Rik Mulder | Searcharxiv

arXiv2025

Exact zero modes in interacting Majorana X- and Y-junctions

We report the emergence of exact zero modes in junctions of two, three and four short interacting Majorana wires, equivalent to a chain with an impurity bond, Y- and X- junctions respectively. These exact zero modes arise from incommensurate short-range correlations induced by interacting Majorana fermions and manifest as exact level crossings between in-gap states upon continuously tuning the interaction strength. In a junction of only two chains we report exact zero modes and parity switching as soon as the coupling between the chains across a junction is positive. Remarkably, for junctions with multiple chains the in-gap states group up into sets of parity pairs -- pairs of states with opposite parity and similar energies. We demonstrate that the formation of these parity pairs are always due to the effective interaction of the outer edges of the junction. The behavior within each pair can be efficiently described by two coupled chains. In the Y-junction, we detect four in-gap states (two parity pairs) that show exact zero modes not only within each pair but also between them. This is attributed to an additional Majorana fermion localized at the center of junction that is protected by symmetry. Therefore, coupling between the Majorana fermions at the outer edges of the junction is mediated by that in the center. We argue that this is a generic feature of junctions with an odd number of arms. In the X-junction we detect eight in-gap states (four parity pairs) that are the result of two Majorana degrees of freedom localized at the center of the junction. However, we demonstrate that, by contrast to the Y-junction, the appearance of Majorana fermions at the center of the X-junction is not protected and the interaction across the junction can be tuned to the point where there are only Majorana fermions localized at the four outer edges of the junction, forming four in-gap states.

cond-mat.str-el↗

arXiv2020

Optimising the Performance of Convolutional Neural Networks across Computing Systems using Transfer Learning

The choice of convolutional routines (primitives) to implement neural networks has a tremendous impact on their inference performance (execution speed) on a given hardware platform. To optimise a neural network by primitive selection, the optimal primitive is identified for each layer of the network. This process requires a lengthy profiling stage, iterating over all the available primitives for each layer configuration, to measure their execution time on the target platform. Because each primitive exploits the hardware in different ways, new profiling is needed to obtain the best performance when moving to another platform. In this work, we propose to replace this prohibitively expensive profiling stage with a machine learning based approach of performance modeling. Our approach speeds up the optimisation time drastically. After training, our performance model can estimate the performance of convolutional primitives in any layer configuration. The time to optimise the execution of large neural networks via primitive selection is reduced from hours to just seconds. Our performance model is easily transferable to other target platforms. We demonstrate this by training a performance model on an Intel platform and performing transfer learning to AMD and ARM processor devices with minimal profiled samples.

cs.LG↗