In equity markets, stocks are conventionally labeled by equity indices (company names). By relabeling stocks according to their ranks in capitalization, rather than their equity indices (company names), a different, more stable market structure can emerge. Specifically, we will gain a different perspective on market dynamics by focusing on the stock that occupies a certain rank in capitalization while the corresponding company name may change. We refer to a market labeled by the equity indices (company names) as a market in name space and one labeled by ranks in capitalization as a market in rank space . Market in rank space was explored by Fernholtz et al. who observed a stable distribution of capitalization across different ranks in the U.S. equity market over different time periods [11,16]. They further introduced an explanatory hybrid-Atlas model under stochastic portfolio theory, a framework that enables analyzing portfolios in rank space [5,15]. Empirically, B. Healy et al. analyzed the U.S. equity data and showed that the market in rank space is driven by a dominant single factor [14], in contrast to the multi-factor-driven market in name space [9,10,19]. While the primary market factor in rank space has been extensively studied, the residual returns - those not explained by this primary factor in stock returns - remain a fertile land of adventure.

Low-rank compression is an important model compression strategy for obtaining compact neural network models. In general, because the rank values directly determine the model complexity and model accuracy, proper selection of layer-wise rank is very critical and desired. To date, though many low-rank compression approaches, either selecting the ranks in a manual or automatic way, have been proposed, they suffer from costly manual trials or unsatisfied compression performance. In addition, all of the existing works are not designed in a hardware-aware way, limiting the practical performance of the compressed models on real-world hardware platforms. To address these challenges, in this paper we propose HALOC, a hardware-aware automatic low-rank compression framework. By interpreting automatic rank selection from an architecture search perspective, we develop an end-to-end solution to determine the suitable layer-wise ranks in a differentiable and hardware-aware way. We further propose design principles and mitigation strategy to efficiently explore the rank space and reduce the potential interference problem. Experimental results on different datasets and hardware platforms demonstrate the effectiveness of our proposed approach. On CIFAR-10 dataset, HALOC enables 0.07% and 0.38% accuracy increase over the uncompressed ResNet-20 and VGG-16 models with 72.20% and 86.44% fewer FLOPs, respectively. On ImageNet dataset, HALOC achieves 0.9% higher top-1 accuracy than the original ResNet-18 model with 66.16% fewer FLOPs. HALOC also shows 0.66% higher top-1 accuracy increase than the state-of-the-art automatic low-rank compression solution with fewer computational and memory costs. In addition, HALOC demonstrates the practical speedups on different hardware platforms, verified by the measurement results on desktop GPU, embedded GPU and ASIC accelerator.