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Paper Citation Record · LEDGER

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders

As of 7 August 2026, this Paper Citation Record lists 70 of 70 outbound references and 0 inbound Pith citation observations for arXiv:2505.24668.

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

pith.paper-citation-record.v1
2505.24668 v1

Coverage vector

measured 70 of 70 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:27:49.739360Z

measured 70 of 70 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

70 of 70 outbound references displayed

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  • verified fuzzy41
  • unresolved21
  • parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c3382407-b7f4-4bd5-b0f0-81f1bd646270 · outbound

This paper cites The loss landscape of deep linear neural networks: a second-order analysis.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders The loss landscape of deep linear neural networks: a second-order analysis

Reference 1

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Observation 32175d06-e524-4dba-9f1b-79242ec33cbe · outbound

This paper cites A Random Matrix Perspective on Mixtures of Nonlinearities in High Dimensions.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders A Random Matrix Perspective on Mixtures of Nonlinearities in High Dimensions

Reference 2

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Observation 07e403a2-d3d2-4011-af8f-276fcab2fb81 · outbound

This paper cites Complex analysis.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Complex analysis

Reference 3

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Observation 6f881f1a-2c89-4b95-a7ae-fcb6a5417466 · outbound

This paper cites Generalization of two-layer neural networks: An asymptotic viewpoint.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Generalization of two-layer neural networks: An asymptotic viewpoint

Reference 4

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 4fa62057-983b-48f2-8b6d-07c62e23d644 · outbound

This paper cites High-dimensional analysis of double descent for linear regression with random projections.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders High-dimensional analysis of double descent for linear regression with random projections

Reference 5

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Observation 74a3a999-1ff5-40fa-8df8-93bc29121c0e · outbound

This paper cites Spectral analysis of large dimensional random matrices.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Spectral analysis of large dimensional random matrices

Reference 6

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Observation dd6eccf3-4b08-4fca-8598-34625f26e655 · outbound

This paper cites Eigenvalues of Large Sample Covariance Matrices of Spiked Population Models.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Eigenvalues of Large Sample Covariance Matrices of Spiked Population Models

Reference 7

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Observation b93c874f-1168-44fa-9321-a2326173fd42 · outbound

This paper cites Neural networks and principal component analysis: Learning from examples without local minima.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Neural networks and principal component analysis: Learning from examples without local minima

Reference 8

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Observation bb3564a2-b4aa-49f2-aecd-d9a8eec0287e · outbound

This paper cites Benign overfitting in linear regression.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Benign overfitting in linear regression

Reference 9

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Source-reported events for the cited work

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Observation d5c6259c-316d-45a3-ba9f-bfd51249ca00 · outbound

This paper cites Reconciling modern machine-learning practice and the classical bias–variance trade-off.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Reconciling modern machine-learning practice and the classical bias–variance trade-off

Reference 10

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Observation 75d10350-b7d2-4618-9eb3-12c38d07242f · outbound

This paper cites On the Exact Covariance of Products of Random Variables.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders On the Exact Covariance of Products of Random Variables

Reference 11

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Observation c23fe395-c66e-4399-9d77-4c6b25c4b8ac · outbound

This paper cites Random Matrix Methods for Machine Learning.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Random Matrix Methods for Machine Learning

Reference 12

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Observation ae9d378f-c170-46c7-8eb0-a7891cf841ca · outbound

This paper cites High-dimensional asymptotics of denoising autoencoders.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders High-dimensional asymptotics of denoising autoencoders

Reference 13

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Observation d8dacd5a-9afc-4edd-bbba-dfc58e2d2d00 · outbound

This paper cites A U-turn on Double Descent: Rethinking Parameter Counting in Statistical Learning.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders A U-turn on Double Descent: Rethinking Parameter Counting in Statistical Learning

Reference 14

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Observation dabfaf67-b9b9-4601-975c-fd2674324083 · outbound

This paper cites Procedures for Reduced-Rank Regression.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Procedures for Reduced-Rank Regression

Reference 15

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Observation a374868f-0da5-4e64-9635-2e1954727d5c · outbound

This paper cites On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices

Reference 16

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Observation 5d16ee29-df90-4365-985b-f41bbb2f5b99 · outbound

This paper cites Probability: theory and examples.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Probability: theory and examples

Reference 17

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Observation 7a97a089-b584-4c47-882d-bad1b4d8c50a · outbound

This paper cites The approximation of one matrix by another of lower rank.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders The approximation of one matrix by another of lower rank

Reference 18

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Observation d22f530d-53df-4985-a004-5d7ad2a2996a · outbound

This paper cites The rank of a random matrix.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders The rank of a random matrix

Reference 19

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Observation 2e7b1b9a-31f0-451d-a914-c8e67e95c0f1 · outbound

This paper cites No Double Descent in Prin- cipal Component Regression: A High-Dimensional Analysis.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders No Double Descent in Prin- cipal Component Regression: A High-Dimensional Analysis

Reference 20

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Observation 42333fd8-4a77-42ee-9f2c-6141b85aff37 · outbound

This paper cites Asymptotic errors for convex penalized linear regression beyond Gaussian matrices.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Asymptotic errors for convex penalized linear regression beyond Gaussian matrices

Reference 21

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Observation 6316d234-b4ad-4374-9509-3e79ac379202 · outbound

This paper cites Surprises in High-Dimensional Ridgeless Least Squares Interpolation.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Surprises in High-Dimensional Ridgeless Least Squares Interpolation

Reference 22

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Observation 2bd4384f-9de7-44a3-bacc-8d432eac5a6d · outbound

This paper cites Deep Residual Learning for Image Recognition.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Deep Residual Learning for Image Recognition

Reference 23

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Observation 003c0e7f-cf6b-4e47-91c1-454efebccd66 · outbound

This paper cites Denoising Diffusion Probabilistic Models.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Denoising Diffusion Probabilistic Models

Reference 24

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Observation 84173857-16ca-417a-80e5-00f029483f00 · outbound

This paper cites No Double Descent in Self-Supervised Learning.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders No Double Descent in Self-Supervised Learning

Reference 25

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Observation 060068b9-6cd5-4109-907b-f752a9812f1a · outbound

This paper cites On the Distribution of the Largest Eigenvalue in Principal Components Analysis.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders On the Distribution of the Largest Eigenvalue in Principal Components Analysis

Reference 26

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Observation 424d10e9-36f8-44fd-9333-7a5275423a3a · outbound

This paper cites Double Descent and Overfitting under Noisy Inputs and Distribution Shift for Linear Denoisers.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Double Descent and Overfitting under Noisy Inputs and Distribution Shift for Linear Denoisers

Reference 27

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Source-reported events for the cited work

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Observation 4179fc1e-5a88-4eb9-ad7a-5ceed14ee473 · outbound

This paper cites Deep Learning without Poor Local Minima.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Deep Learning without Poor Local Minima

Reference 28

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Unavailable: canonical work link unavailable.

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Observation e4a2ee23-fa2f-42c5-a54a-640c8bf8aa61 · outbound

This paper cites Learning multiple layers of features from tiny images.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Learning multiple layers of features from tiny images

Reference 29

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 124a79b6-9d2f-4509-a23f-6538458ab8fa · outbound

This paper cites Does Double Descent Occur in Self-Supervised Learning?.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Does Double Descent Occur in Self-Supervised Learning?

Reference 30

Resolution
verified exact
local_arxiv, observed 2026-08-07T12:27:50.039042Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 6a874912-3319-4b96-9339-7cde935143e8 · outbound

This paper cites Reduced rank ridge regression and its kernel extensions.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Reduced rank ridge regression and its kernel extensions

Reference 31

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 90226f3f-0d0d-4e3c-b957-5a81266f1804 · outbound

This paper cites Deep Double Descent: Where Bigger Models and More Data Hurt.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Deep Double Descent: Where Bigger Models and More Data Hurt

Reference 32

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verified fuzzy
raw_fallback, observed 2026-08-07T12:27:58.417106Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation e7e23329-b414-4882-a99a-c80dcb7858dc · outbound

This paper cites Learning dynamics of linear denoising autoencoders.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Learning dynamics of linear denoising autoencoders

Reference 33

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raw_fallback, observed 2026-08-07T12:27:58.220630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation a992d39d-bc81-48ef-8174-2f5eef014dbc · outbound

This paper cites Multiple Descents in Unsupervised Learning: The Role of Noise, Domain Shift and Anomalies.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Multiple Descents in Unsupervised Learning: The Role of Noise, Domain Shift and Anomalies

Reference 34

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no resolver link, observed 2026-08-07T12:27:45.911204Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T12:27:45.911204Z digest=sha256:223a70ecd10660c250cbc5294f53ec560330f461d8c4efa4ab2000d79e8fbfeb

Observation e790c74d-f8c0-432f-93e8-514647dca8db · outbound

This paper cites U-Net: Convolutional Networks for Biomedical Image Segmentation.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders U-Net: Convolutional Networks for Biomedical Image Segmentation

Reference 35

Resolution
unresolved
no resolver link, observed 2026-08-07T12:27:45.950324Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T12:27:45.950324Z digest=sha256:e7770a2f97afb979fcc4ef7ac58066ba92849c82aa9a68344a262eca8195b9da

Observation 369c895a-e7a8-4d79-864c-cf8e37779a1a · outbound

This paper cites Smallest singular value of a random rectangular matrix.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Smallest singular value of a random rectangular matrix

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:58.016057Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:45.999637Z digest=sha256:26e97d80d29b11068abe4d1c78e753e666288d3f1f34cdefd1baf222651cb60e

Observation 778fd46c-c8cd-4dd7-ab69-80c8b70045fd · outbound

This paper cites On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices

Reference 37

Resolution
unresolved
no resolver link, observed 2026-08-07T12:27:46.074059Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T12:27:46.074059Z digest=sha256:29c78b918bd0fcb6e77ce978dd2e431545f21bec6f3f4f7bf08b79a898ae35b9

Observation 5500fdf2-914d-410a-87f3-45672d00bcbf · outbound

This paper cites Training Data Size Induced Double Descent For Denoising Neural Networks and the Role of Training Noise Level.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Training Data Size Induced Double Descent For Denoising Neural Networks and the Role of Training Noise Level

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:57.826532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:46.156358Z digest=sha256:c0812a2430f4eedd21cd7569b234536dbe9a96452daac39e95ff97603bd2610f

Observation d05cf9f2-ec45-4e2d-815d-6e0e1ba5ee14 · outbound

This paper cites Topics in random matrix theory.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Topics in random matrix theory

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:57.543393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:46.244583Z digest=sha256:5f201b498bedd63526393506c32a8fed7aea6eab63f8041bad60c9ea48c0974e

Observation b33f2293-636f-4986-b77b-8d4b7b26394f · outbound

This paper cites Dimensionality Reduction, Regulariza- tion, and Generalization in Overparameterized Regressions.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Dimensionality Reduction, Regulariza- tion, and Generalization in Overparameterized Regressions

Reference 40

Resolution
unresolved
no resolver link, observed 2026-08-07T12:27:46.354318Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T12:27:46.354318Z digest=sha256:c42e57c62078417d94128de837b12fd01661a572515bce717af254f58c472a92

Observation ff6eb2e7-00a3-44c5-80e3-5e9112f224d0 · outbound

This paper cites Pure and Spurious Critical Points: a Geometric Study of Linear Networks.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Pure and Spurious Critical Points: a Geometric Study of Linear Networks

Reference 41

Resolution
unresolved
no resolver link, observed 2026-08-07T12:27:46.425167Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T12:27:46.425167Z digest=sha256:65838905ba78870272223a7e6e5bcfa0a26837ee2429a0e7a34968949810845f

Observation 08c7c6ad-2850-42fa-802e-e2711cdf6d22 · outbound

This paper cites Why are Big Data Matrices Approximately Low Rank?.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Why are Big Data Matrices Approximately Low Rank?

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:57.386944Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:46.500666Z digest=sha256:9e4290f2209c20e4fe7b1b8daeae7d6f030e4ceeb175ee5c0e3850ac081cb051

Observation f4e9e3a2-36a9-4236-af53-fbc1f4e07682 · outbound

This paper cites High-dimensional probability: An introduction with applications in data science.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders High-dimensional probability: An introduction with applications in data science

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:57.209168Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:46.803418Z digest=sha256:13f35cb41ecb7df9f48577e5b824f92de0c6fec74dc5dfe3330e5b8e58dd703f

Observation 47a05f12-5448-4cc0-acb6-530197062b70 · outbound

This paper cites Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:57.027388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:46.923074Z digest=sha256:e0eea71b4370d26a97c4a2ba14f97171ab37732252da7659d8784bcae694ca3e

Observation 672e4306-bc06-4489-81c8-86a3b5dee2f2 · outbound

This paper cites The weighted Moore–Penrose inverse of modified matrices.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders The weighted Moore–Penrose inverse of modified matrices

Reference 45

Resolution
malformed identifier
no resolver link, observed 2026-08-07T12:27:47.043216Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T12:27:47.043216Z digest=sha256:761b12a8d1b8944da2d686b313bd6ddd2d7f73180d0ec7e4076580c542a148ed

Observation 44a9cc3a-2efc-4be3-b4b5-f0fe195de5f7 · outbound

This paper cites Optimal exact least squares rank minimization.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Optimal exact least squares rank minimization

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:56.883247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:47.206242Z digest=sha256:053264697110abd6b66c9c2602eeac616e2977a65f7b1d2f0662db523a6a370d

Observation e461eb08-d054-4641-81e8-73a2d862a280 · outbound

This paper cites Critical Points of Neural Networks: Analytical Forms and Landscape Properties.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Critical Points of Neural Networks: Analytical Forms and Landscape Properties

Reference 47

Resolution
unresolved
no resolver link, observed 2026-08-07T12:27:47.335155Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T12:27:47.335155Z digest=sha256:f5306a9d77a80cc5b4c1dd2b8267def721ce88acf8a9b2f71d0ffb4481a8525f

Observation ade236b3-d254-49fe-bf79-c0023557612a · outbound

This paper cites The above eq.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders The above eq

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:56.661887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:47.480915Z digest=sha256:ec2291a2d7337c923733bbd40e0e3b07a7367abf923637500eba12cf684a3f04

Observation 6e028243-7526-480b-a3d3-6cf72973fdd6 · outbound

This paper cites For a real probability measureµ with support supp(µ), the Stieltjes Transform of µ is defined as mµ(α) = Z 1 x − α dµ(x), α ∈ C\supp(µ).

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders For a real probability measureµ with support supp(µ), the Stieltjes Transform of µ is defined as mµ(α) = Z 1 x − α dµ(x), α ∈ C\supp(µ)

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:56.489778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:47.592878Z digest=sha256:7a6de84b3d000dd8cce7ff85062ca91d160706637ba41fa833aca8a0dd2c2285

Observation 9b370979-922b-4fa8-a6cd-546f29ed25f7 · outbound

This paper cites Let A ∈ Rp×p, and x, y ∈ Rp.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Let A ∈ Rp×p, and x, y ∈ Rp

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:56.282275Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:47.755848Z digest=sha256:567726812612acdf2107f6d30c3896e7ebf2650d2f7c89c5eea66c845bd9b4a8

Observation e5120d7e-6d2d-437d-8e20-d718ed3a3fa5 · outbound

This paper cites For α ∈ C\R+, let ˜Q(α) = ˜A ˜AT − αId −1 = NP i=1 ˜ai˜aT i − αId −1 , where ˜A ∈ Rd×N is a i.i.d real gaussian random matrix, whose entries are sampled from N (0, 1).

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders For α ∈ C\R+, let ˜Q(α) = ˜A ˜AT − αId −1 = NP i=1 ˜ai˜aT i − αId −1 , where ˜A ∈ Rd×N is a i.i.d real gaussian random matrix, whose entries are sampled from N (0, 1)

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:56.113121Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:47.912450Z digest=sha256:7259b4a09e05ff16a6d66e89907b112d85a77b43ac7e022de03ac1d6b3a41c9c

Observation f8a27999-54ab-4a92-97f3-f00dff2cbbd4 · outbound

This paper cites For symmetric and positive semi-definite B, M ∈ Rd×d, and α ∈ C\R+, let M := hP j=1 lixixT i for fixed h, and li ∈ R, xi ∈ Rd.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders For symmetric and positive semi-definite B, M ∈ Rd×d, and α ∈ C\R+, let M := hP j=1 lixixT i for fixed h, and li ∈ R, xi ∈ Rd

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:55.927324Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:48.045531Z digest=sha256:ada5c2bc29959f8aacf419350f616f3fcb03db3e1f807d4a4d08324ad1448bbf

Observation af255f0f-70b2-42e2-ad6f-e74040c846a9 · outbound

This paper cites For A ∈ Rp×q, B ∈ Rq×p, and λ ∈ R\{0}.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders For A ∈ Rp×q, B ∈ Rq×p, and λ ∈ R\{0}

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:55.746290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:48.179494Z digest=sha256:caa9d927bdd769275ee304d929e419c9657fb62619ca8f7762c9e870c0866bea

Observation d91b332f-155f-4538-a66a-7cb25b2c076e · outbound

This paper cites For A ∈ Rp×p, U ∈ Rp×q, V ∈ Rq×p, we have that (A + UVT )−1 = A−1 − A−1U(Iq + VT A−1U)−1VT A−1.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders For A ∈ Rp×p, U ∈ Rp×q, V ∈ Rq×p, we have that (A + UVT )−1 = A−1 − A−1U(Iq + VT A−1U)−1VT A−1

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:55.529423Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:48.308428Z digest=sha256:16c5d44cff574d7c3f08dc17446190fd3af1bc2b3e388ed856432aead5cd77d8

Observation 1acf796c-d1a0-4e15-8c9c-a166d3b130b9 · outbound

This paper cites Furthermore, B has rB eigenvalues equal to 1 and the rest equal to 0.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Furthermore, B has rB eigenvalues equal to 1 and the rest equal to 0

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:55.332808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:48.461047Z digest=sha256:93242d1a9175b8da678520cdf54dbfe5dd877abff5a7883349d877c5f9e01c0f

Observation c2419cf3-f5b0-4cad-afcb-595230adeb5c · outbound

This paper cites an unresolved cited work.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Unresolved cited work

Reference 59

Resolution
unresolved
raw_fallback, observed 2026-08-07T12:27:55.128152Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:48.601342Z digest=sha256:a2bd08db8c63bfad5fd5925b8aa2393e81e83c51835cfe894e38c8172ed7de90

Observation b8446f14-2f57-4e04-9caf-721b2f336f60 · outbound

This paper cites an unresolved cited work.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Unresolved cited work

Reference 60

Resolution
unresolved
raw_fallback, observed 2026-08-07T12:27:54.984576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:48.737074Z digest=sha256:79fb6e0c0000300ae26e2c0c889903d0f0eae704190bb0b0da41edc119d3d317

Observation 403995a4-c0c5-4fd1-955c-ded5ba981de3 · outbound

This paper cites an unresolved cited work.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Unresolved cited work

Reference 61

Resolution
unresolved
raw_fallback, observed 2026-08-07T12:27:54.634950Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:48.880505Z digest=sha256:cb4b78681beedbea0fd3c83c4580d218e2cbe21ecf1b2ee83e01beaa3396c9d2

Observation e87cb913-9f44-4547-b442-23f14d0697ef · outbound

This paper cites Furthermore, assume rZ = n.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Furthermore, assume rZ = n

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:54.242374Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:49.008577Z digest=sha256:3c219ef098c1c91d7daa95fae9be29dfa2db890242e795d6d3c86f94659fbeb9

Observation fc516b88-f6b4-43ba-87b5-c7d17acbf6b9 · outbound

This paper cites an unresolved cited work.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Unresolved cited work

Reference 63

Resolution
unresolved
raw_fallback, observed 2026-08-07T12:27:53.851726Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:49.147336Z digest=sha256:4a103a248067d2b4a9e745ef85a32f46abfdb19e82e428256bea0936f0eed4e8

Observation 7afabcea-52eb-4040-88f3-637340b72d58 · outbound

This paper cites ⇐" direction of the proof follows from a straightforward calculation, and we therefore omit the details. For the.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders ⇐" direction of the proof follows from a straightforward calculation, and we therefore omit the details. For the

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:53.521222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:49.315854Z digest=sha256:e789d864331cbd2a3b626131988f727b4f47700edd79688ed913d85c6af04dd0

Observation 3b295444-e6d8-4d3e-81a4-48549653f2bd · outbound

This paper cites Due to the fact that AI a A†(AI a A†)⊤ = UATaU⊤ A = AI a A†, we have that − Tr(AI a A†(Wsc c )⊤) = Tr(AI a A†(AI a A†)⊤) − Tr(AI a A†H⊤(K1)−1H)− Tr(AI a A†H⊤K−⊤ 1 Z(P⊤P)−⊤D ˜U⊤).

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Due to the fact that AI a A†(AI a A†)⊤ = UATaU⊤ A = AI a A†, we have that − Tr(AI a A†(Wsc c )⊤) = Tr(AI a A†(AI a A†)⊤) − Tr(AI a A†H⊤(K1)−1H)− Tr(AI a A†H⊤K−⊤ 1 Z(P⊤P)−⊤D ˜U⊤)

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:53.188571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:49.506590Z digest=sha256:dc7120872de79aa7384d82bbb016b9bc2a070e5fe8b505bf4a0d3d222d890125

Observation 7491b7f2-99ad-4d39-bdf8-32125b190b02 · outbound

This paper cites The second term has also mean 0 due to Lemma E.9, thus only the variance needs to be bounded for this term.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders The second term has also mean 0 due to Lemma E.9, thus only the variance needs to be bounded for this term

Reference 66

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:52.874067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:49.527737Z digest=sha256:99d86bc472ee28d824c10cb96bbdcc9469fcd3e0801c717787b4af4f569bb3e8

Observation a5858bda-f9b3-4408-8e1b-4eb8e0ed98a6 · outbound

This paper cites The first term is, from Lemma E.7, and Lemma 8 of [27], − Tr(AI a A†H⊤K−1 1 H) = − |I a| n η2 trn c Tr((η2 trnD−2 + Ir)−1) + o |I a| n.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders The first term is, from Lemma E.7, and Lemma 8 of [27], − Tr(AI a A†H⊤K−1 1 H) = − |I a| n η2 trn c Tr((η2 trnD−2 + Ir)−1) + o |I a| n

Reference 67

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:52.629355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:49.531793Z digest=sha256:fa6843bbdf9d17355480ecdf8f0dff445c0d5a003fe16f4cf6c12a96e40f8475

Observation 900a3e4e-e53d-44b5-8fcf-ff6f54c37a94 · outbound

This paper cites The first term has zero mean, as shown in Lemma E.9.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders The first term has zero mean, as shown in Lemma E.9

Reference 68

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:52.350175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T12:27:49.593356Z digest=sha256:1a89fc547a4920833b9440fa362af9530ef8c24f625e531ba4275b491712bff4

Observation 1cbf5831-78a7-437a-935a-21f29466d353 · outbound

This paper cites For the element-wise variance, Lemma E.3 and Lemmas 4, 6, 7, and 8 from [27] imply that it is of order o(1).

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders For the element-wise variance, Lemma E.3 and Lemmas 4, 6, 7, and 8 from [27] imply that it is of order o(1)

Reference 69

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T12:27:52.040518Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation f2389f91-f460-474b-ba28-6f7c485bb69d · outbound

This paper cites an unresolved cited work.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Unresolved cited work

Reference 70

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation a399c26f-aaff-4f3e-ac5c-dfcfc11cffc8 · outbound

This paper cites Why are Big Data Matrices Approximately Low Rank?.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Why are Big Data Matrices Approximately Low Rank?

Reference 2018

Resolution
unresolved
no resolver link, observed 2026-08-07T12:27:46.656377Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T12:27:46.656377Z digest=sha256:3ac912e1c9eac653b154cfa8b5dbefa9baabe1215b80e782c8721e358efe3347

Observation 971d7c18-f602-4a74-b27b-dd9f142e949b · outbound

This paper cites Deep Double Descent: Where Bigger Models and More Data Hurt.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Deep Double Descent: Where Bigger Models and More Data Hurt

Reference 2019

Resolution
unresolved
no resolver link, observed 2026-08-07T12:27:45.771869Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation bc7151f9-61b2-451d-9adb-6889dac84207 · outbound

This paper cites Surprises in High-Dimensional Ridgeless Least Squares Interpolation.

Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders Surprises in High-Dimensional Ridgeless Least Squares Interpolation

Reference 2020

Resolution
unresolved
no resolver link, observed 2026-08-07T12:27:45.045673Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Pith citing papers

No inbound Pith citation observations are available.