Related papers: Learning Euler Factors of Elliptic Curves

Given an elliptic curve $E$ over $\mathbb{Q}$ and non-zero integer $r$, the Lang--Trotter conjecture predicts a striking asymptotic formula for the number of good primes $p\leqslant x$, denoted by $\pi_{E,r}(x)$, such that the Frobenius…

We present a class of algorithms capable of directly training deep neural networks with respect to large families of task-specific performance measures such as the F-measure and the Kullback-Leibler divergence that are structured and…

We train artificial neural networks to distinguish the geometric phases of a set of bands in 1D photonic crystals. We find that the trained network yields remarkably accurate predictions of the topological phases for 1D photonic crystals,…

Let $E_1$ and $E_2$ be $\overline{\mathbb{Q}}$-nonisogenous, semistable elliptic curves over $\mathbb{Q}$, having respective conductors $N_{E_1}$ and $N_{E_2}$ and both without complex multiplication. For each prime $p$, denote by…

Unsupervised estimation of latent variable models is a fundamental problem central to numerous applications of machine learning and statistics. This work presents a principled approach for estimating broad classes of such models, including…

In this paper, we analyze the theta series associated to the quadratic form $Q(\mathbf{x}) := x_1^2 + x_2^2 + x_3^2 + x_4^2$ with congruence conditions on $x_i$ modulo $2, 3, 4$, and $6$. By employing special operators on modular,…

Pattern learning in an important problem in Natural Language Processing (NLP). Some exhaustive pattern learning (EPL) methods (Bod, 1992) were proved to be flawed (Johnson, 2002), while similar algorithms (Och and Ney, 2004) showed great…

We present a novel class of Physics-Informed Neural Networks that is formulated based on the principles of Evidential Deep Learning, where the model incorporates uncertainty quantification by learning parameters of a higher-order…

How can we explain the predictions of a black-box model? In this paper, we use influence functions -- a classic technique from robust statistics -- to trace a model's prediction through the learning algorithm and back to its training data,…

When neural networks are employed for high-stakes decision-making, it is desirable that they provide explanations for their prediction in order for us to understand the features that have contributed to the decision. At the same time, it is…

In this paper, we introduce an efficient method for computing curves minimizing a variant of the Euler-Mumford elastica energy, with fixed endpoints and tangents at these endpoints, where the bending energy is enhanced with a user defined…

In this paper, we propose a novel machine learning method based on an adaptive tensor neural network subspace for solving quasiperiodic elliptic problems. To this end, we first provide a theoretical analysis of the associated quasiperiodic…

Predicting the effects of physical perturbations on optical channels is critical for advanced photonic devices, but existing modelling techniques are often computationally intensive or require exhaustive characterisation. We present a novel…

Transfer learning enhances learning across tasks, by leveraging previously learned representations -- if they are properly chosen. We describe an efficient method to accurately estimate the appropriateness of a previously trained model for…

This paper provides additional results relevant to the setting, model, and estimators of Auerbach (2019a). Section 1 contains results about the large sample properties of the estimators from Section 2 of Auerbach (2019a). Section 2…

There is an ongoing debate on whether neural networks can grasp the quasi-regularities in languages like humans. In a typical quasi-regularity task, English past tense inflections, the neural network model has long been criticized that it…

Recent research suggests that the feed-forward module within Transformers can be viewed as a collection of key-value memories, where the keys learn to capture specific patterns from the input based on the training examples. The values then…

We use a supervised machine-learning model based on a neural network to predict the temporal and spectral intensity profiles of the pulses that form upon nonlinear propagation in optical fibers with both normal and anomalous second-order…

Transformer-based models generate hidden states that are difficult to interpret. In this work, we analyze hidden states and modify them at inference, with a focus on motion forecasting. We use linear probing to analyze whether interpretable…

We construct new families of elliptic curves over \(\FF_{p^2}\) with efficiently computable endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the same way as Gallant-Lambert-Vanstone (GLV) and…