll end up killing ☠️ your latents 👻 and end up with averaging them all out, indiscriminately, ending up with plain boring MSE (fig 1.3)! 🤒
From fig 2.1–3, you can see how more z's contribute to Fᵦ(y).
This is nice, 'cos during training (fig 3.3, bottom) *The Force* will be strong with a wider region of your manifold, and no longer with the single Jedi. This in turns will lead to a more even pull and will avoid overfitting (fig 3.3, top). Still, we're fine here because z ∈ ℝ.
Read 6 tweets
21 Oct 20
This week we've learnt how to perform inference with a latent variable 👻 energy 🔋 based model. 🤓
These models are very convenient when we cannot use a standard feed-forward net that maps vector to vector, and allow us to learn one-to-many and many-to-one relationships.
Take the example of the horn 📯 (this time I drew it correctly, i.e. points do not lie on a grid 𐄳). Given an x there are multiple correct y's, actually, there is a whole ellipse (∞ nb of points) that's associated with it!
Or, forget the x, even considering y alone…
there are (often) two values of y₂ per a given y₁! Use MSE and you'll get a point in the middle… which is WRONG.

What's a “latent variable” you may ask now.
Well, it's a ghost 👻 variable. It was indeed used to generate the data (θ) but we don't have access to (z).
Read 7 tweets
29 Apr 20
Graph Convolutional Networks… from attention!
In attention 𝒂 is computed with a [soft]argmax over scores. In GCNs 𝒂 is simply given, and it's called "adjacency vector".
Slides: github.com/Atcold/pytorch…
Notebook: github.com/Atcold/pytorch…
Summary of today's class.

Slide 1: *shows title*.
Slide 2: *recalls self-attention*.
Slide 3: *shows 𝒂, points out it's given*.
The end.

I've spent the last week reading everything about these GCNs and… LOL, they quickly found a spot in my mind, next to attention!
The key concept here is the *sparsity* (constraints) of the graph.
In self-attention, every element in the set looks at each and every other element.
If a sparse graph is given, we limit each element (node / vertex) to look only at a few other elements (nodes / vertices).
Read 6 tweets
22 Apr 20
“Set to set” and “set to vector” mappings using self/cross hard/soft attention. We combined a (two) attention module(s) with a (two) k=1 1D convolution to get a transformer encoder (decoder).
Slides: github.com/Atcold/pytorch…
Notebook: github.com/Atcold/pytorch…
This week's slides were quite dense, but we've been building up momentum since the beginning of class, 3 months ago.
We recalled concepts from:
• Linear Algebra (Ax as lin. comb. of A's columns weighted by x's components, or scalar products or A's rows against x)
• Recurrent Nets (stacking x[t] with h[t–1] and concatenating W_x and W_h)
• Autoencoders (encoder-decoder architecture)
• k=1 1D convolutions (that does not assume correlation between neighbouring features and act as a dim. adapter)
and put in practice with @PyTorch.
Read 9 tweets
15 May 18
Impressive, especially the TikZ diagrams 🙇‍♂️
Would you mind using $\mathbb{R}$ for the blackboard R?
Thanks for using $\bm{}$ for vectors and $^\top$ for the transposition.
What about $\mathbb{I}$ for the identity matrix?
Use $\varnothing$ instead of $\emptyset$?
Also, isn't the gradient (column vector) the transposed of the Jacobian (row vector)?
What about having the differential operator d upright, and not like a variable?
Figure 5.6 uses bold upright font, instead of the italic one.
Read 6 tweets

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