Paper Citation Record · LEDGER

From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks

As of 10 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 9 inbound Pith citation observations for arXiv:2409.14623.

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

pith.paper-citation-record.v1
2409.14623 v2

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 9 of 9 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 9 of 9 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-09T11:54:36.860380Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-06-29T16:33:39.685349Z

Reference resolution

0 of 0 outbound references displayed

verified exact0
verified fuzzy0
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 487aad8a-f5b0-4bc3-aceb-248014afba66 · inbound

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer cites this paper.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-09T11:54:36.860380Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 912eaccd-4bb1-4b41-b64f-11e825bebde8 · inbound

Feature learning is decoupled from generalization in high capacity neural networks cites this paper.

Feature learning is decoupled from generalization in high capacity neural networks From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T14:17:37.071621Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b62f45f1-5b68-4dfb-a104-6c16ddc0e9fa · inbound

You Had One Job: Per-Task Quantization Using LLMs' Hidden Representations cites this paper.

You Had One Job: Per-Task Quantization Using LLMs' Hidden Representations From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks

Reference 15

Resolution: metadata mismatch; arxiv_id, observed 2026-05-21T18:50:30.203891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f435ab1f-0d80-42e7-9d1e-a1092187ae9f · inbound

You Had One Job: Per-Task Quantization Using LLMs' Hidden Representations cites this paper.

You Had One Job: Per-Task Quantization Using LLMs' Hidden Representations From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-03T23:21:38.003926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bb9fab7a-155a-40e6-b22b-bbfcdc86025d · inbound

A Theory of How Pretraining Shapes Inductive Bias in Fine-Tuning cites this paper.

A Theory of How Pretraining Shapes Inductive Bias in Fine-Tuning From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-02T21:30:50.893495Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 07662729-5119-4428-8849-cbf5de598618 · inbound

Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer cites this paper.

Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks

Reference 63

Resolution: verified exact; arxiv_id, observed 2026-05-11T03:05:53.479198Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0f656cf8-262b-4363-bd14-ab1bd8a63e17 · inbound

Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer cites this paper.

Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks

Reference 68

Resolution: verified exact; arxiv_id, observed 2026-05-22T10:26:24.179720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3ba970f4-9dcf-4620-872f-4836cbe951e8 · inbound

Signal-to-Noise Ratio and Sample Size Govern Representational Alignment in Neural Networks cites this paper.

Signal-to-Noise Ratio and Sample Size Govern Representational Alignment in Neural Networks From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks

Reference 20

Resolution: metadata mismatch; arxiv_id, observed 2026-06-29T16:33:39.686733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b0a81c82-badd-4a6b-829e-e1e2999aa7d3 · inbound

How are linear representations learned? Exact solutions to the dynamics of abstraction cites this paper.

How are linear representations learned? Exact solutions to the dynamics of abstraction From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks

Reference 31

Resolution: unresolved; no resolver link, observed 2026-07-13T06:19:30.027337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.