We investigate the potential of tensor network based machine learning methods to scale to large image and text data sets. For that, we study how the mutual information between a subregion and its complement scales with the subsystem size $L$, similarly to how it is done in quantum many-body physics. We find that for text, the mutual information scales as a power law $L^\nu$ with a close to volume law exponent, indicating that text cannot be efficiently described by 1D tensor networks. For images, the scaling is close to an area law, hinting at 2D tensor networks such as PEPS could have an adequate expressibility. For the numerical analysis, we introduce a mutual information estimator based on autoregressive networks, and we also use convolutional neural networks in a neural estimator method.
翻译:因此,我们研究一个次区域之间的相互信息及其与子系统规模相补充的尺度如何具有充分的可表达性。对于数字多体物理学,我们发现,对于文本而言,相互信息尺度是一种权力法,与量法相近,表明文本无法被1D 温度网络有效描述。对于图像来说,缩放速度接近于区域法,暗示PEPS等2D 10°网络可以具有充分的可表达性。对于数字分析,我们采用基于自动递增网络的相互信息估计器,我们还使用神经测量法的共振神经网络。