Paper Citation Record · LEDGER

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth

As of 9 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2607.14018.

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

pith.paper-citation-record.v1
2607.14018 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T03:08:35.920695Z

measured 28 of 28 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 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

28 of 28 outbound references displayed

verified exact0
verified fuzzy0
unresolved28
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e48fb2be-2297-48ac-8c9a-88159c794113 · outbound

This paper cites Only Large Weights (And Not Skip Connections) Can Prevent the Perils of Rank Collapse.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth Only Large Weights (And Not Skip Connections) Can Prevent the Perils of Rank Collapse

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:33.307962Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 00a60409-d957-4b5e-998b-be61f14b88c5 · outbound

This paper cites Low-Rank Learning by Design: the Role of Network Architecture and Activation Linearity in Gradient Rank Collapse.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth Low-Rank Learning by Design: the Role of Network Architecture and Activation Linearity in Gradient Rank Collapse

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:33.459795Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2f78be75-bc4c-4ba5-b114-99c6adc04c26 · outbound

This paper cites Each Sk multiplies k branch Jacobians, so it inherits the rank deficiency of a k-fold branch composition, weighted byβ k.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth Each Sk multiplies k branch Jacobians, so it inherits the rank deficiency of a k-fold branch composition, weighted byβ k

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:35.574804Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 273679db-de8d-4d2e-aed1-ea71ae1f0cad · outbound

This paper cites A dash marks a configuration that does not reach0.4at any learning rate in the sweep (3×10 −5 to10 −2).

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth A dash marks a configuration that does not reach0.4at any learning rate in the sweep (3×10 −5 to10 −2)

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:35.823673Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06080479-a95f-48bf-8ee2-dbbaec113f33 · outbound

This paper cites Exact attention sensitivity and the geometry of transformer stability.arXiv preprint arXiv:2602.18849,.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth Exact attention sensitivity and the geometry of transformer stability.arXiv preprint arXiv:2602.18849,

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:33.954746Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a18b744d-80b7-49d7-8bff-d8873eeca8f7 · outbound

This paper cites Gemma 2: Improving Open Language Models at a Practical Size.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth Gemma 2: Improving Open Language Models at a Practical Size

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:34.141662Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dee6e0eb-ce83-4d74-a0f4-2e1b2064ac60 · outbound

This paper cites Gemma 3 Technical Report.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth Gemma 3 Technical Report

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:34.224246Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bff7ff00-57e9-4fef-bd98-e4b29c746f49 · outbound

This paper cites Kimi K2: Open Agentic Intelligence.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth Kimi K2: Open Agentic Intelligence

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:34.417739Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 18987e3a-67f6-440b-b156-fb44c1a64ccb · outbound

This paper cites BranchNorm: Robustly scaling extremely deep transformers.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth BranchNorm: Robustly scaling extremely deep transformers

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:34.552050Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a94b6d69-0fe4-42f2-b1e5-d02798593350 · outbound

This paper cites The Llama 3 Herd of Models.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth The Llama 3 Herd of Models

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:34.611621Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7d316a65-7278-4e75-9304-53ef6fb70121 · outbound

This paper cites gpt-oss-120b & gpt-oss-20b Model Card.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth gpt-oss-120b & gpt-oss-20b Model Card

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:34.824744Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9ae25059-0d74-4d40-89f4-ef847f09db69 · outbound

This paper cites Qwen3 Technical Report.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth Qwen3 Technical Report

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:34.907923Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 900e3749-5352-4242-bdec-812979d4370d · outbound

This paper cites NormFormer: Improved Transformer Pretraining with Extra Normalization.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth NormFormer: Improved Transformer Pretraining with Extra Normalization

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:35.091316Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5889ff37-be9f-4862-aada-7d1bbd9ff7fc · outbound

This paper cites B2T connection: Serving stability and performance in deep transformers.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth B2T connection: Serving stability and performance in deep transformers

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:35.217838Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 827d113d-7c31-4d7e-86ac-3bb3ffb716f9 · outbound

This paper cites Tensor Programs IVb: Adaptive Optimization in the Infinite-Width Limit.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth Tensor Programs IVb: Adaptive Optimization in the Infinite-Width Limit

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:35.369376Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 87a008c7-51b4-4bbd-9f8e-1c512d8b3f6e · outbound

This paper cites an unresolved cited work.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:35.741338Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e816ea9-e4c7-439a-8548-a9838ded34b0 · outbound

This paper cites (c)A centered activation has no mean to align (mean−0.000).

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth (c)A centered activation has no mean to align (mean−0.000)

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:35.870297Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1dd2402c-3f46-455e-9225-5101237e875b · outbound

This paper cites We call the expected fraction of units with nonzero derivative the survival rate,p(σ) = Prz∼N(0,1) [σ′(z)̸= 0].

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth We call the expected fraction of units with nonzero derivative the survival rate,p(σ) = Prz∼N(0,1) [σ′(z)̸= 0]

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:35.920695Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bc5f3824-41da-44c4-b328-d09da15f831b · outbound

This paper cites GLU Variants Improve Transformer.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth GLU Variants Improve Transformer

Reference 2014

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:35.002142Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c4654426-a0e4-448e-b38b-6af51e9993c0 · outbound

This paper cites SpanNorm: Reconciling Training Stability and Performance in Deep Transformers.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth SpanNorm: Reconciling Training Stability and Performance in Deep Transformers

Reference 2016

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:35.290649Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 226ffbf1-939e-4791-b448-58554c01edd8 · outbound

This paper cites Layer Normalization.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth Layer Normalization

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:33.370890Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3621f71f-ef55-46cb-9473-39f0fac4c6ab · outbound

This paper cites DeepSeek-V3 Technical Report.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth DeepSeek-V3 Technical Report

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:33.731421Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a6800d9-0742-4de5-b3a5-7b6ece99915e · outbound

This paper cites MiniMax-01: Scaling Foundation Models with Lightning Attention.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth MiniMax-01: Scaling Foundation Models with Lightning Attention

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:34.681235Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d11e4e1e-c8cd-43b4-981b-c6921e56d763 · outbound

This paper cites When do spectral gradient updates help in deep learning?arXiv preprint arXiv:2512.04299,.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth When do spectral gradient updates help in deep learning?arXiv preprint arXiv:2512.04299,

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:33.607706Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7734077f-6a38-41c1-bf25-19947ff1f201 · outbound

This paper cites Gaussian Error Linear Units (GELUs).

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth Gaussian Error Linear Units (GELUs)

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:34.348358Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36a606cc-72b7-457b-b9f5-7d88010952b2 · outbound

This paper cites Post-LayerNorm is back: Stable, ExpressivE, and deep.arXiv preprint arXiv:2601.19895,.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth Post-LayerNorm is back: Stable, ExpressivE, and deep.arXiv preprint arXiv:2601.19895,

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:33.527787Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 441c7ac1-0dea-4e4e-8ebd-64729a209e57 · outbound

This paper cites On residual network depth.arXiv preprint arXiv:2510.03470,.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth On residual network depth.arXiv preprint arXiv:2510.03470,

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:33.859389Z

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Unavailable: canonical work link unavailable.

Observation e396381d-7467-4da9-bf64-adcbd04e9bc0 · outbound

This paper cites The depth delusion: Why transformers should be wider, not deeper.arXiv preprint arXiv:2601.20994,.

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth The depth delusion: Why transformers should be wider, not deeper.arXiv preprint arXiv:2601.20994,

Reference 2026

Resolution: unresolved; no resolver link, observed 2026-08-02T03:08:34.059511Z

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Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.