Master Presentation: Jacob Toot
When:Tu 07-07-2026 11.00 a.m. - 12.00 p.m.Where:Feringa Building 5614.0102
Masterpresentation Jacob Toot
When:
7 juli 2026, 11:00Where:
FBG 5614.0102
Title:
Machine learning quasisymmetries
Abstract:
Symmetries are central in physics: exact symmetries generate conservation laws,
constrain interactions, and classify phases of matter. Symmetry breaking also proves to be an important instrument in many theories, showing that symmetries need not hold or be exact to be physically relevant. This raises
a broader question of whether approximate symmetries, named quasisymmetries throughout this thesis, can play an important role as do the
exact ones, and if so, what tools are needed to detect and characterise them. This thesis develops such tools by using cut-and-project
sets in one and two dimensions as a model of approximate translational
symmetry, and by applying machine-learning architectures to five tasks: classification,
parameter reconstruction, and continuation in 1D, and dimensional identification and
basis-vector reconstruction in 2D.
In 1D, a convolutional network separates cut-and-project sequences from
unrelated aperiodic sequences, but cannot distinguish rational-slope (periodic)
from irrational-slope (quasiperiodic) instances once noise is added, a limitation
expected for finite sequences. A neural spline
flow (NSF) recovers the generating slope and acceptance window from noisy
sequences at, and above, noise levels where an exact algorithmic model fails; multimodal
posteriors that appear at high noise are shown to correspond to regions with similar tile lengths. A gated recurrent unit
predicts the next tile correctly in 99.7% of cases and produces valid 150-step
continuations in 75% of rollouts, outperforming both transformer configurations
tested.
In 2D, a convolutional network identifies the parent-lattice dimension
N={4,…,9} of a rhombus tiling from its diffraction pattern at
89.4% accuracy. For N=5, an NSF conditioned on the diffraction pattern and an
edge-length histogram recovers the ten basis-vector components with
posteriors whose calibration remains stable under corruption of the vertex positions. Machine
learning can recognise, reconstruct and extend structure carrying approximate
translational symmetry from finite observations, but distinguishing true
quasiperiodicity from long-period periodicity remains fundamentally hard in noisy,
finite sequences.