提出高效稳定的概率张量网络学习方法，显著降低计算开销。
Efficient Probabilistic Tensor Networks
- 基于简化思路实现参数学习，兼容自动微分且数值稳定。
- 在MNIST上生成模型延迟降低10倍，变量规模扩大10倍。
- 适合大规模概率建模与密度估计任务的高效实现。
张量网络（TNs）通过共享参数实现大张量的紧凑表示。在概率建模中，概率张量网络（PTNs）可实现边际计算的高效处理。然而，现有PTN参数学习方法要么计算成本高且不完全兼容自动微分框架，要么数值不稳定。本文提出一种概念简洁的高效学习方法，具备数值稳定性。实验表明，该方法在时间与空间复杂度上均有显著提升，在MNIST数据集上的生成模型延迟降低10倍；应用于多种密度估计基准时，可学习变量数比此前方法多10倍。代码已公开于github.com/marawangamal/ptn。
原文摘要 · Abstract (English)
Tensor networks (TNs) enable compact representations of large tensors through shared parameters. Their use in probabilistic modeling is particularly appealing, as probabilistic tensor networks (PTNs) allow for tractable computation of marginals. However, existing approaches for learning parameters of PTNs are either computationally demanding and not fully compatible with automatic differentiation frameworks, or numerically unstable. In this work, we propose a conceptually simple approach for learning PTNs efficiently, that is numerically stable. We show our method provides significant improvements in time and space complexity, achieving 10x reduction in latency for generative modeling on the MNIST dataset. Furthermore, our approach enables learning of distributions with 10x more variables than previous approaches when applied to a variety of density estimation benchmarks. Our code is publicly available at github.com/marawangamal/ptn.
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