# CNM: An Interpretable Complex-valued Network for Matching

arXiv: https://arxiv.org/abs/1904.05298 · HTML: https://mlsanity.com/paper/1904.05298/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2019.

## Built on by (most cited first, 13 of 13)

- [Explainable AI: current status and future directions](https://mlsanity.com/paper/2107.07045/) (2021)
- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [Quantum-Inspired Machine Learning: a Survey](https://mlsanity.com/paper/2308.11269/) (2023)
- [A Quantum Probability Driven Framework for Joint Multi-Modal Sarcasm, Sentiment and Emotion Analysis](https://mlsanity.com/paper/2306.03650/) (2023)
- [Quantum-Brain: Quantum-Inspired Neural Network Approach to Vision-Brain Understanding](https://mlsanity.com/paper/2411.13378/) (2024)
- [Procedural Adherence and Interpretability Through Neuro-Symbolic Generative Agents](https://mlsanity.com/paper/2402.16905/) (2024)
- [Quantum Cognitively Motivated Decision Fusion for Video Sentiment Analysis](https://mlsanity.com/paper/2101.04406/) (2021)
- [Quantum Natural Language Processing: A Comprehensive Review of Models, Methods, and Applications](https://mlsanity.com/paper/2504.09909/) (2025)
- [Adapting Pre-trained Language Models for Quantum Natural Language Processing](https://mlsanity.com/paper/2302.13812/) (2023)
- [Interpreting Criminal Charge Prediction and Its Algorithmic Bias via Quantum-Inspired Complex Valued Networks](https://mlsanity.com/paper/2106.13456/) (2021)
- [Quantum-inspired Interpretable Deep Learning Architecture for Text Sentiment Analysis](https://mlsanity.com/paper/2408.07891/) (2024)
- [QiNN-QJ: A Quantum-inspired Neural Network with Quantum Jump for Multimodal Sentiment Analysis](https://mlsanity.com/paper/2510.27091/) (2025)
- [Language Has Two Parameters: Narrative-Induced Semantic Plasticity and Phase-Sensitive Interpretation](https://mlsanity.com/paper/2608.18041/) (2026)

## Abstract (arXiv)

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.