Athis Osathapan | Searcharxiv

arXiv2024

All-loop group-theory constraints for four-point amplitudes of SU($N$), SO($N$), and Sp($N$) gauge theories

In the decomposition of gauge-theory amplitudes into kinematic and color factors, the color factors (at a given loop order $L$) span a proper subspace of the extended trace space (which consists of single and multiple traces of generators of the gauge group, graded by powers of $N$). Using an iterative process, we systematically construct the $L$-loop color space of four-point amplitudes of fields in the adjoint representation of SU($N$), SO($N$), or Sp($N$). We define the null space as the orthogonal complement of the color space. For SU($N$), we confirm the existence of four independent null vectors (for $L \ge 2$) and for SO($N$) and Sp($N$), we establish the existence of seventeen independent null vectors (for $L \ge 5$). Each null vector corresponds to a group-theory constraint on the color-ordered amplitudes of the gauge theory.

hep-th↗

arXiv2024

Moments of Clarity: Streamlining Latent Spaces in Machine Learning using Moment Pooling

Many machine learning applications involve learning a latent representation of data, which is often high-dimensional and difficult to directly interpret. In this work, we propose "Moment Pooling", a natural extension of Deep Sets networks which drastically decrease latent space dimensionality of these networks while maintaining or even improving performance. Moment Pooling generalizes the summation in Deep Sets to arbitrary multivariate moments, which enables the model to achieve a much higher effective latent dimensionality for a fixed latent dimension. We demonstrate Moment Pooling on the collider physics task of quark/gluon jet classification by extending Energy Flow Networks (EFNs) to Moment EFNs. We find that Moment EFNs with latent dimensions as small as 1 perform similarly to ordinary EFNs with higher latent dimension. This small latent dimension allows for the internal representation to be directly visualized and interpreted, which in turn enables the learned internal jet representation to be extracted in closed form.

hep-ph↗