Papers › Long Expressive Memory for Sequence Modeling
Long Expressive Memory for Sequence Modeling
T. Konstantin Rusch, Siddhartha Mishra, N. Benjamin Erichson, Michael W. Mahoney
We propose a novel method called Long Expressive Memory (LEM) for learning long-term sequential dependencies. LEM is gradient-based, it can efficiently process sequential tasks with very long-term dependencies, and it is sufficiently expressive to be able to learn complicated input-output maps. To derive LEM, we consider a system of multiscale ordinary differential equations, as well as a suitable time-discretization of this system. For LEM, we derive rigorous bounds to show the mitigation of the exploding and vanishing gradients problem, a well-known challenge for gradient-based recurrent sequential learning methods. We also prove that LEM can approximate a large class of dynamical systems to high accuracy. Our empirical results, ranging from image and time-series classification through dynamical systems prediction to speech recognition and language modeling, demonstrate that LEM outperforms state-of-the-art recurrent neural networks, gated recurrent units, and long short-term memory models.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
For agents, Syntology's MCP tool lists every function and class Syntology harvested from this paper and whether it ran (how to connect): get_harvested_code_for_paper(arxiv_id="2110.04744")
Code
Syntology Ran 1 of 10 code samples harvested from 2 repositories linked to this paper; 9 have no recorded run. Of those that ran: 1 ran with no contract checked.
By repository: official repository: 1 sample from 1 repository, 1 ran; found in paper text by Syntology: 9 samples from 1 repository, 0 ran. The run record, sample by sample. “Ran” means executed on a synthesized input, not that the code is correct or reproduces the paper.
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
10 samples harvested; 1 ran; 0 honoured the contract we drafted; 9 have no recorded run. Read from Syntology's graph 2026-09-24; that is when this build read the record, not when the samples ran.
Licence: 1 of the 10 samples is pointer only, meaning Syntology does not serve that copy's text. This page shows no code text for any sample; each one links to its file in the repository.
Harvested from 2 repositories linked to this paper, official or community; each sample names its own and says which. “Ran” means the sample executed on a synthesized input. It does not mean the output is correct, and nothing here reproduces the paper's results. “Honoured” and “violated” refer to a contract Syntology drafted from the code itself; “our draft was wrong” and “fixture could not drive it” are failures of Syntology's instrument, not of the code.
Each sample ends with its code_sha256, Syntology's identity for that exact code. An agent fetches the stored sample with Syntology's MCP tool get_code(code_sha256="…") (how to connect); click an identity to copy that call.
Repository labels, per sample. official repository: The archive marks this repository official for the paper. named in the paper: The archive records that the paper mentions this repository; it is not marked official. community (archive-listed): In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper. found in paper text by Syntology: Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted. community: Not in the archive's code links for this paper; a community repository Syntology harvested. Samples from a repository marked official are listed first. Licence labels name the repository's licence as recorded at harvest. “Pointer only” means Syntology does not serve that copy's text, for one of four reasons: no licence file was found; the licence was not identified; the licence is recorded as permissive but that copy's record is not marked cleared; or the licence is outside the permissive list Syntology serves text under (MIT, Apache-2.0, BSD and similar). Some licences outside that list permit redistribution, such as WTFPL, and GPL-3.0 under its conditions; they are simply not on the list. Hover a licence label for the reason. File links open the file on GitHub at the default branch, which may have changed since the harvest.
9cfb904b319e5586 · report
2c67d2b0758d5fe0 · report
c598ebd47e698d5c · report
184a036257da4448 · report
db14e2261c3a6e84 · report
41b09314d9718a2f · report
e9fa8fcbfffec562 · report
e82bc4ce41514342 · report
d52c0a249edc34f9 · report
fe22ebdbafcd2a30 · report
Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Sequential Image Classification | Sequential MNIST | LEM | Permuted Accuracy | 96.6% | #18 of 30 | Archive leaderboard | report |
| Sequential Image Classification | Sequential MNIST | LEM | Unpermuted Accuracy | 99.5% | #18 of 30 | Archive leaderboard | report |
| Sequential Image Classification | noise padded CIFAR-10 | LEM | % Test Accuracy | 60.5 | #3 of 7 | Archive leaderboard | report |
| Time Series Classification | EigenWorms | LEM | % Test Accuracy | 92.3 | #1 of 8 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections