The code in this repo evaluates the performance of transformer architectures on small, mathematical datasets. It is based on this paper. Even with these small datasets, you can see some strange generalization phenomena unique to the overparametrized regime. The first plot shows train/test accuracy over optimization steps for the modular subtraction data. After completely overfitting the training data, you see the test performance shoot up. For other datasets like composition of permutations, this jump happens order of magnitudes of steps after the neural net has memorized the training data and much more rapidly. There is not a precise theoretical explanation of this behavior, but current thinking suggests that some combination of weight decay and SGD's algorithmic regularization properties may force the training process towards a "smooth" interpolating solution, i.e. a flat local minimum, which has good generalization behavior. The second plot shows the well-documented double descent curve where test loss increases upto the interpolation threshold and then comes down.
It would be interesting to see the results as you increase the amount of noise in the training data. To run that analysis, change the outlier_size argument in the run_configs.yaml.
To train/test the models, run the main.py script. Settings are handled with hydra and you can add a custom yaml file to the config directory.