Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks | Paper Citation Record

Observation 8f94153f-536f-4924-a84d-83e8da8550f8 · outbound

This paper cites LeCun, I.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks LeCun, I

Reference 1

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Observation e49a0fcb-764a-4955-a4b6-c308e3b76859 · outbound

This paper cites Geiger, S.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Geiger, S

Reference 2

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Observation 97bc08bd-193f-4154-b2fd-2d233228e71b · outbound

This paper cites Becker, Y.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Becker, Y

Reference 3

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Observation a91b46b6-45b4-4ee7-812d-5ce49b04e2d5 · outbound

This paper cites Atanasov, A.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Atanasov, A

Reference 4

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Observation 8fe59182-7e71-4bbf-86ff-9d6678687a0a · outbound

This paper cites Cohen, S.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Cohen, S

Reference 5

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Observation 23564282-3f0d-4beb-8da2-13a3a0e06df4 · outbound

This paper cites Amari, Natural Gradient Works Efficiently in Learn- ing, Neural Computation10, 251 (1998).

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Amari, Natural Gradient Works Efficiently in Learn- ing, Neural Computation10, 251 (1998)

Reference 6

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Observation 653d8dbb-e590-4854-be5c-ee48c51f6d86 · outbound

This paper cites Martens, Deep learning via Hessian-free optimization, inProceedings of the 27th International Conference on International Conference on Machine Learning(Omni- press, 2010) p.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Martens, Deep learning via Hessian-free optimization, inProceedings of the 27th International Conference on International Conference on Machine Learning(Omni- press, 2010) p

Reference 7

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Observation a7d1611a-4e65-4953-9aab-c6539d0924b5 · outbound

This paper cites Martens and R.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Martens and R

Reference 8

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Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Unresolved cited work

Reference 9

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Observation a7f6fbf9-ba91-4da6-a6b4-e4966f071303 · outbound

This paper cites Hochreiter and J.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Hochreiter and J

Reference 10

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Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Unresolved cited work

Reference 11

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Observation 9a070090-4d22-4bae-a962-faabe81e096a · outbound

This paper cites Foret, A.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Foret, A

Reference 12

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Observation 0b97072d-8b16-44d6-ba18-a2b012120e63 · outbound

This paper cites Chaudhari, A.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Chaudhari, A

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.057235Z

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Observation 532375bc-2c1e-4f5c-b678-d97d52fb6f38 · outbound

This paper cites Three Factors Influencing Minima in SGD.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Three Factors Influencing Minima in SGD

Reference 14

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Observation 6bdfec7a-0feb-450e-93e1-61238f911943 · outbound

This paper cites LeCun, J.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks LeCun, J

Reference 15

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Observation 00c18935-62a2-474c-8f6f-e084866ec32f · outbound

This paper cites Hassibi and D.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Hassibi and D

Reference 16

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Observation 36827b68-bded-42a1-999f-bd8d6a1af9c2 · outbound

This paper cites an unresolved cited work.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Unresolved cited work

Reference 17

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Observation 40c34b61-66f1-4dae-9a33-6cbdc6f77b2a · outbound

This paper cites Frantar, S.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Frantar, S

Reference 18

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Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Unresolved cited work

Reference 19

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Observation 8b5d717c-af90-4e8f-afc2-32a242d142dc · outbound

This paper cites Moosavi-Dezfooli, A.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Moosavi-Dezfooli, A

Reference 20

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Observation a0b56ba0-cdb8-400f-8acc-53e28b5e74f6 · outbound

This paper cites Singla and S.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Singla and S

Reference 21

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Observation 1aa2993f-5a6c-498a-a600-4388e8aba2aa · outbound

This paper cites Garipov, P.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Garipov, P

Reference 22

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Observation 0c7170d9-6058-4a65-bf40-8e3762f8b906 · outbound

This paper cites Weight-space symmetry in deep networks gives rise to permutation saddles, connected by equal-loss valleys across the loss landscape.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Weight-space symmetry in deep networks gives rise to permutation saddles, connected by equal-loss valleys across the loss landscape

Reference 23

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Observation afc774cc-d754-4a71-9420-77a82d50ac0b · outbound

This paper cites Ainsworth, J.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Ainsworth, J

Reference 24

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This paper cites an unresolved cited work.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Unresolved cited work

Reference 25

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Observation 0641bc18-e0c5-47de-8b54-df9eda5b3775 · outbound

This paper cites Eigenvalues of the Hessian in Deep Learning: Singularity and Beyond.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Eigenvalues of the Hessian in Deep Learning: Singularity and Beyond

Reference 26

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Observation 4d4d0a9a-8e33-4518-8452-e84a897f80b4 · outbound

This paper cites Empirical Analysis of the Hessian of Over-Parametrized Neural Networks.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Empirical Analysis of the Hessian of Over-Parametrized Neural Networks

Reference 27

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Observation f131c92d-f74e-47b8-bf4e-ec32f0751287 · outbound

This paper cites Ghorbani, S.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Ghorbani, S

Reference 28

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Observation f6d92600-b94f-4710-8457-dcf1ea11c84a · outbound

This paper cites Papyan, Measurements of Three-Level Hierarchical StructureintheOutliersintheSpectrumofDeepnetHes- sians, inProceedings of the 36th International Conference on Machine Learning, Vol.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Papyan, Measurements of Three-Level Hierarchical StructureintheOutliersintheSpectrumofDeepnetHes- sians, inProceedings of the 36th International Conference on Machine Learning, Vol

Reference 29

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Observation b0cc1ef3-93e7-4760-9c9c-22cd9eec4e24 · outbound

This paper cites Papyan, Traces of Class/Cross-Class Structure Per- vade Deep Learning Spectra, Journal of Machine Learn- ing Research21, 1 (2020).

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Papyan, Traces of Class/Cross-Class Structure Per- vade Deep Learning Spectra, Journal of Machine Learn- ing Research21, 1 (2020)

Reference 30

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Observation b82e06b4-36d2-4d7a-8c6e-1c155d399c11 · outbound

This paper cites Arjevani and M.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Arjevani and M

Reference 31

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Observation 15aa8dd6-91a0-4478-9c5c-496df97c542a · outbound

This paper cites Arjevani and M.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Arjevani and M

Reference 32

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Observation ca8fddde-1c48-47e1-8944-0e90666df400 · outbound

This paper cites Pennington and P.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Pennington and P

Reference 33

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Observation 669d5c8f-b3d5-4c24-988f-28d0541a9258 · outbound

This paper cites Karakida, S.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Karakida, S

Reference 34

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Observation 6b611d5a-4b0c-484c-8126-b9aa6c55e6b0 · outbound

This paper cites Karakida, S.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Karakida, S

Reference 35

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Observation e572933c-cd91-44a7-bdc8-b982538b572a · outbound

This paper cites Emergent properties of the local geometry of neural loss landscapes.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Emergent properties of the local geometry of neural loss landscapes

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-07-10T16:57:24.481933Z

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Observation c7e8a72f-2529-4857-9aaa-ecd2e94b53bf · outbound

This paper cites Gradient Descent Happens in a Tiny Subspace.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Gradient Descent Happens in a Tiny Subspace

Reference 37

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Observation a2e89494-25a0-4df1-a167-2dbba6de20fa · outbound

This paper cites an unresolved cited work.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Unresolved cited work

Reference 38

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Observation c238fb27-d2f1-4fe0-9e8f-21f5c10a6f44 · outbound

This paper cites Simsek, F.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Simsek, F

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:24.969209Z

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Observation 17a2f6b3-d54f-45f8-a33d-b4df623ae569 · outbound

This paper cites Kunin, J.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Kunin, J

Reference 40

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Observation 960aa39f-0b42-45d0-ba4d-646143712bdf · outbound

This paper cites Tanaka and D.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Tanaka and D

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:24.982389Z

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Observation 2ef7f82a-4ccf-4347-87b8-8b8af5b5a23e · outbound

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Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Unresolved cited work

Reference 42

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Observation a6d87d36-1adc-416d-ad6b-3974b4826445 · outbound

This paper cites Marcotte, R.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Marcotte, R

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.040949Z

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Observation abf5c44e-389c-46d6-b433-f8f694f8ce7f · outbound

This paper cites Watanabe,Algebraic geometry and statistical learning theory, Vol.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Watanabe,Algebraic geometry and statistical learning theory, Vol

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:24.967512Z

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Observation e17149d4-f727-45e7-a021-bdfc8e32194f · outbound

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Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Unresolved cited work

Reference 45

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Observation cfff6f7f-08ff-4dac-8400-0d1ed96d6b40 · outbound

This paper cites an unresolved cited work.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-07-10T16:57:24.961237Z

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Observation 64dfa7a3-0345-4dd7-a445-dd315618cf3d · outbound

This paper cites Bernacchia, M.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Bernacchia, M

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:24.976671Z

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Observation 1dae4ecd-7c4e-4777-aebe-1b7c92da1d3b · outbound

This paper cites an unresolved cited work.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Unresolved cited work

Reference 48

Resolution: unresolved; raw_fallback, observed 2026-07-10T16:57:25.066479Z

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Observation 18757022-5098-49fe-b5b6-e2d683b62e73 · outbound

This paper cites Heskes, On “natural” learning and pruning in multi- layered perceptrons, Neural Computation12, 881 (2000).

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Heskes, On “natural” learning and pruning in multi- layered perceptrons, Neural Computation12, 881 (2000)

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.056008Z

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Observation 47193fba-1265-47c0-bd71-41e9b98b19f3 · outbound

This paper cites an unresolved cited work.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Unresolved cited work

Reference 50

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Observation f8b8b89f-51bd-4eb5-a372-43b52c3c26bf · outbound

This paper cites an unresolved cited work.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Unresolved cited work

Reference 51

Resolution: unresolved; raw_fallback, observed 2026-07-10T16:57:25.060253Z

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Observation d1e3f89a-c007-4789-92cd-727b5192918b · outbound

This paper cites Kawaguchi, Deep Learning without Poor Local Min- ima, inAdvances in Neural Information Processing Sys- tems, Vol.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Kawaguchi, Deep Learning without Poor Local Min- ima, inAdvances in Neural Information Processing Sys- tems, Vol

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.073966Z

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Observation cce3e5fc-b334-432a-9f26-e6f0edf8a47b · outbound

This paper cites an unresolved cited work.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Unresolved cited work

Reference 53

Resolution: unresolved; raw_fallback, observed 2026-07-10T16:57:25.053533Z

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Observation 9e7b508e-0876-4668-bf3d-7129b9031897 · outbound

This paper cites Karakida, S.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Karakida, S

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.062310Z

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Observation 668b2607-9659-4b6b-94c5-7a21625b8356 · outbound

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

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Krizhevsky,Learning multiple layers of features from tiny images, Tech

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.045445Z

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Observation 5e74b8f6-7272-40f6-8115-f15f1c1d4e11 · outbound

This paper cites Zhang, S.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Zhang, S

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.043608Z

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Observation abd29034-fbfc-4b40-8366-e16a8b121205 · outbound

This paper cites independent compo- nents.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks independent compo- nents

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.046407Z

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Observation 81964b55-e507-4430-9883-6e6424283024 · outbound

This paper cites an unresolved cited work.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Unresolved cited work

Reference 58

Resolution: unresolved; raw_fallback, observed 2026-07-10T16:57:25.062677Z

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Observation 77a9a3a1-f990-4058-b503-15f3e43a5888 · outbound

This paper cites Fukushima, Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position, Biological cybernetics36, 193 (1980).

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Fukushima, Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position, Biological cybernetics36, 193 (1980)

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.075968Z

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Observation 40f9a8a4-0a82-42ca-987b-f682b4a568bf · outbound

This paper cites LeCun, L.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks LeCun, L

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.033271Z

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Observation 05003bc3-4c89-49ba-bb02-72dcff419c52 · outbound

This paper cites Goodfellow, Y.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Goodfellow, Y

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.025909Z

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Observation d9e3110c-010d-4e58-868a-85cf0b89ccb9 · outbound

This paper cites Revisiting Natural Gradient for Deep Networks.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Revisiting Natural Gradient for Deep Networks

Reference 62

Resolution: verified exact; local_arxiv, observed 2026-07-10T16:57:24.485080Z

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Observation b96a516b-f6e8-41a3-99af-92fc18ce271c · outbound

This paper cites Kühn and B.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Kühn and B

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.022092Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 58d5780c-2ea9-4ac3-9012-7cd37ce1bbef · outbound

This paper cites Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.061094Z

Source-reported events for the cited work

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Observation 1a4403ff-d2b1-4124-a0d6-9b8476ca538d · outbound

This paper cites For all (k,n )∈{1,...,M}2, at least one of the two blocks in Eq.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks For all (k,n )∈{1,...,M}2, at least one of the two blocks in Eq

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.064537Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation dc637271-fe03-45c9-bbc3-0727f881281c · outbound

This paper cites In this case one would naively obtainM2 generators.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks In this case one would naively obtainM2 generators

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.059132Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ac7da85c-5d5d-4cdd-83fd-d36e183b4f13 · outbound

This paper cites independent components.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks independent components

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.035437Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 977c46da-dbb7-4009-a76e-d0c2ccc74cd4 · outbound

This paper cites 15156–15172.

Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks 15156–15172

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T16:57:25.014257Z

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