Khurshed Fitter | Searcharxiv

arXiv2024

A Max-Flow approach to Random Tensor Networks

We study the entanglement entropy of a random tensor network (RTN) using tools from free probability theory. Random tensor networks are simple toy models that help the understanding of the entanglement behavior of a boundary region in the ADS/CFT context. One can think of random tensor networks are specific probabilistic models for tensors having some particular geometry dictated by a graph (or network) structure. We first introduce our model of RTN, obtained by contracting maximally entangled states (corresponding to the edges of the graph) on the tensor product of Gaussian tensors (corresponding to the vertices of the graph). We study the entanglement spectrum of the resulting random spectrum along a given bipartition of the local Hilbert spaces. We provide the limiting eigenvalue distribution of the reduced density operator of the RTN state, in the limit of large local dimension. The limit value is described via a maximum flow optimization problem in a new graph corresponding to the geometry of the RTN and the given bipartition. In the case of series-parallel graphs, we provide an explicit formula for the limiting eigenvalue distribution using classical and free multiplicative convolutions. We discuss the physical implications of our results, allowing us to go beyond the semiclassical regime without any cut assumption, specifically in terms of finite corrections to the average entanglement entropy of the RTN.

quant-ph↗

arXiv2024

Enhancing Context Through Contrast

Neural machine translation benefits from semantically rich representations. Considerable progress in learning such representations has been achieved by language modelling and mutual information maximization objectives using contrastive learning. The language-dependent nature of language modelling introduces a trade-off between the universality of the learned representations and the model's performance on the language modelling tasks. Although contrastive learning improves performance, its success cannot be attributed to mutual information alone. We propose a novel Context Enhancement step to improve performance on neural machine translation by maximizing mutual information using the Barlow Twins loss. Unlike other approaches, we do not explicitly augment the data but view languages as implicit augmentations, eradicating the risk of disrupting semantic information. Further, our method does not learn embeddings from scratch and can be generalised to any set of pre-trained embeddings. Finally, we evaluate the language-agnosticism of our embeddings through language classification and use them for neural machine translation to compare with state-of-the-art approaches.

cs.CL↗