This paper presents a comprehensive investigation into the decay mechanisms inherent in linear complexity sequence models. We systematically delineate the design space of decay mechanisms across four pivotal dimensions: parameterization strategy, which refers to the computational methodology for decay; parameter sharing, which involves the utilization of supplementary parameters for decay computation; decay granularity, comparing scalar versus vector-based decay; and compatibility with relative positional encoding methods, such as Rotary Position Embedding (RoPE). Through an extensive series of experiments conducted on diverse language modeling tasks, we uncovered several critical insights. Firstly, the design of the parameterization strategy for decay requires meticulous consideration. Our findings indicate that effective configurations are typically confined to a specific range of parameters. Secondly, parameter sharing cannot be used arbitrarily, as it may cause decay values to be too large or too small, thereby significantly impacting performance. Thirdly, under identical parameterization strategies, scalar decay generally underperforms compared to its vector-based counterpart. However, in certain scenarios with alternative parameterization strategies, scalar decay may unexpectedly surpass vector decay in efficacy. Lastly, our analysis reveals that RoPE, a commonly employed relative positional encoding method, typically fails to provide tangible benefits to the majority of linear attention mechanisms.

Linear attention mechanisms have gained prominence in causal language models due to their linear computational complexity and enhanced speed. However, the inherent decay mechanism in linear attention presents challenges when applied to multi-dimensional sequence modeling tasks, such as image processing and multi-modal learning. In these scenarios, the utilization of sequential scanning to establish a global receptive field necessitates multiple scans for multi-dimensional data, thereby leading to inefficiencies. This paper identifies the inefficiency caused by a "multiplicative" linear recurrence and proposes an efficient alternative "additive" linear recurrence to avoid the issue, as it can handle multi-dimensional data within a single scan. We further develop an efficient multi-dimensional sequential modeling framework called LightNet based on the new recurrence. Moreover, we present two new multi-dimensional linear relative positional encoding methods, MD-TPE and MD-LRPE to enhance the model's ability to discern positional information in multi-dimensional scenarios. Our empirical evaluations across various tasks, including image classification, image generation, bidirectional language modeling, and autoregressive language modeling, demonstrate the efficacy of LightNet, showcasing its potential as a versatile and efficient solution for multi-dimensional sequential modeling.

Benefiting from the search efficiency, differentiable neural architecture search (NAS) has evolved as the most dominant alternative to automatically design competitive deep neural networks (DNNs). We note that DNNs must be executed under strictly hard performance constraints in real-world scenarios, for example, the runtime latency on autonomous vehicles. However, to obtain the architecture that meets the given performance constraint, previous hardware-aware differentiable NAS methods have to repeat a plethora of search runs to manually tune the hyper-parameters by trial and error, and thus the total design cost increases proportionally. To resolve this, we introduce a lightweight hardware-aware differentiable NAS framework dubbed LightNAS, striving to find the required architecture that satisfies various performance constraints through a one-time search (i.e., \underline{\textit{you only search once}}). Extensive experiments are conducted to show the superiority of LightNAS over previous state-of-the-art methods.