将信息平面引入量子学习，提升模型压缩与训练效率。
Information plane and compression-gnostic feedback in quantum machine learning
- 用信息平面分析量子模型学习过程中的数据压缩机制。
- 通过损失函数正则化或学习率调度，显著提升测试准确率和收敛速度。
- 适用于量子电路与经典神经网络的性能优化，适合研究者参考。
信息平面（Tishby et al. arXiv:physics/0004057, Shwartz-Ziv et al. arXiv:1703.00810）被提出作为分析神经网络学习动态的工具，能定量揭示模型如何逼近最小充分统计量。本文将该工具扩展至量子学习模型领域。进一步研究发现，信息平面提供的压缩程度洞察可用于改进学习算法：一种是通过损失函数的乘性正则化，另一种是采用与压缩无关的学习率调度器（针对基于梯度下降的算法）。两种方法在实现中效果等价。我们在多个分类与回归任务上对所提算法进行基准测试，使用变分量子电路。结果表明，无论是合成数据还是真实世界数据集，测试准确率与收敛速度均有提升。此外，通过一个实例分析了这些改进对经典神经网络分类性能的影响。
原文摘要 · Abstract (English)
The information plane (Tishby et al. arXiv:physics/0004057, Shwartz-Ziv et al. arXiv:1703.00810) has been proposed as an analytical tool for studying the learning dynamics of neural networks. It provides quantitative insight on how the model approaches the learned state by approximating a minimal sufficient statistics. In this paper we extend this tool to the domain of quantum learning models. In a second step, we study how the insight on how much the model compresses the input data (provided by the information plane) can be used to improve a learning algorithm. Specifically, we consider two ways to do so: via a multiplicative regularization of the loss function, or with a compression-gnostic scheduler of the learning rate (for algorithms based on gradient descent). Both ways turn out to be equivalent in our implementation. Finally, we benchmark the proposed learning algorithms on several classification and regression tasks using variational quantum circuits. The results demonstrate an improvement in test accuracy and convergence speed for both synthetic and real-world datasets. Additionally, with one example we analyzed the impact of the proposed modifications on the performances of neural networks in a classification task.
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