Note: Leviathan is my take to make a drop in replacement of Attention models with similar performance. This whole idea occured to me while I was reading from a lot of domains and doing a ton of math.

Leviathan - Let’s modify and improve the Transformer model(from scratch).

Transformers have been the go-to architecture for modern deep learning stack from the moment they were introduced. They are quite powerful, and many successful architectures have been made from them which have been SOTA in their respective domain.

Tackling on changing the architecture of Transformers is a easy problem, and resources such as “Illustrated Transformers” have helped a lot deeply understand the intricacies of it. It is one thing to read the paper and do the math, and another to debug like a child. Fortunately, this was a problem that I’ve been thinking a lot about in the past, the implementation was a different beast. All that was left was running some experiments and comparing it to the transformer baseline.

I’ve tried to implement this model called “Leviathan” which is a modified version of Transformers that uses correlation score(an analogy taken from signal processing). The implementation can be found here, and here’s my reasoning on why I think it performs similar to Transformers.

Why Correlation ? I read somewhere that self-attention(simple scaled dot product attention) can be seen as a Graph Neural Network, where each token in the input sequence is a mode, and edges denote the relationship between each token, and that attention layers is a directed acyclic graph - which makes sense as different context gives different meanings to how different tokens are connected.

If we think of tokens as signals, attention can be used to capture long range dependencies in signals, and correlation is great when there is delay in the signals. Correlation, or to be more general, Cross Correlation is a more general way to find similarity between signals. Try thinking of dot product as basically just cross correlation with zero lag.

Suppose instead of a vanilla dot product, we used cross correlation - which ultimately uses a sliding window product, and now due to the “lag” in the tokens, there are effectively more nodes in the graph, which basically allows for more ways in which signals(tokens) can be connected. Having more nodes means we can learn rich features, as there are now more ways in which a bunch of tokens interact.

Architectural Design I wanted to have the correlation metric to be a drop in replacement to the scaled dot product attention. I tried to implement the algorithm using scipy signals module which looks something like this :

Instead of having Transformer architectures, I named my architecture with correlation scores as Leviathan. Leviathan language models are very similar to GPT2 in terms of implementation.

Experimentation Results Although I’m very much limited by the availability of GPU, (only having access to free tier GPUs in Colaboratory) I had to experiment with small models, and therefore the results might be underwhelming when compared to conventional approaches. However, I’ve kept track of some model statistics using Weights and Biases that can be found here.(this contains the negative log likelihood error, and we’ll do one for bits per char as well - which can be found here !) As far as general results go, for a small Leviathan model of around ~50K parameters on the tiny shakespeare dataset, the model logged validation loss from around 4 to 2.7 after 7500 epochs for a simple model with 2 heads and 512 context length(from 3.6 to 1.5 BPC in the same model, but for 6500 epochs(In the WANDB report, I accidently put the negative BPC, and realized only after complete training )). The training notebook can be found here.

What more do we need ? I did this project as I wanted to understand the attention mechanism in detail, and what better way to do it than dismantling it piece by piece and understanding each component. This project was also received very well within the github community, as it managed to get 8 stars and several discussions for which I’m really glad.

I want to continue to do more experimentd in this project as it was something that I really enjoyed(and also, a problem that really frustrated me(but in a good way)). I have thought of making a sparse Mixture of Experts language model based on Leviathan architectures (which can be found in the “future” folder in the git repository for the project).

Apart from that, I’ve also thought of making a separate architecture using Involution scores - which is basically a mix between attention and convolution. Involution is more effective and efficient than CNNs, and is much simpler than self-attention.