Simplifying and Understanding State Space Models with Diagonal Linear RNNs

• URL: http://arxiv.org/abs/2212.00768v3
• Date: Tue, 14 Nov 2023 16:52:48 GMT
• Title: Simplifying and Understanding State Space Models with Diagonal Linear RNNs
• Authors: Ankit Gupta, Harsh Mehta, Jonathan Berant
• Abstract summary: This work disposes of the discretization step, and proposes a model based on vanilla Diagonal Linear RNNs. We empirically show that, despite being conceptually much simpler, $mathrmDLR$ is as performant as previously-proposed SSMs. We also characterize the expressivity of SSMs and attention-based models via a suite of $13$ synthetic sequence-to-sequence tasks.
• Score: 56.33053691749856
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Sequence models based on linear state spaces (SSMs) have recently emerged as a promising choice of architecture for modeling long range dependencies across various modalities. However, they invariably rely on discretization of a continuous state space, which complicates their presentation and understanding. In this work, we dispose of the discretization step, and propose a model based on vanilla Diagonal Linear RNNs ($\mathrm{DLR}$). We empirically show that, despite being conceptually much simpler, $\mathrm{DLR}$ is as performant as previously-proposed SSMs on a variety of tasks and benchmarks including Long Range Arena and raw speech classification. Moreover, we characterize the expressivity of SSMs (including $\mathrm{DLR}$) and attention-based models via a suite of $13$ synthetic sequence-to-sequence tasks involving interactions over tens of thousands of tokens, ranging from simple operations, such as shifting an input sequence, to detecting co-dependent visual features over long spatial ranges in flattened images. We find that while SSMs report near-perfect performance on tasks that can be modeled via $\textit{few}$ convolutional kernels, they struggle on tasks requiring $\textit{many}$ such kernels and especially when the desired sequence manipulation is $\textit{context-dependent}$. Despite these limitations, $\mathrm{DLR}$ reaches high performance on two higher-order reasoning tasks $\mathrm{ListOpsSubTrees}$ and $\mathrm{PathfinderSegmentation}\text{-}\mathrm{256}$ with input lengths $8K$ and $65K$ respectively, and gives encouraging performance on $\mathrm{PathfinderSegmentation}\text{-}\mathrm{512}$ with input length $262K$ for which attention is not a viable choice.

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