If you think about it for some time then you’ll come to realise transformers are autoencoders on steroids. A small input space is expanded onto a big manifold and contracted again.
Now, suppose you want to impose a function to regulate the output of an autoencoder. It’s actually pretty obvious that you need exactly one layer to do so… f(manifold).
What you're suggesting seems to go implausibly far beyond what the paper says.
RL post-training alters the parameters of the transformer, while your f(manifold) idea seems to suggest that a new layer on top would suffice, no need to alter the transformer itself at all.
It would be extremely handy if that were so, but I'm guessing it isn't, or it would be the prevailing approach.
I might be misunderstanding your point but this conflates the distinguishing features of each. you mention expansion but autoencoders canonically compress their inputs. autoencoders have an explicit encoder and decoder. most transformers we interact with these days (LLMs) are decoder only. the manifold isn't typically something the model is applied to directly. we apply the function/model to the latent representations. those are what live on the manifold.
Now that’s interesting.. what exactly distinguishes latent representations and the manifold? IMHO, those are the same, and you’re constructing a piecewise function of the manifold itself. Decoders also produce manifolds much in the same way, with the distinction being that the encoder isn’t learned but static after initialisation. So fundamentally it is still DOING the same operation.
The latent representations of the data are like points on a surface. That surface is the manifold. We don't typically have the full manifold and can only sample points from it by embedding data into it.
Worth noting a different manifold "exists" after each transformation (e.g. layer). You only sample from the same manifold when you apply the same transformation(s).
Took me a short time to understand what you mean with "autoencoders on steroids", but I believe you mean they are autoencoders with an inverse bottleneck - an intermediate representation that isn't smaller, but that's much larger than the input space. Is my understanding of your comment correct?
Kind of. Autoencoders don’t need to have an embedding that’s smaller than the input. Their only requirement is that they compress information and thus create reconstruction loss. Typically however they are not trained this way because they don’t converge.. transformers do the same thing, but they can squeeze much more bits of information through one pass because the way they are designed. This holds true even for decoder only networks because they’re still doing the same thing
If you think about it for some time then you’ll come to realise transformers are autoencoders on steroids. A small input space is expanded onto a big manifold and contracted again. Now, suppose you want to impose a function to regulate the output of an autoencoder. It’s actually pretty obvious that you need exactly one layer to do so… f(manifold).
What you're suggesting seems to go implausibly far beyond what the paper says.
RL post-training alters the parameters of the transformer, while your f(manifold) idea seems to suggest that a new layer on top would suffice, no need to alter the transformer itself at all.
It would be extremely handy if that were so, but I'm guessing it isn't, or it would be the prevailing approach.
I might be misunderstanding your point but this conflates the distinguishing features of each. you mention expansion but autoencoders canonically compress their inputs. autoencoders have an explicit encoder and decoder. most transformers we interact with these days (LLMs) are decoder only. the manifold isn't typically something the model is applied to directly. we apply the function/model to the latent representations. those are what live on the manifold.
Now that’s interesting.. what exactly distinguishes latent representations and the manifold? IMHO, those are the same, and you’re constructing a piecewise function of the manifold itself. Decoders also produce manifolds much in the same way, with the distinction being that the encoder isn’t learned but static after initialisation. So fundamentally it is still DOING the same operation.
The latent representations of the data are like points on a surface. That surface is the manifold. We don't typically have the full manifold and can only sample points from it by embedding data into it.
Worth noting a different manifold "exists" after each transformation (e.g. layer). You only sample from the same manifold when you apply the same transformation(s).
Took me a short time to understand what you mean with "autoencoders on steroids", but I believe you mean they are autoencoders with an inverse bottleneck - an intermediate representation that isn't smaller, but that's much larger than the input space. Is my understanding of your comment correct?
Kind of. Autoencoders don’t need to have an embedding that’s smaller than the input. Their only requirement is that they compress information and thus create reconstruction loss. Typically however they are not trained this way because they don’t converge.. transformers do the same thing, but they can squeeze much more bits of information through one pass because the way they are designed. This holds true even for decoder only networks because they’re still doing the same thing