8 papers
Improving ML Attacks on LWE with Data Repetition and Stepwise Regression
Alberto Alfarano, Eshika Saxena, Emily Wenger +2
The Learning with Errors (LWE) problem is a hard math problem in lattice-based cryptography. In the simplest case of binary secrets, it is the subset sum problem, with error. Effec…
Transformers know more than they can tell -- Learning the Collatz sequence
François Charton, Ashvni Narayanan
We investigate transformer prediction of long Collatz steps, a complex arithmetic function that maps odd integers to their distant successors in the Collatz sequence ( $u_{n+1}=u_n…
Making Hard Problems Easier with Custom Data Distributions and Loss Regularization: A Case Study in Modular Arithmetic
Eshika Saxena, Alberto Alfarano, François Charton +3
Recent work showed that ML-based attacks on Learning with Errors (LWE), a hard problem used in post-quantum cryptography, outperform classical algebraic attacks in certain settings…
Learning Euler Factors of Elliptic Curves
Angelica Babei, François Charton, Edgar Costa +5
We apply transformer models and feedforward neural networks to predict Frobenius traces from elliptic curves given other traces . We train further models to predict $a_p…
PatternBoost: Constructions in Mathematics with a Little Help from AI
François Charton, Jordan S. Ellenberg, Adam Zsolt Wagner +1
We introduce PatternBoost, a flexible method for finding interesting constructions in mathematics. Our algorithm alternates between two phases. In the first ``local'' phase, a clas…
Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers
Alberto Alfarano, François Charton, Amaury Hayat
Despite their spectacular progress, language models still struggle on complex reasoning tasks, such as advanced mathematics. We consider a long-standing open problem in mathematics…