We apply one-dimensional convolutional neural networks to the Frobenius traces of elliptic curves over $\mathbb{Q}$ and evaluate and interpret their predictive capacity. In keeping with similar experiments by Kazalicki--Vlah, Bujanović--Kazalicki--Novak, and Pozdnyakov, we observe high accuracy predictions for the analytic rank across a range of conductors. We interpret the prediction using saliency curves and explore the interesting interplay between murmurations and Mestre--Nagao sums, the details of which vary with the conductor and the (predicted) rank.

Self-attention architectures, which are rapidly pushing the frontier innatural language processing, demonstrate asurprising depth-inefficient behavior: previous works indicate that increasing the internal representation (network width) isjust as useful as increasing the number of self-attention layers (network depth).

However,maximum-marginclassifiers areinherently robusttoperturbations ofdata at prediction time, and this implication is at odds with concrete evidence that neural networks, in practice, are brittle toadversarial examples [71]and distribution shifts [52,58,44,65]. Hence, the linear setting, while convenient to analyze, is insufficient to capture the non-robustness of neural networkstrainedonrealdatasets.Goingbeyondthelinearsetting,severalworks[ 1,49,74]arguethat neuralnetworksgeneralize wellbecause standard training procedures haveabiastowardslearning

In Algorithm 1 we give the full clustering algorithm used for each of the T fixing iterations. In Figure 1 we show how the layers' In Figure 2 we show the impact of increasing the regularisation strength.