Pith Number

pith:KANXA7MJ

pith:2026:KANXA7MJHPATK5CC72CCGD4IZ5

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Parallel-in-Time Training of Recurrent Neural Networks for Dynamical Systems Reconstruction

Daniel Durstewitz, Florian G\"otz, Florian Hess

Generalized teacher forcing in the DEER framework enables stable parallel-in-time training of nonlinear recurrent models on sequences longer than 10,000 steps, yielding better reconstruction of dynamical systems with long time scales.

arxiv:2605.12683 v1 · 2026-05-12 · cs.LG · cs.AI · cs.DC · physics.comp-ph

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Claims

C1strongest claim

Using GTF-DEER, we investigate the benefits of training on extremely long sequences (T>10^4) for DSR. Our results show that access to such long trajectories significantly improves DSR if the data features long time scales.

C2weakest assumption

That the parallel-in-time algorithms, including the new GTF variant, maintain numerical stability and learning effectiveness for general nonlinear dynamics across arbitrary sequence lengths without hidden constraints or post-hoc adjustments.

C3one line summary

GTF-DEER augments the DEER framework with Generalized Teacher Forcing to allow effective parallel training of nonlinear recurrent models on extremely long sequences, improving dynamical systems reconstruction for data with long time scales.

References

82 extracted · 82 resolved · 3 Pith anchors

[1] Balanced neural ODEs: nonlinear model order reduction and koopman operator approximations 2025

[2] Martinez Alvarez, Rare¸ s Ro¸ sca, and Cristian G 2009

[3] Benjamin Erichson, Vanessa Lin, and Michael W 2020

[4] Scheduled sampling for sequence prediction with recurrent neural networks.Advances in neural information processing systems, 28 2015

[5] Y . Bengio, P. Simard, and P. Frasconi. Learning long-term dependencies with gradient descent is difficult.IEEE transactions on neural networks, 5(2):157–166, 1994 1994

Formal links

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Receipt and verification

First computed	2026-05-18T03:09:49.971009Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

501b707d893bc1357442fe84230f88cf74aa7e2593a1daefa07b8b6c704bd89b

Aliases

arxiv: 2605.12683 · arxiv_version: 2605.12683v1 · doi: 10.48550/arxiv.2605.12683 · pith_short_12: KANXA7MJHPAT · pith_short_16: KANXA7MJHPATK5CC · pith_short_8: KANXA7MJ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KANXA7MJHPATK5CC72CCGD4IZ5 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 501b707d893bc1357442fe84230f88cf74aa7e2593a1daefa07b8b6c704bd89b

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "53dfe2eb4add8b39eff7960bd25d4f9a8f6053c4ea05f9fdd9cb53458f4f63b4",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.DC",
      "physics.comp-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-12T19:32:32Z",
    "title_canon_sha256": "c3b46719491e04900891462c48b5ecdf47b1afc9a287a877bd088e2267908b41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12683",
    "kind": "arxiv",
    "version": 1
  }
}