Paper Citation Record · LEDGER

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank

As of 17 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2507.11962.

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

pith.paper-citation-record.v1
2507.11962 v1

Coverage vector

measured 38 of 38 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-06T17:06:11.242018Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

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measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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Source: cited_works

Reference resolution

38 of 38 outbound references displayed

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External citation measurements

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Outbound references

Observation 08e4b6a0-103a-4e32-9c01-b578108af52e · outbound

This paper cites Emergence of Invariance and Disentanglement in Deep Representations.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Emergence of Invariance and Disentanglement in Deep Representations

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:06:14.262741Z

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Observation 2596662a-9a52-413a-902e-670de299664d · outbound

This paper cites Mart ´ın.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Mart ´ın

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:06:14.236472Z

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Observation 5b0eddb9-7315-4031-b946-457229321a66 · outbound

This paper cites Physically guided neural network based on transfer learning (TL-PGNN) for hypersonic heat flux prediction.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Physically guided neural network based on transfer learning (TL-PGNN) for hypersonic heat flux prediction

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:06:14.217943Z

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Observation 0fc75396-1c6e-4e37-8017-200a45185c09 · outbound

This paper cites A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks

Reference 4

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Observation 171c80d9-1f05-40bb-bce1-a46e2ea8c844 · outbound

This paper cites Es’kin, Alexey O.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Es’kin, Alexey O

Reference 5

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Observation 2872aa38-5055-40e8-b70f-4ce9c7953a09 · outbound

This paper cites Landscape and training regimes in deep learning.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Landscape and training regimes in deep learning

Reference 6

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Observation 59f51205-bbab-4f67-a6fb-f00389d02d9c · outbound

This paper cites N Ghia, and C.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank N Ghia, and C

Reference 7

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Observation 16fad44a-4303-430b-b558-07a8b917785c · outbound

This paper cites Understanding the difficulty of training deep feedfor- ward neural networks.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Understanding the difficulty of training deep feedfor- ward neural networks

Reference 8

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Observation f940745b-8509-4f65-8a63-d852e0de871d · outbound

This paper cites Makridakis.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Makridakis

Reference 9

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Observation 05375783-5f17-48a0-88c6-339ed26d1e90 · outbound

This paper cites How to start training: The effect of initialization and archi- tecture.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank How to start training: The effect of initialization and archi- tecture

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:06:14.076229Z

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Observation d0e784fa-9b85-4795-9455-6c7d689e7c90 · outbound

This paper cites Deep residual learning for image recognition.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Deep residual learning for image recognition

Reference 11

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Observation f8a33bdd-0c50-407b-a6cd-903747995ac9 · outbound

This paper cites and Em Karniadakis, George.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank and Em Karniadakis, George

Reference 12

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Observation 78de319a-c3cb-4043-8e91-cfca66ccdc8a · outbound

This paper cites Jagtap, Ehsan Kharazmi, and George Em Karniadakis.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Jagtap, Ehsan Kharazmi, and George Em Karniadakis

Reference 13

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Observation 5ccae37c-b6cb-43fa-bd94-215f6adb8ebf · outbound

This paper cites Characterizing possible failure modes in physics-informed neural networks.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Characterizing possible failure modes in physics-informed neural networks

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:06:14.006146Z

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Observation 43d07f6f-4309-4de0-89e1-7a0d480c5355 · outbound

This paper cites Visualizing the Loss Landscape of Neural Nets.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Visualizing the Loss Landscape of Neural Nets

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:06:13.984971Z

Source-reported events for the cited work

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Observation 0c8c6717-9a9c-4b28-a4d4-b72dd344f77d · outbound

This paper cites A Cyclical Learning Rate Method in Deep Learning Training.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank A Cyclical Learning Rate Method in Deep Learning Training

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:06:13.966931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 90d673c2-c780-40a8-9c32-4965eced487a · outbound

This paper cites Solving a class of multi- scale elliptic PDEs by Fourier-based mixed physics informed neural networks.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Solving a class of multi- scale elliptic PDEs by Fourier-based mixed physics informed neural networks

Reference 17

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Observation 3d1b2ef6-0c0f-47e7-b1e3-4f818c128afd · outbound

This paper cites Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:06:13.924161Z

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Observation bbca9164-0ec3-4830-bdf4-33332e6a1cc3 · outbound

This paper cites Con- vergence analysis of pinns with over-parameterization.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Con- vergence analysis of pinns with over-parameterization

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:06:13.905870Z

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Observation f51478dc-0dd3-4a0c-8f98-327d76f310f5 · outbound

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Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Unresolved cited work

Reference 20

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Observation 71ce3cd8-f60e-43c6-ba10-76a5781192e2 · outbound

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Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Unresolved cited work

Reference 21

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Observation 5e069c0e-8d42-4bc4-aad9-78d6210b2ff4 · outbound

This paper cites On the Spectral Bias of Neural Networks.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank On the Spectral Bias of Neural Networks

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:06:13.844220Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 26816827-e28f-47f1-b388-0c89b65ab47a · outbound

This paper cites Physics-informed neural net- works: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Physics-informed neural net- works: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 23

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Observation b0a63ba4-3e82-4c07-a46a-1f615692f36a · outbound

This paper cites DGM: A deep learning algorithm for solv- ing partial differential equations.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank DGM: A deep learning algorithm for solv- ing partial differential equations

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:06:13.681198Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 7a8d8c76-ff25-4252-af5e-3b254edc9a0e · outbound

This paper cites PirateNets: Physics-informed deep learning with residual adaptive networks.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank PirateNets: Physics-informed deep learning with residual adaptive networks

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:06:13.475964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 79cb9b14-da40-4f8e-a0e0-41040cf30763 · outbound

This paper cites Respecting causality for training physics-informed neural networks.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Respecting causality for training physics-informed neural networks

Reference 26

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Observation 32cfec6f-6c3e-4f4d-af3c-f9a30addc141 · outbound

This paper cites An Expert’s Guide to Training Physics-informed Neural Networks, 2023.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank An Expert’s Guide to Training Physics-informed Neural Networks, 2023

Reference 27

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Observation 33ebe01f-a637-4773-9b05-beac11182f5c · outbound

This paper cites Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks

Reference 28

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Observation 27899645-8cfa-4916-b4f2-09e7a786e444 · outbound

This paper cites When and why PINNs fail to train: A neural tangent kernel perspective.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank When and why PINNs fail to train: A neural tangent kernel perspective

Reference 29

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Observation ee16558a-0141-4ae2-87e1-ad2224c7376e · outbound

This paper cites Bordas, and Chao Jiang.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Bordas, and Chao Jiang

Reference 30

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Observation 27d966bf-eb70-4900-8753-50582eebf4b4 · outbound

This paper cites Finite neuron method and convergence analysis.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Finite neuron method and convergence analysis

Reference 31

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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This paper cites Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Net- works.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Net- works

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:06:12.333321Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ab140248-994e-4336-82ca-56039dd23b55 · outbound

This paper cites Overview Frequency Principle/Spectral Bias in Deep Learning.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Overview Frequency Principle/Spectral Bias in Deep Learning

Reference 33

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Observation 968f078e-1b76-4bde-b3f6-fc75af72a3e7 · outbound

This paper cites Training Behavior of Deep Neural Net- work in Frequency Domain.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Training Behavior of Deep Neural Net- work in Frequency Domain

Reference 34

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6f58c896-8228-488c-9471-2bd9b890fab1 · outbound

This paper cites $\epsilon$-rank and the Staircase Phenomenon: New Insights into Neural Network Training Dynamics.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank $\epsilon$-rank and the Staircase Phenomenon: New Insights into Neural Network Training Dynamics

Reference 35

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Observation ee21728a-dc21-4c5a-b0d9-8f14078051ff · outbound

This paper cites Accurate adaptive deep learning method for solving elliptic problems.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Accurate adaptive deep learning method for solving elliptic problems

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:06:11.828502Z

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Observation ae9bdddb-5cfb-483a-9b52-f501687f32d2 · outbound

This paper cites Why Shallow Networks Struggle to Approximate and Learn High Frequencies.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Why Shallow Networks Struggle to Approximate and Learn High Frequencies

Reference 37

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Observation 2f5b2608-f94c-4694-a0d9-b673e2a4e836 · outbound

This paper cites Loss jump during loss switch in solving pdes with neural networks.

Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank Loss jump during loss switch in solving pdes with neural networks

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:06:11.466507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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