Quantum-inspired Complex Word Embedding

A challenging task for word embeddings is to capture the emergent meaning or polarity of a combination of individual words. For example, existing approaches in word embeddings will assign high probabilities to the words ”Penguin” and ”Fly” if they frequently co-occur, but it fails to capture the fact that they occur in an opposite sense - Penguins do not fly. We hypothesize that humans do not associate a single polarity or sentiment to each word. The word contributes to the overall polarity of a combination of words depending upon which other words it is combined with. This is analogous to the behavior of microscopic particles which exist in all possible states at the same time and interfere with each other to give rise to new states depending upon their relative phases. We make use of the Hilbert Space representation of such particles in Quantum Mechanics where we subscribe a relative phase to each word, which is a complex number, and investigate two such quantum inspired models to derive the meaning of a combination of words. The proposed models achieve better performances than state-ofthe-art non-quantum models on the binary sentence classification task

A Quantum Many-body Wave Function Inspired Language Modeling Approach

The recently proposed quantum language model (QLM) aimed at a principled approach to modeling term dependency by applying the quantum probability theory. The latest development for a more effective QLM has adopted word embeddings as a kind of global dependency information and integrated the quantum-inspired idea in a neural network architecture. While these quantum-inspired LMs are theoretically more general and also practically effective, they have two major limitations. First, they have not taken into account the interaction among words with multiple meanings, which is common and important in understanding natural language text. Second, the integration of the quantum-inspired LM with the neural network was mainly for effective training of parameters, yet lacking a theoretical foundation accounting for such integration. To address these two issues, in this paper, we propose a Quantum Many-body Wave Function (QMWF) inspired language modeling approach. The QMWF inspired LM can adopt the tensor product to model the aforesaid interaction among words. It also enables us to reveal the inherent necessity of using Convolutional Neural Network (CNN) in QMWF language modeling. Furthermore, our approach delivers a simple algorithm to represent and match text/sentence pairs. Systematic evaluation shows the effectiveness of the proposed QMWF-LM algorithm, in comparison with the state of the art quantum-inspired LMs and a couple of CNN-based methods, on three typical Question Answering (QA) datasets.Comment: 10 pages,4 figures,CIK

CNM: An Interpretable Complex-valued Network for Matching

This paper seeks to model human language by the mathematical framework of quantum physics. With the well-designed mathematical formulations in quantum physics, this framework unifies different linguistic units in a single complex-valued vector space, e.g. words as particles in quantum states and sentences as mixed systems. A complex-valued network is built to implement this framework for semantic matching. With well-constrained complex-valued components, the network admits interpretations to explicit physical meanings. The proposed complex-valued network for matching (CNM) achieves comparable performances to strong CNN and RNN baselines on two benchmarking question answering (QA) datasets

A remark on Berezin's quantization and cut locus

The consequences for Berezin's quantization on symmetric spaces of the identity of the set of coherent vectors orthogonal to a fixed one with the cut locus are stated precisely. It is shown that functions expressing the coherent states, the covariant symbols of operators, the diastasis function, the characteristic and two-point functions are defined when one variable does not belong to the cut locus of the other one.Comment: 8 pages, Latex2e, ams fonts, to appear in "Quantizations, Deformations and Coherent States", Edited by S. Twareque Ali, A. Odzijewicz and A. Strasburger, Proceedings of the XV Workshop on Geometric Methods in Physics, Bia\l owie\.{z}a, Poland, 1-7 july 1996, Rep. Math. Phys

The quantum chiral Minkowski and conformal superspaces

We give a quantum deformation of the chiral super Minkowski space in four dimensions as the big cell inside a quantum super Grassmannian. The quantization is performed in such way that the actions of the Poincar\'e and conformal quantum supergroups on the quantum Minkowski and quantum conformal superspaces are presented.Comment: 54 page