Paper Citation Record · LEDGER

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression

As of 18 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2606.01292.

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

pith.paper-citation-record.v1
2606.01292 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T11:50:26.030339Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

23 of 23 outbound references displayed

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External citation measurements

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Outbound references

Observation 549e6bb5-cab6-44ec-be1b-b09a4781cca3 · outbound

This paper cites Scaling and renormalization in high-dimensional regression.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression Scaling and renormalization in high-dimensional regression

Reference 1

Resolution: metadata mismatch; local_arxiv, observed 2026-06-28T17:22:24.118665Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 645d5ca0-819a-4662-9f84-047f4ed8b3c9 · outbound

This paper cites doi: 10.1038/s41586-025-09422-z.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression doi: 10.1038/s41586-025-09422-z

Reference 2

Resolution: metadata mismatch; doi, observed 2026-06-28T17:22:24.115176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation aec240e3-873c-4610-a8ea-3c1d4af55983 · outbound

This paper cites The Optimality of (Accelerated) SGD for High-Dimensional Quadratic Optimization.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression The Optimality of (Accelerated) SGD for High-Dimensional Quadratic Optimization

Reference 3

Resolution: malformed identifier; arxiv_id, observed 2026-06-28T17:22:25.085893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1fe01a40-55ed-45b5-8340-585421da2044 · outbound

This paper cites We take the trace of the RHS of Eq.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression We take the trace of the RHS of Eq

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

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Observation deb8a5d9-3de5-4126-8c54-6720934dc8aa · outbound

This paper cites If the target functionw ∗ is not fully realizable within the feature space (i.e., w∗ has a component in the null space of Σ), an irreducible approximation error exists.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression If the target functionw ∗ is not fully realizable within the feature space (i.e., w∗ has a component in the null space of Σ), an irreducible approximation error exists

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

Source-reported events for the cited work

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Observation 78f292be-c570-4f45-9bc1-2eeef06a6e21 · outbound

This paper cites an unresolved cited work.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a0ac1c5-742c-46bd-85ca-26c5e6ffbf6d · outbound

This paper cites an unresolved cited work.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

Source-reported events for the cited work

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Observation 79c4bd5a-73be-405a-9979-cc0ad514c692 · outbound

This paper cites an unresolved cited work.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cafefed0-60bf-4119-8945-4e2ff31ac73b · outbound

This paper cites an unresolved cited work.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

Source-reported events for the cited work

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Observation 966a8269-b9b5-43bd-9961-0db1cb9d7538 · outbound

This paper cites an unresolved cited work.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

Source-reported events for the cited work

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Observation 7b4f08e8-aabf-4827-b657-db694bd5ed8f · outbound

This paper cites an unresolved cited work.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

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Observation f0210b6f-a6e7-44a2-84dd-48ace3c133b0 · outbound

This paper cites Then we shall have the desired upper bound.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression Then we shall have the desired upper bound

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

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Observation 50ba3451-b74d-4a37-afe0-58d5fa6ca8d5 · outbound

This paper cites The minimal-norm solution tomin w ∥M⊤ S w−w ∗∥2 is: w∗ S = (M⊤ S )+w∗.(130) Knowledge Transfer:The teacher first learns the ground truth, yielding w∗ T = (M⊤ T)+w∗.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression The minimal-norm solution tomin w ∥M⊤ S w−w ∗∥2 is: w∗ S = (M⊤ S )+w∗.(130) Knowledge Transfer:The teacher first learns the ground truth, yielding w∗ T = (M⊤ T)+w∗

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

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Observation f490e955-bd48-4eba-8d7d-f617bd7035ed · outbound

This paper cites an unresolved cited work.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c112c364-7579-4200-a9b2-d09946580ad1 · outbound

This paper cites For the transfer student, the prediction isM ⊤ S wopt T2S =Π SΠTw∗.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression For the transfer student, the prediction isM ⊤ S wopt T2S =Π SΠTw∗

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11d2b633-5a7b-49b5-8aac-a7577a6f7599 · outbound

This paper cites an unresolved cited work.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

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Observation 5504fa70-4590-46be-b30e-a2a70e986429 · outbound

This paper cites • Tail Bias:Since Σ is trace-class (P λk <∞ ), the tail energy sumP∞ i=k∗+1 λi(w(i))2 must vanish as the start index k∗ → ∞.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression • Tail Bias:Since Σ is trace-class (P λk <∞ ), the tail energy sumP∞ i=k∗+1 λi(w(i))2 must vanish as the start index k∗ → ∞

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 50d1d706-6fee-4dcd-9de4-2d0d338aed99 · outbound

This paper cites Provided the bias terms O(γ0) and alignment errors are small compared to this variance reduction, we have the strict inequality: E[RT2S]<E[R T].(179) This completes the proof.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression Provided the bias terms O(γ0) and alignment errors are small compared to this variance reduction, we have the strict inequality: E[RT2S]<E[R T].(179) This completes the proof

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

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Observation fb36d5bc-8031-46bb-b4c8-e0651f2564ed · outbound

This paper cites We assume the teacher’s sample sizeNis sufficiently large (N γ 0λk† ≫1) such that the teacher has fully learned the signal.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression We assume the teacher’s sample sizeNis sufficiently large (N γ 0λk† ≫1) such that the teacher has fully learned the signal

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

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Observation fdc8c455-4ffa-401e-baa4-3b06c9c750de · outbound

This paper cites 35 What Makes a Strong Model? • Inherited Variance (Head):The teacher’s noise is white in the projected space.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression 35 What Makes a Strong Model? • Inherited Variance (Head):The teacher’s noise is white in the projected space

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

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Observation 329679d6-08cf-4d12-9089-9e80b1525a55 · outbound

This paper cites Setting the derivative to zero: 1 N −2α S(k†)2αS(k∗ S)−2αS−1N 1−αT αT = 0.(186) Solving fork ∗ S: (k∗ S)2αS+1 ≍(k †)2αSN 1−αT αT ·N = (k†)2αSN 1−αT +αT αT = (k†)2αSN 1 αT.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression Setting the derivative to zero: 1 N −2α S(k†)2αS(k∗ S)−2αS−1N 1−αT αT = 0.(186) Solving fork ∗ S: (k∗ S)2αS+1 ≍(k †)2αSN 1−αT αT ·N = (k†)2αSN 1−αT +αT αT = (k†)2αSN 1 αT

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 467ecdb0-7490-4a12-b90c-05fa46f0c6be · outbound

This paper cites Overparameterized Linear.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression Overparameterized Linear

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11a17d47-34cc-4a82-9314-5414d342b8e5 · outbound

This paper cites an unresolved cited work.

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-28T17:18:02.810457Z

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Unavailable: canonical work link unavailable.

Pith citing papers

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