Paper Citation Record · LEDGER

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning

As of 19 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 2 inbound Pith citation observations for arXiv:2501.19067.

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

pith.paper-citation-record.v1
2501.19067 v2

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T21:34:28.423054Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:21:58.289655Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T06:06:40.548149Z

Reference resolution

18 of 18 outbound references displayed

verified exact3
verified fuzzy9
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ed57d9c3-8aa4-4729-aa50-f4515ca11c23 · outbound

This paper cites As Table 2 shows, the numeric bounds obtained this way can be tighter bound than the upper bound from the Theorem.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning As Table 2 shows, the numeric bounds obtained this way can be tighter bound than the upper bound from the Theorem

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:34:28.899505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c122617c-77ae-4314-8eea-e2010cfb06fa · outbound

This paper cites For each E ∈ E, let lE : S∞ n=1 F n → N be the length function of the multi-task encoder given E.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning For each E ∈ E, let lE : S∞ n=1 F n → N be the length function of the multi-task encoder given E

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:34:28.887763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1fad952c-6916-4a31-94fe-f4b29ec71d80 · outbound

This paper cites , fn) − R(f1,.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning , fn) − R(f1,

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:34:28.910937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 82f123e3-0247-471d-96b6-d323c7dbe9de · outbound

This paper cites Unleashing the Power of Multi-Task Learning: A Comprehensive Survey Spanning Traditional, Deep, and Pretrained Foundation Model Eras.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning Unleashing the Power of Multi-Task Learning: A Comprehensive Survey Spanning Traditional, Deep, and Pretrained Foundation Model Eras

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-09T21:34:28.373059Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c2eba7d1-f75a-402b-9a07-978f00ce36ba · outbound

This paper cites Federated Learning with Non-IID Data.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning Federated Learning with Non-IID Data

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-09T21:34:28.377171Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3c2eba39-a27c-4886-a0f8-8c2143a12375 · outbound

This paper cites an unresolved cited work.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-09T21:34:28.876451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 48745fec-6347-4510-ba76-74b5a5a61e5c · outbound

This paper cites We instantiate (17) with a value tE;F such that 2√mne−tE;F mn = wE;F , i.e.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning We instantiate (17) with a value tE;F such that 2√mne−tE;F mn = wE;F , i.e

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:34:28.866337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cfa8e904-7cb0-48a4-963f-e16c4118bd7f · outbound

This paper cites an unresolved cited work.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-09T21:34:28.855509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c17ea713-03b8-4dd5-9f60-a1c3a5fdada3 · outbound

This paper cites Then we have: E[et kl( Y t | µ t )] ≤ 2 √ t (21) where kl(q|p) = q log q p + (1− q) log1−q 1−p is the Kullback-Leibler divergence between Bernoulli distributions with mean q and p.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning Then we have: E[et kl( Y t | µ t )] ≤ 2 √ t (21) where kl(q|p) = q log q p + (1− q) log1−q 1−p is the Kullback-Leibler divergence between Bernoulli distributions with mean q and p

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:34:28.845402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9fe5f07c-fcfa-4f44-b05b-36df577acd0d · outbound

This paper cites B.2 Model architectures For the MNIST experiments, we use convolutional networks used in Amit & Meir (2018).

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning B.2 Model architectures For the MNIST experiments, we use convolutional networks used in Amit & Meir (2018)

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:34:28.834630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5d490a25-4faf-4ec1-9d77-ac00ad10ec93 · outbound

This paper cites (2024), and a ViT model pretrained from ImageNet (Dosovitskiy et al., 2021).

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning (2024), and a ViT model pretrained from ImageNet (Dosovitskiy et al., 2021)

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:34:28.822816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0e1fd733-c4ca-4af4-8b40-c9ce2c7a6f38 · outbound

This paper cites far more than the available number of samples per task.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning far more than the available number of samples per task

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:34:28.811711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8c0c2c59-b44c-4795-9b8a-30c08db12e6d · outbound

This paper cites By this construction, the matrix P ∈ RD×d never has to be explicitly instantiated, which makes the memory and computational overhead tractable.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning By this construction, the matrix P ∈ RD×d never has to be explicitly instantiated, which makes the memory and computational overhead tractable

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:34:28.800763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b2406062-db33-4bb4-8b16-d3e6ea888e86 · outbound

This paper cites an unresolved cited work.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-09T21:34:28.789301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a5175669-0060-4dd6-a9c9-57ea1796f11c · outbound

This paper cites BitNet: Scaling 1-bit Transformers for Large Language Models.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning BitNet: Scaling 1-bit Transformers for Large Language Models

Reference 1971

Resolution: unresolved; no resolver link, observed 2026-08-09T21:34:28.369362Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b1ca76b-601b-41b5-819d-26e098338e6e · outbound

This paper cites PAC-Bayes Bounds for Meta-learning with Data-Dependent Prior.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning PAC-Bayes Bounds for Meta-learning with Data-Dependent Prior

Reference 2018

Resolution: verified exact; local_arxiv, observed 2026-08-09T21:34:28.778131Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation eb086567-092c-41ce-8636-f21dd08e6ba2 · outbound

This paper cites Bayes meets Bernstein at the Meta Level: an Analysis of Fast Rates in Meta-Learning with PAC-Bayes.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning Bayes meets Bernstein at the Meta Level: an Analysis of Fast Rates in Meta-Learning with PAC-Bayes

Reference 2022

Resolution: verified exact; local_arxiv, observed 2026-08-09T21:34:28.495200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d9e06bbf-441a-4089-85c2-7f22347f3ad9 · outbound

This paper cites A note on the PAC Bayesian theorem.

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning A note on the PAC Bayesian theorem

Reference 2024

Resolution: verified exact; arxiv_id_nonexistent, observed 2026-08-09T21:34:28.760986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

Observation 4e2b1fda-f970-46d1-b360-1d182824253f · inbound

Federated Learning with Unlabeled Clients: Personalization Can Happen in Low Dimensions cites this paper.

Federated Learning with Unlabeled Clients: Personalization Can Happen in Low Dimensions From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T15:21:58.289655Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0afa58dd-e5d7-4816-819f-cd4373287e03 · inbound

Deep Multitask Learning for Mixed-Type Outcomes with Shared Sparsity cites this paper.

Deep Multitask Learning for Mixed-Type Outcomes with Shared Sparsity From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning

Reference 28

Resolution: verified exact; arxiv_id, observed 2026-07-02T06:06:40.550027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.