Paper Citation Record · LEDGER

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks

As of 4 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 3 inbound Pith citation observations for arXiv:2508.12121.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2508.12121 v5

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-18T22:55:08.245141Z

measured 46 of 46 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-04T06:34:03.388597+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T18:25:45.421473Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-06-30T08:14:26.101219Z

Reference resolution

43 of 43 outbound references displayed

verified exact10
verified fuzzy30
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f211771f-7512-44e2-a660-ad19331a9a46 · outbound

This paper cites On the difficulty of training recurrent neural networks.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks On the difficulty of training recurrent neural networks

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.997392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation b04674ce-2a6f-49f5-b892-b626668664cf · outbound

This paper cites Recurrent neural networks: vanishing and exploding gradients are not the end of the story.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Recurrent neural networks: vanishing and exploding gradients are not the end of the story

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.961041Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation c6ae864d-1c90-4376-8935-a5cb9c19e88c · outbound

This paper cites Random orthogonal additive filters: A solution to the van- ishing/exploding gradient of deep neural networks.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Random orthogonal additive filters: A solution to the van- ishing/exploding gradient of deep neural networks

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.950867Z

Source-reported events for the cited work

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Observation e6d22542-8151-4df5-ae76-52756d9d8565 · outbound

This paper cites Efficiently Modeling Long Sequences with Structured State Spaces.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Efficiently Modeling Long Sequences with Structured State Spaces

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-05-18T22:56:53.090297Z

Source-reported events for the cited work

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Observation ab352fa3-20e6-40a8-9b50-34272b635a27 · outbound

This paper cites Combining recurrent, convolutional, and continuous-time models with linear state space layers.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Combining recurrent, convolutional, and continuous-time models with linear state space layers

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.973062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 89bd8fea-3be9-4a9d-b57e-69649a622e17 · outbound

This paper cites The- oretical foundations of deep selective state-space models.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks The- oretical foundations of deep selective state-space models

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.980207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 353fbccc-3a5a-4265-9870-719e2930951f · outbound

This paper cites Wide neural networks of any depth evolve as linear models under gradient descent.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Wide neural networks of any depth evolve as linear models under gradient descent

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.953965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation c0efe837-4a93-46e3-ab53-02b0dbafa55b · outbound

This paper cites Exact solutions to the nonlinear dynamics of learning in deep linear neural networks.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Exact solutions to the nonlinear dynamics of learning in deep linear neural networks

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-05-18T22:56:53.084512Z

Source-reported events for the cited work

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Observation a7a4674d-9409-4c65-9015-6225c241fbf7 · outbound

This paper cites Orthogonal recurrent neural networks with scaled Cayley transform.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Orthogonal recurrent neural networks with scaled Cayley transform

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.957522Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation b2501153-d220-4620-88bd-d34509dee70b · outbound

This paper cites Efficient or- thogonal parametrisation of recurrent neural networks using householder reflections.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Efficient or- thogonal parametrisation of recurrent neural networks using householder reflections

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.964088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 89e192ec-57cc-4f6e-8682-a8480b528a2b · outbound

This paper cites Unitary evolution recurrent neural networks.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Unitary evolution recurrent neural networks

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.947692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation a40be806-1602-4e3d-85d3-7e30a81bc8e8 · outbound

This paper cites Full- capacity unitary recurrent neural networks.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Full- capacity unitary recurrent neural networks

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.990267Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 0db2ed53-b035-4913-b059-f03d2f72a607 · outbound

This paper cites On orthogonality and learning recurrent networks with long term dependencies.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks On orthogonality and learning recurrent networks with long term dependencies

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.983744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 7a2c8a29-b131-44ae-9f13-e440692ce421 · outbound

This paper cites Lipschitz Recurrent Neural Networks.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Lipschitz Recurrent Neural Networks

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-18T22:56:53.079495Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 12354a7a-c443-46c9-add7-db0abbf01730 · outbound

This paper cites Non-normal Recurrent Neural Network (nnRNN): learning long time dependencies while improving expressivity with transient dynamics.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Non-normal Recurrent Neural Network (nnRNN): learning long time dependencies while improving expressivity with transient dynamics

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-18T22:56:53.095224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation d330ffd7-560d-4321-b3e1-4d8ceef26c46 · outbound

This paper cites RNNs incrementally evolving on an equilibrium manifold: A panacea for vanishing and exploding gradients?.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks RNNs incrementally evolving on an equilibrium manifold: A panacea for vanishing and exploding gradients?

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.976737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 8d1c8dd4-881e-40a8-91f5-2efba6367df1 · outbound

This paper cites AntisymmetricRNN: A dynamical system view on recurrent neural networks.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks AntisymmetricRNN: A dynamical system view on recurrent neural networks

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:54.001225Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation bbedf6cc-f1ec-468c-a22b-db747f5676f4 · outbound

This paper cites Coupled oscillatory recurrent neural network (cornn): An accurate and (gradient) stable architecture for learning long time dependencies.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Coupled oscillatory recurrent neural network (cornn): An accurate and (gradient) stable architecture for learning long time dependencies

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.993632Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 4e2291be-a2df-45a6-9663-7cd79c39ca20 · outbound

This paper cites Long Expressive Memory for Sequence Modeling.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Long Expressive Memory for Sequence Modeling

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-05-18T22:56:53.074205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 5f5ae107-cb6f-4051-9efc-de1f65970b89 · outbound

This paper cites A clockwork RNN.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks A clockwork RNN

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.966771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation bad1cee6-5426-4d86-a6e2-cc46b044d718 · outbound

This paper cites Dynamical isometry and a mean field theory of RNNs: Gating enables signal propagation in recurrent neural networks.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Dynamical isometry and a mean field theory of RNNs: Gating enables signal propagation in recurrent neural networks

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.969804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 8dd79e26-8867-4b9f-aabd-89214dd38094 · outbound

This paper cites Dynamical Isometry and a Mean Field Theory of LSTMs and GRUs.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Dynamical Isometry and a Mean Field Theory of LSTMs and GRUs

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-05-18T22:56:53.069687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 1c583dac-2a54-4bc5-a826-04117f3f28f3 · outbound

This paper cites Resurrecting the sigmoid in deep learning through dynamical isometry: theory and practice.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Resurrecting the sigmoid in deep learning through dynamical isometry: theory and practice

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:54.005528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation a19ec61c-b24f-495b-ab85-d61518182afb · outbound

This paper cites Gating revisited: Deep multi-layer rnns that can be trained.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Gating revisited: Deep multi-layer rnns that can be trained

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.986888Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 89ae9eda-c50a-44a6-bcc4-cd46fd8e4dd3 · outbound

This paper cites The unreasonable effectiveness of the forget gate.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks The unreasonable effectiveness of the forget gate

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-05-18T22:56:53.060486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation d87d8ffc-b123-478b-81e9-df3a48681389 · outbound

This paper cites Theory of gating in recurrent neural networks.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Theory of gating in recurrent neural networks

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.902763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 17afe4e7-845f-4888-89f3-3101bdd7a3a9 · outbound

This paper cites Gates create slow modes in recurrent neural networks.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Gates create slow modes in recurrent neural networks

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.944547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 5cc43551-6de6-40fe-815c-7aa5d37dbb13 · outbound

This paper cites Adaptive time scales in recurrent neural networks.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Adaptive time scales in recurrent neural networks

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.917922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 73957f23-c072-4b76-924b-7c8d6b249f21 · outbound

This paper cites Can recurrent neural networks warp time?.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Can recurrent neural networks warp time?

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.905972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 23967350-2931-43ef-8aba-86f86dcab035 · outbound

This paper cites Optimization and applications of echo state networks with leaky-integrator neurons.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Optimization and applications of echo state networks with leaky-integrator neurons

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.938082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 7090d4ae-ec89-419f-abfc-2fc7c27aa5ca · outbound

This paper cites Backpropagation through time: what it does and how to do it.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Backpropagation through time: what it does and how to do it

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.941358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 730947af-0410-46c0-9408-74d179ea8f72 · outbound

This paper cites An overview of gradient descent optimization algorithms.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks An overview of gradient descent optimization algorithms

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-05-18T22:56:53.055492Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 3e85532c-0cec-4a35-9f16-2ade2bd70d20 · outbound

This paper cites Long short-term memory.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Long short-term memory

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.896308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 984688a7-b763-4b09-ba5b-0f19434a5e2c · outbound

This paper cites Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation

Reference 34

Resolution: verified exact; local_arxiv, observed 2026-05-18T22:56:53.065155Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation e0c2a609-5360-4eb3-9f6f-be4c1a489cf6 · outbound

This paper cites Attention is all you need.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Attention is all you need

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.934686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 75f61c9b-f7f2-44f5-abd9-1df708be0d1e · outbound

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Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-05-18T22:56:53.899257Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 89e8ea66-6c92-4451-9652-eaaee10f62c4 · outbound

This paper cites an unresolved cited work.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-05-18T22:56:53.931569Z

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Observation bb086ed9-e410-49fa-aca4-e6ef37c8d7a8 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Adam: A Method for Stochastic Optimization

Reference 38

Resolution: verified exact; local_arxiv, observed 2026-05-18T22:56:53.050661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 87eec651-35c7-4f25-a325-c8bba785b83e · outbound

This paper cites Since the space is finite-dimensional, all norms are equivalent.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Since the space is finite-dimensional, all norms are equivalent

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.928285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 5643366b-19e2-4810-9da2-4e00990d4b73 · outbound

This paper cites The direction of perturbation E in (57) is now the tuple E ≡ (B1, B2.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks The direction of perturbation E in (57) is now the tuple E ≡ (B1, B2

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.921153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 530c547d-5771-4def-a316-a88ad32a6611 · outbound

This paper cites We now apply the product rule (58) to Fn by setting g(ε) = Fn−1(ε), h (ε) = An + εBn.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks We now apply the product rule (58) to Fn by setting g(ε) = Fn−1(ε), h (ε) = An + εBn

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.910271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation b0b41e47-471e-4ece-83ef-0d7ec1e64cfc · outbound

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Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-05-18T22:56:53.924650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation b4a15046-73c8-4970-9fed-49c45013aad8 · outbound

This paper cites In the main text, Bj represents gate-induced corrections, which are typically low-norm compared to the dominant dynamics in Aj.

Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks In the main text, Bj represents gate-induced corrections, which are typically low-norm compared to the dominant dynamics in Aj

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T22:56:53.914409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Pith citing papers

Observation e1068dd9-3aea-4276-823d-b096244f2c99 · inbound

Learnability Window in Gated Recurrent Neural Networks cites this paper.

Learnability Window in Gated Recurrent Neural Networks Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-03T18:25:45.421473Z

Source-reported events for the cited work

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Observation 8c846844-d4ea-46a4-b9d5-2f313eddab1b · inbound

Anti-Collapse Dynamics and the Emergence of Multi-Time-Scale Learning in Recurrent Neural Networks cites this paper.

Anti-Collapse Dynamics and the Emergence of Multi-Time-Scale Learning in Recurrent Neural Networks Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks

Reference 35

Resolution: verified exact; local_arxiv, observed 2026-06-30T08:14:26.102657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation edc7a33d-a7a7-4e92-8b53-f3a711caeeb9 · inbound

Anti-Collapse Dynamics and the Emergence of Multi-Time-Scale Learning in Recurrent Neural Networks cites this paper.

Anti-Collapse Dynamics and the Emergence of Multi-Time-Scale Learning in Recurrent Neural Networks Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-02T09:43:28.106394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.