{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/simplifying-and-understanding-state-space","title":"Simplifying and Understanding State Space Models with Diagonal Linear RNNs","arxiv_id":"2212.00768","date":"2022-12-01","proceeding":null,"authors":["Ankit Gupta","Harsh Mehta","Jonathan Berant"],"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.","url_abs":"https://arxiv.org/abs/2212.00768v3","url_pdf":"https://arxiv.org/pdf/2212.00768v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"simplifying-and-understanding-state-space","repo_url":"https://github.com/ag1988/dlr","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":null,"task_name":"8k"},{"task_slug":"state-space-models","task_name":"State Space Models"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2212.00768","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2212.00768"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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