Paper Citation Record · LEDGER

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization

As of 16 August 2026, this Paper Citation Record lists 64 of 64 outbound references and 1 inbound Pith citation observation for arXiv:1908.09375.

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

pith.paper-citation-record.v1
1908.09375 v1

Coverage vector

measured 64 of 64 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T11:19:57.727204Z

measured 65 of 65 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-14T11:19:57.465759Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-14T11:19:58.034789Z

Reference resolution

64 of 64 outbound references displayed

verified exact4
verified fuzzy35
unresolved20
parse uncertain0
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External citation measurements

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Outbound references

Observation 12d5c648-c232-4d73-9f59-349c09780f26 · outbound

This paper cites However, our theoretical understanding of deep learning, and thus the ability of developing principled improvements, has lagged behind.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization However, our theoretical understanding of deep learning, and thus the ability of developing principled improvements, has lagged behind

Reference 1

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Observation 44b298cf-52bf-42cf-9dea-6226430ac65b · outbound

This paper cites When Can Deep Networks Avoid the Curse of Dimension- ality?.We start with the ﬁrst set of questions, summarizing results in (5–7), and (8, 9).

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization When Can Deep Networks Avoid the Curse of Dimension- ality?.We start with the ﬁrst set of questions, summarizing results in (5–7), and (8, 9)

Reference 2

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Observation 99804ad5-d446-4bcd-886d-9c4e52d1b252 · outbound

This paper cites Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization

Reference 3

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Observation 5cc32a6a-b7af-4f0e-a631-3244aeb305be · outbound

This paper cites solution.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization solution

Reference 4

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This paper cites implicit.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization implicit

Reference 5

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Observation 0cc6da0c-b2cb-493a-acb6-72118bcfa7f1 · outbound

This paper cites asymptotic minima.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization asymptotic minima

Reference 6

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Observation b8b30674-0a31-4033-8205-23fd79899925 · outbound

This paper cites CBMM memo 041.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization CBMM memo 041

Reference 7

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Observation eb030c31-becb-40a5-a75c-c3a41280478c · outbound

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Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Unresolved cited work

Reference 8

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Observation 334fe2ee-1388-4586-8491-8e5188395900 · outbound

This paper cites (2019) Theory of deep learning III: Dynamics and generalization in deep networks.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization (2019) Theory of deep learning III: Dynamics and generalization in deep networks

Reference 9

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Observation 399b78de-1953-4aa9-b490-99a3d2a34210 · outbound

This paper cites ArXiv e-prints.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization ArXiv e-prints

Reference 10

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Observation 9fadc0e6-c47a-41be-a590-ec2cc661f912 · outbound

This paper cites Gradient Descent Maximizes the Margin of Homogeneous Neural Networks.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Gradient Descent Maximizes the Margin of Homogeneous Neural Networks

Reference 11

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Observation 5a598f90-6447-4b3d-a607-20ff92366349 · outbound

This paper cites Lexicographic and Depth-Sensitive Margins in Homogeneous and Non-Homogeneous Deep Models.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Lexicographic and Depth-Sensitive Margins in Homogeneous and Non-Homogeneous Deep Models

Reference 12

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Observation 16e3e9d5-bdf7-4392-a7e9-68d65e47f578 · outbound

This paper cites Center for Brains, Minds and Machines (CBMM) Memo No.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Center for Brains, Minds and Machines (CBMM) Memo No

Reference 13

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Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Unresolved cited work

Reference 14

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Observation c96bd70d-55bb-4db9-9a10-14ed619d8650 · outbound

This paper cites Acta Numerica 8:143–195.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Acta Numerica 8:143–195

Reference 15

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Observation 93c7a79d-7125-493f-b1e5-ff62667c6a23 · outbound

This paper cites 45, also in arXiv.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization 45, also in arXiv

Reference 16

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Observation 3f561cd8-b3ee-4acd-972f-75581c4018fe · outbound

This paper cites Center for Brains, Minds and Machines (CBMM) Memo No.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Center for Brains, Minds and Machines (CBMM) Memo No

Reference 17

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Observation d75fbb6e-6633-4fb9-a63e-68aafd7d65c6 · outbound

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Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Unresolved cited work

Reference 18

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Observation cac9c96c-0354-4876-b2f8-d9b85907b5f7 · outbound

This paper cites Advances in Computational Mathematics pp.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Advances in Computational Mathematics pp

Reference 19

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Observation 0c015293-f31c-486f-b41d-0a40727bddad · outbound

This paper cites Assuming ϵof the form ϵ∝1 logt we obtain−1 t log2t =−B 1 t log2t.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Assuming ϵof the form ϵ∝1 logt we obtain−1 t log2t =−B 1 t log2t

Reference 20

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Observation 3c34acfa-d301-49c4-9e97-67ab2ba350cd · outbound

This paper cites Proceedings of the 1993 IEEE-SP Workshop.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Proceedings of the 1993 IEEE-SP Workshop

Reference 21

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Observation 1ee61363-4b43-4e12-932b-50bbe5a1a284 · outbound

This paper cites Mathematics of Computation 63(208):607–623.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Mathematics of Computation 63(208):607–623

Reference 22

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Observation c0b2383b-aad4-403c-a94c-82b23b0c0095 · outbound

This paper cites Advances in Computational Mathematics 5(1):233–243.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Advances in Computational Mathematics 5(1):233–243

Reference 23

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Observation 454d5557-959e-405b-8ca0-7737fad1d77e · outbound

This paper cites Notices of the American Mathematical Society (AMS) 50(5):537–544.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Notices of the American Mathematical Society (AMS) 50(5):537–544

Reference 24

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Observation d085b27a-24c4-4608-a89d-8cd3353a0d72 · outbound

This paper cites F .and Pascanu R, Cho K, Bengio Y (2014) On the number of linear regions of deep neural networks.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization F .and Pascanu R, Cho K, Bengio Y (2014) On the number of linear regions of deep neural networks

Reference 25

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Observation 208bc8b1-14a2-4577-a4e0-c5a41de187d6 · outbound

This paper cites An Algorithm for Training Polynomial Networks.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization An Algorithm for Training Polynomial Networks

Reference 26

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Observation 0994ef9e-07ae-469d-b343-dab8a06ad913 · outbound

This paper cites Unsupervised Learning of Invariant Representations in Hierarchical Architectures.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Unsupervised Learning of Invariant Representations in Hierarchical Architectures

Reference 27

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This paper cites (2015) Unsupervised learning of invariant representations.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization (2015) Unsupervised learning of invariant representations

Reference 28

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Observation 4f9f3621-84fa-4d7d-b606-4f6d292c1e5c · outbound

This paper cites CBMM memo 037.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization CBMM memo 037

Reference 29

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This paper cites Center for Brains, Minds and Machines (CBMM) Memo No.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Center for Brains, Minds and Machines (CBMM) Memo No

Reference 30

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This paper cites Representation Benefits of Deep Feedforward Networks.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Representation Benefits of Deep Feedforward Networks

Reference 31

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Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Depth-Width Tradeoffs in Approximating Natural Functions with Neural Networks

Reference 32

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This paper cites 058, MIT Center for Brains, Minds and Machines), Technical report.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization 058, MIT Center for Brains, Minds and Machines), Technical report

Reference 33

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Observation d45c3d99-bd39-47d6-a3b2-e6a5df809b9d · outbound

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Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Nonlinear Approximation and (Deep) ReLU Networks

Reference 34

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Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization How to Escape Saddle Points Efficiently

Reference 35

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Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Escaping From Saddle Points --- Online Stochastic Gradient for Tensor Decomposition

Reference 36

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Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Feldman V, Rakhlin A, Shamir O

Reference 37

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Reference 38

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Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization (JMLR.org), pp

Reference 39

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This paper cites IEEE T ransactions on Information Theory 65(2):742–769.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization IEEE T ransactions on Information Theory 65(2):742–769

Reference 40

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Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization (Curran Associates Inc., USA), pp

Reference 41

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Reference 42

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Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Dy J, Krause A

Reference 43

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Observation b3579b59-004c-4b3c-8bae-c6cc3dadee99 · outbound

This paper cites Gradient Descent Finds Global Minima of Deep Neural Networks.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Gradient Descent Finds Global Minima of Deep Neural Networks

Reference 44

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Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization (JMLR.org), pp

Reference 45

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This paper cites Learning Non-overlapping Convolutional Neural Networks with Multiple Kernels.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Learning Non-overlapping Convolutional Neural Networks with Multiple Kernels

Reference 46

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Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization arXiv e-prints

Reference 47

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Observation ebbf0534-56d5-4a00-9460-c66b94016a1f · outbound

This paper cites Bengio S, et al.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Bengio S, et al

Reference 48

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Observation e27a8207-de39-4aa6-9990-3dd07cc26c76 · outbound

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Reference 49

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Observation 3f19bf87-5e49-422c-9625-253fe8b637b3 · outbound

This paper cites Stochastic Gradient Descent Optimizes Over-parameterized Deep ReLU Networks.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Stochastic Gradient Descent Optimizes Over-parameterized Deep ReLU Networks

Reference 50

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This paper cites Theory II: Landscape of the Empirical Risk in Deep Learning.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Theory II: Landscape of the Empirical Risk in Deep Learning

Reference 51

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Observation a07296df-67be-4314-907d-8f9da65512c3 · outbound

This paper cites (2017) Theory of deep learning IIb: Optimization properties of SGD.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization (2017) Theory of deep learning IIb: Optimization properties of SGD

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:19:58.246758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d1403aa3-57cd-4133-91a1-fbe05bbe71d0 · outbound

This paper cites arXiv:180.3251 [cs, math].

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization arXiv:180.3251 [cs, math]

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:19:58.233393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation babd726b-e659-449a-b1f5-4b1414444e95 · outbound

This paper cites Guyon I, et al.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Guyon I, et al

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:19:58.219706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 79733b5d-6349-403e-aba9-7530e7dd4ff6 · outbound

This paper cites Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-14T11:19:57.689211Z

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Observation 97f4b57a-68f9-46ed-8e77-3cd33fd713f4 · outbound

This paper cites Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks

Reference 56

Resolution: unresolved; no resolver link, observed 2026-08-14T11:19:57.693724Z

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Observation cbbac062-c01f-4108-8af8-e7d528043a29 · outbound

This paper cites Regularization Matters: Generalization and Optimization of Neural Nets v.s. their Induced Kernel.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Regularization Matters: Generalization and Optimization of Neural Nets v.s. their Induced Kernel

Reference 57

Resolution: unresolved; no resolver link, observed 2026-08-14T11:19:57.697941Z

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Unavailable: canonical work link unavailable.

Observation 407731e1-fd03-4ab9-97af-fa27b262fa3f · outbound

This paper cites Fisher-Rao Metric, Geometry, and Complexity of Neural Networks.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Fisher-Rao Metric, Geometry, and Complexity of Neural Networks

Reference 58

Resolution: unresolved; no resolver link, observed 2026-08-14T11:19:57.702099Z

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Unavailable: canonical work link unavailable.

Observation f37ba6b5-daf5-4e5b-adfb-1d0e76b766b9 · outbound

This paper cites an unresolved cited work.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Unresolved cited work

Reference 59

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:19:58.109597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 817abe15-dba8-4f2f-8c51-c1598654bce1 · outbound

This paper cites an unresolved cited work.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Unresolved cited work

Reference 60

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:19:58.095985Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 56348cb3-5fc2-498e-bd12-c61f6e851e40 · outbound

This paper cites IEEE T ransactions on Signal Processing 48(6):1843–1847.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization IEEE T ransactions on Signal Processing 48(6):1843–1847

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:19:58.081802Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ee2fe951-61ec-41af-aef3-84b4dabce0c6 · outbound

This paper cites Advances in Neural Information Processing Systems.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Advances in Neural Information Processing Systems

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:19:58.067815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8f75a5e6-fe0e-436b-9029-bd405843827c · outbound

This paper cites A Surprising Linear Relationship Predicts Test Performance in Deep Networks.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization A Surprising Linear Relationship Predicts Test Performance in Deep Networks

Reference 63

Resolution: verified exact; local_arxiv, observed 2026-08-14T11:19:57.768662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2aaca15f-20be-4eee-a380-e3c8d9efc742 · outbound

This paper cites Signal Processing 55:137–139.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization Signal Processing 55:137–139

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:19:58.053528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

Observation 99804ad5-d446-4bcd-886d-9c4e52d1b252 · inbound