Paper Citation Record · LEDGER

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories

As of 14 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 3 inbound Pith citation observations for arXiv:2412.18756.

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

pith.paper-citation-record.v1
2412.18756 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T04:36:32.204110Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-30T15:56:46.678986Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-18T14:01:28.074283Z

Reference resolution

28 of 28 outbound references displayed

verified exact4
verified fuzzy2
unresolved21
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3517b08a-6313-4d32-8b1c-26d7ae5548c7 · outbound

This paper cites Asymptotics of feature learning in two-layer networks after one gradient-step.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Asymptotics of feature learning in two-layer networks after one gradient-step

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.038109Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d8de97ac-3092-40da-9c7e-8ab2417c7805 · outbound

This paper cites A Geometrical Analysis of Kernel Ridge Regression and its Applications.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories A Geometrical Analysis of Kernel Ridge Regression and its Applications

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.058227Z

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Unavailable: canonical work link unavailable.

Observation 51a1b87e-d6a6-4969-84e8-019b34317a65 · outbound

This paper cites Disentangling feature and lazy training in deep neural networks.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Disentangling feature and lazy training in deep neural networks

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:36:32.886390Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 455e7fe4-ec85-4d39-ad7d-52a1eb6ae3f9 · outbound

This paper cites URL https: //doi.org/10.1214/20-AOS1990.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories URL https: //doi.org/10.1214/20-AOS1990

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.072125Z

Source-reported events for the cited work

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Observation a76c8b3f-b5e7-4c17-bdec-c7268fddd0ed · outbound

This paper cites Finite Depth and Width Corrections to the Neural Tangent Kernel.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Finite Depth and Width Corrections to the Neural Tangent Kernel

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.078516Z

Source-reported events for the cited work

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Observation 927b3043-1263-4899-b646-59bd3e24f388 · outbound

This paper cites Sharp Asymptotics of Kernel Ridge Regression Beyond the Linear Regime.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Sharp Asymptotics of Kernel Ridge Regression Beyond the Linear Regime

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.085843Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e11575a8-093a-45bd-bc69-41e7d01d4a6e · outbound

This paper cites Improving Adaptivity via Over-Parameterization in Sequence Models.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Improving Adaptivity via Over-Parameterization in Sequence Models

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-11T04:36:32.612085Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e668b5ee-8579-441a-8206-767e9b2db9f2 · outbound

This paper cites URL https://doi.org/10.1214/19-AOS1849.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories URL https://doi.org/10.1214/19-AOS1849

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.130490Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 79c64076-8102-4815-b074-e339ee1137e8 · outbound

This paper cites Optimal Rate of Kernel Regression in Large Dimensions.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Optimal Rate of Kernel Regression in Large Dimensions

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.137166Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation da59c207-ceab-4d6d-a9b2-c6a78528353d · outbound

This paper cites Benign, Tempered, or Catastrophic: A Taxonomy of Overfitting.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Benign, Tempered, or Catastrophic: A Taxonomy of Overfitting

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.143811Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ffe35d1e-8857-44d1-b7b0-c2dde4ccb93b · outbound

This paper cites Spectrum of inner-product kernel matrices in the polynomial regime and multiple descent phenomenon in kernel ridge regression.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Spectrum of inner-product kernel matrices in the polynomial regime and multiple descent phenomenon in kernel ridge regression

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.150378Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 32c08120-e198-4a27-9861-ff60026728a2 · outbound

This paper cites A non-asymptotic theory of Kernel Ridge Regression: deterministic equivalents, test error, and GCV estimator.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories A non-asymptotic theory of Kernel Ridge Regression: deterministic equivalents, test error, and GCV estimator

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.156934Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 75330558-2d30-44df-a8b6-0b709fc034cb · outbound

This paper cites A Theory of Non-Linear Feature Learning with One Gradient Step in Two-Layer Neural Networks.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories A Theory of Non-Linear Feature Learning with One Gradient Step in Two-Layer Neural Networks

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.163578Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06f2fd3a-d4e8-4d7f-a0a9-44c3ee3a9911 · outbound

This paper cites Generalization Guarantees for Neural Networks via Harnessing the Low-rank Structure of the Jacobian.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Generalization Guarantees for Neural Networks via Harnessing the Low-rank Structure of the Jacobian

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.169879Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b4d5e54-3474-4ad6-82b2-69a0bd4010d6 · outbound

This paper cites A Theory of Neural Tangent Kernel Alignment and Its Influence on Training.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories A Theory of Neural Tangent Kernel Alignment and Its Influence on Training

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.183489Z

Source-reported events for the cited work

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Observation 7a3fd1b7-7519-4197-a38b-e3201a7fd318 · outbound

This paper cites Feature Learning in Infinite-Width Neural Networks.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Feature Learning in Infinite-Width Neural Networks

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.197212Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f901e5c-b664-47a5-a86a-c9e5ce0cbf36 · outbound

This paper cites Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensions.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensions

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.204110Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 313196ee-4a9b-4bdd-ac2a-98750b100e9e · outbound

This paper cites Jianqing Fan, Cong Ma, and Yiqiao Zhong.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Jianqing Fan, Cong Ma, and Yiqiao Zhong

Reference 1996

Resolution: verified exact; doi, observed 2026-08-11T04:36:32.308777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2c253b90-0ee0-45df-9dbe-61c1d762e605 · outbound

This paper cites Neural spectrum alignment: Empirical study.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Neural spectrum alignment: Empirical study

Reference 2001

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:36:32.862589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2d90223a-b4d2-4ccb-9699-e8c4a52fd406 · outbound

This paper cites Mechanism of feature learning in convolutional neural networks.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Mechanism of feature learning in convolutional neural networks

Reference 2007

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.019182Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a3d8938-e178-4a9c-ab4f-328ac75b4f38 · outbound

This paper cites A Survey on Statistical Theory of Deep Learning: Approximation, Training Dynamics, and Generative Models.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories A Survey on Statistical Theory of Deep Learning: Approximation, Training Dynamics, and Generative Models

Reference 2009

Resolution: verified exact; local_arxiv, observed 2026-08-11T04:36:32.378779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 77b057d3-dfab-4c25-9296-d963e76baaa5 · outbound

This paper cites URL https://doi.org/10.1214/08-AOS648.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories URL https://doi.org/10.1214/08-AOS648

Reference 2010

Resolution: verified exact; doi, observed 2026-08-11T04:36:32.275175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 58152eb7-328a-496c-b6d5-77e4c8be3215 · outbound

This paper cites Mechanism of feature learning in deep fully connected networks and kernel machines that recursively learn features.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Mechanism of feature learning in deep fully connected networks and kernel machines that recursively learn features

Reference 2018

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.176405Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ec8b3515-b5d3-43e0-bce9-9b050a8ddd7c · outbound

This paper cites Generalization Ability of Wide Neural Networks on $\mathbb{R}$.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Generalization Ability of Wide Neural Networks on $\mathbb{R}$

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.107556Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 22b7ea4f-e69c-460f-8d72-a714a21fe878 · outbound

This paper cites Generalization in Kernel Regression Under Realistic Assumptions.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Generalization in Kernel Regression Under Realistic Assumptions

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.011823Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fa86431a-df41-4314-9fb5-a8535fcabfaf · outbound

This paper cites How Two-Layer Neural Networks Learn, One (Giant) Step at a Time.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories How Two-Layer Neural Networks Learn, One (Giant) Step at a Time

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.044680Z

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Observation 12f8b6ac-69a9-4f2c-8d37-1318bee47e9a · outbound

This paper cites Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decay.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decay

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-11T04:36:32.122676Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 658ed5a2-dde8-4994-bd04-a024d0cd8e33 · outbound

This paper cites On the Impacts of the Random Initialization in the Neural Tangent Kernel Theory.

Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories On the Impacts of the Random Initialization in the Neural Tangent Kernel Theory

Reference 2024

Resolution: metadata mismatch; local_arxiv, observed 2026-08-11T04:36:32.782867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

Observation f6a3ed5b-8500-4037-b498-41f376941199 · inbound

Alignment-Sensitive Minimax Rates for Spectral Algorithms with Learned Kernels cites this paper.

Alignment-Sensitive Minimax Rates for Spectral Algorithms with Learned Kernels Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories

Reference 54

Resolution: verified exact; arxiv_id, observed 2026-07-29T01:25:26.226530Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 1b7d53aa-7687-43f9-ad99-d5d00d15c24d · inbound

Supporting Evidence for the Adaptive Feature Program across Diverse Models cites this paper.

Supporting Evidence for the Adaptive Feature Program across Diverse Models Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories

Reference 3

Resolution: metadata mismatch; arxiv_id, observed 2026-07-29T01:25:26.226530Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a8d5c886-82c7-430e-bf16-f63866706bea · inbound

Breaking the Curse with BAND: Nonparametric Distribution Estimation in High Dimensions cites this paper.

Breaking the Curse with BAND: Nonparametric Distribution Estimation in High Dimensions Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories

Reference 204

Resolution: unresolved; no resolver link, observed 2026-07-30T15:56:46.678986Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.