Paper Citation Record · LEDGER

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data

As of 10 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 5 inbound Pith citation observations for arXiv:2509.05213.

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

pith.paper-citation-record.v1
2509.05213 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T05:38:50.831695Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T05:38:47.459352Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-01T09:15:44.228508Z

Reference resolution

28 of 28 outbound references displayed

verified exact1
verified fuzzy18
unresolved9
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d3b710fc-de09-4d9b-8aa5-02982a92b676 · outbound

This paper cites an unresolved cited work.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-05T05:38:55.922265Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5b3b3762-4d1c-4532-a013-6ef1fce95c76 · outbound

This paper cites An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-05T05:38:47.459352Z

Source-reported events for the cited work

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Observation b6a00513-dc5a-41f0-abc3-6474943aceb3 · outbound

This paper cites A server coordinatesnclients, where each clienti∈[n]holds a local loss functionf i(x).

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data A server coordinatesnclients, where each clienti∈[n]holds a local loss functionf i(x)

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:55.715802Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 50572771-b302-433c-aef8-e31b317e63b3 · outbound

This paper cites Our proposed algorithm is summarized in Algorithm 1.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Our proposed algorithm is summarized in Algorithm 1

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:55.515525Z

Source-reported events for the cited work

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Observation b3f0a3a4-590d-4306-9609-0e33de6eb4ae · outbound

This paper cites Assumption 2.Each functionf i(x)isL f -smooth such that ∥∇fi(x)− ∇fi(z)∥≤L f ∥x−z∥,∀i, x, z.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Assumption 2.Each functionf i(x)isL f -smooth such that ∥∇fi(x)− ∇fi(z)∥≤L f ∥x−z∥,∀i, x, z

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:55.326631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9d7bc8b5-1f58-4ae6-8b9e-5f2ba13e410c · outbound

This paper cites In our experiments, we consider three commonly used examples: Coordinate Descent (CD), Ran- dom Generation (RD), and Spherical Smoothing (SS) [8, 9].

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data In our experiments, we consider three commonly used examples: Coordinate Descent (CD), Ran- dom Generation (RD), and Spherical Smoothing (SS) [8, 9]

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:55.119790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ce2317b9-fce2-49a0-acb8-2f97df64f027 · outbound

This paper cites an unresolved cited work.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-05T05:38:54.922426Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8de54c8e-0797-4477-8b5c-1b0ac5a289a9 · outbound

This paper cites Federated Learning: Strategies for Improving Communication Efficiency.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Federated Learning: Strategies for Improving Communication Efficiency

Reference 8

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Source-reported events for the cited work

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Observation 57a99a65-fce4-48a7-ab65-03c074faddf9 · outbound

This paper cites Hybrid federated learning for feature & sample heterogeneity: Algorithms and implementation,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Hybrid federated learning for feature & sample heterogeneity: Algorithms and implementation,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:54.719637Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a1aa3edf-ebf2-4336-b85c-043474af819f · outbound

This paper cites Fedlion: Faster adaptive federated optimization with fewer communica- tion,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Fedlion: Faster adaptive federated optimization with fewer communica- tion,

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:54.518620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 54acf323-2fe5-4dc5-8f3f-14aecd770a64 · outbound

This paper cites Scaffold: Stochastic controlled averaging for federated learning,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Scaffold: Stochastic controlled averaging for federated learning,

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:54.313216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4178600e-df0a-4c4b-8007-3a7c7c9ff93a · outbound

This paper cites LoRA: Low-rank adaptation of large lan- guage models.,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data LoRA: Low-rank adaptation of large lan- guage models.,

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:54.136953Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 58187122-9bcf-425b-bb6e-200f24d1e85a · outbound

This paper cites Ga- lore: Memory-efficient llm training by gradient low- rank projection,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Ga- lore: Memory-efficient llm training by gradient low- rank projection,

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:53.926887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 959dd44e-f8c0-4391-a78d-50f4643d3c22 · outbound

This paper cites Subspace optimization for large language models with convergence guarantees,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Subspace optimization for large language models with convergence guarantees,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:53.755245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3b235319-cbc6-415e-9c95-b02fcd9edc29 · outbound

This paper cites A memory efficient randomized subspace optimization method for training large language mod- els,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data A memory efficient randomized subspace optimization method for training large language mod- els,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:53.538445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 12f1e12d-0084-4053-8f23-4e4765d0f3f2 · outbound

This paper cites Improving LoRA in Privacy-preserving Federated Learning.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Improving LoRA in Privacy-preserving Federated Learning

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-05T05:38:49.370808Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bd136f6e-2fc7-418f-8590-f6fd666fe6bd · outbound

This paper cites Federated Fine-tuning of Large Language Models under Heterogeneous Tasks and Client Resources.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Federated Fine-tuning of Large Language Models under Heterogeneous Tasks and Client Resources

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-05T05:38:49.539833Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1e752900-8fb8-4ec6-9e07-bf7b06a58658 · outbound

This paper cites Communication- efficient federated low-rank update algorithm and its connection to implicit regularization,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Communication- efficient federated low-rank update algorithm and its connection to implicit regularization,

Reference 19

Resolution: verified exact; raw_fallback, observed 2026-08-05T05:38:51.278644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation fee2e038-b13d-4721-a748-3d6be846abbf · outbound

This paper cites FedSVD: Adaptive orthogonaliza- tion for private federated learning with LoRA,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data FedSVD: Adaptive orthogonaliza- tion for private federated learning with LoRA,

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-05T05:38:49.792148Z

Source-reported events for the cited work

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Observation fe19b593-8ca6-43bb-9e81-48635c68714e · outbound

This paper cites FLoCoRA: Fed- erated learning compression with low-rank adaptation,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data FLoCoRA: Fed- erated learning compression with low-rank adaptation,

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:53.368199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 32e8df4b-fec9-4a7a-9bb3-0982efb7a157 · outbound

This paper cites Communication-efficient personalized federated learn- ing for speech-to-text tasks,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Communication-efficient personalized federated learn- ing for speech-to-text tasks,

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:53.113832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation cb778588-41c1-42ce-b032-30d2cde1ac15 · outbound

This paper cites Exploring Gradient Subspaces: Addressing and Overcoming LoRA's Limitations in Federated Fine-Tuning of Large Language Models.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Exploring Gradient Subspaces: Addressing and Overcoming LoRA's Limitations in Federated Fine-Tuning of Large Language Models

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-05T05:38:50.097225Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4fea52f1-9e79-429f-8769-930c1619e502 · outbound

This paper cites A unified and refined convergence analysis for non-convex decentral- ized learning,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data A unified and refined convergence analysis for non-convex decentral- ized learning,

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:52.878475Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8741c4d4-8f3a-4f3c-82a1-9adaa27f03f8 · outbound

This paper cites Linear convergence in federated learning: Tackling client heterogeneity and sparse gradi- ents,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Linear convergence in federated learning: Tackling client heterogeneity and sparse gradi- ents,

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:52.640808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7fdbcdd7-61e6-4888-8b5e-415e95a900ef · outbound

This paper cites Stochastic variance reduction for nonconvex optimization,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Stochastic variance reduction for nonconvex optimization,

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:52.440038Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 26fbc112-3b84-434e-b1be-ddf4cad7490a · outbound

This paper cites Zeroth-order optimization with orthogonal random directions,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Zeroth-order optimization with orthogonal random directions,

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:52.160272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 875ede3e-afcc-451f-ab81-2904ce6e2202 · outbound

This paper cites Deep residual learning for image recognition,.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Deep residual learning for image recognition,

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:38:51.908053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 18ad2f83-1e5b-44f9-9dc0-063247df394f · outbound

This paper cites an unresolved cited work.

An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-05T05:38:51.613999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Pith citing papers

Observation 5b3b3762-4d1c-4532-a013-6ef1fce95c76 · inbound