A Quantum Many-body Wave Function Inspired Language Modeling Approach

[flrngel]

Abstract

• quantum probability theory
• quantum-inspired LMs have two limitations
  • not taken into account interaction among the words with multiple meanings
  • lacking theoretical foundation accounting for effective training parameters
• QMWF
  • can adopt the tensor product to model which interactions mong words

1. Introduction

• two LM approaches
  • classical
  • increase the number of parameters to be estimated for compound dependencies
  • quantum inspired
  • estimates density matrix
  • encodes both single words and compound words (QLM)
• QLM and NNQLM
  • end-toend neural network structure
  • are not modeled to complex interaction among words with multiple meanings
  • no principled manner
• QWMF
  • the wave function can model the interaction among many spinful particles
  • convolutional neural network architecture can be mathematically derived in quantum-inspired language modeling approach
  • outperforms quantum LM counterparts (QLM, NNQLM)

In this paper,

1. propose Quantum Many-body Wave Function based Language Modeling approach
   • able to represent complex interaction among words
2. show fundamental connection between QMWF and CNN
3. performance checking with QA datasets

2. Quantum Preliminaries

2.1. Basic notation and concepts

2.2. Quantum Many-body Wave Functions

3. Quantum many-body wave function inspired language modeling

3.1. Basic intuitions and architecture

• QMWF representation can model probability distribution of compound meanings
  • depends on basis vectors

3.2. Language representation and projection via many-body wave function

• Local representation by product state
• Global representation for all possible compound meanings

3.3. Production realized by convolutional neural network

6. Experiments

My notes

• Can we think that QMWF is generalized version of attention mechanism?
  • sum of a_i^2 is 1
  • M = 1?