Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise | Paper Citation Record

Observation 2c3b7f3a-0cd5-4f03-9ea0-655f9d6d1a85 · outbound

This paper cites arXiv preprint arXiv:2512.16928 , year=.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise arXiv preprint arXiv:2512.16928 , year=

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.570702Z

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Observation a069c6ae-718e-40b7-894f-1028e3752042 · outbound

This paper cites Dion: Distributed Orthonormalized Updates.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Dion: Distributed Orthonormalized Updates

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.580872Z

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Observation 3243c3d6-09bc-4070-9041-003c584c8069 · outbound

This paper cites Amsel, D.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Amsel, D

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.294054Z

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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 4

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Observation a032ab8c-7f61-4f60-babc-daf0a17f551d · outbound

This paper cites Arjevani, Y.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Arjevani, Y

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.078061Z

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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 6

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Observation d089c691-04a7-4b98-89d6-1cb574d8e64b · outbound

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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 7

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Observation 415f337c-fe85-4fc5-8d22-c8bceca7c488 · outbound

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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.152048Z

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Observation 10e1ea61-719b-495b-9b0e-67a59ad5d477 · outbound

This paper cites Balles and P.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Balles and P

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.090798Z

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Observation 5e05e66a-7048-42f7-a662-83c9e3331b07 · outbound

This paper cites Longformer: The Long-Document Transformer.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Longformer: The Long-Document Transformer

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-07-01T14:55:48.613270Z

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Observation 9cbf712f-b99e-4780-883d-2c59b60430eb · outbound

This paper cites Bernstein and L.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Bernstein and L

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.165884Z

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Observation 528074d0-408e-46a5-9bb1-0babafaa1ce2 · outbound

This paper cites Bernstein and L.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Bernstein and L

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.170581Z

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Observation 83e33d72-f18a-4164-be9c-dcfe7d7a7641 · outbound

This paper cites Bernstein, Y-X.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Bernstein, Y-X

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.231156Z

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Observation 30e0d146-ce7a-41bf-b535-2071f8b33737 · outbound

This paper cites Bernstein, J.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Bernstein, J

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.287187Z

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Observation 43149b26-7bed-405d-89c0-f6f37d85a480 · outbound

This paper cites Bubeck, N.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Bubeck, N

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.221264Z

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Observation 8f7135ed-70a2-4a93-bf2a-708dc0b5ea4b · outbound

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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 16

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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.101449Z

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Observation 8aab3f67-aa38-4c28-a64b-e364081a10a2 · outbound

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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.142773Z

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Observation a0a77fb9-04ec-40c7-b440-52a164731d23 · outbound

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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.244658Z

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Observation 5241daed-5214-40dc-9d85-2d095c9b587b · outbound

This paper cites Chezhegov, K.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Chezhegov, K

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.234778Z

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Observation fe569f54-c03c-41f2-a0b4-ddfa585f7333 · outbound

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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.108610Z

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Observation f8b536ee-2872-4e15-b568-1e87865e9ef7 · outbound

This paper cites Muon with Nesterov Momentum: Heavy-Tailed Noise and (Randomized) Inexact Polar Decomposition.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Muon with Nesterov Momentum: Heavy-Tailed Noise and (Randomized) Inexact Polar Decomposition

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-07-01T14:55:48.601512Z

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Observation ea2a82c2-b010-4824-aa47-2a20da5ed544 · outbound

This paper cites Cutkosky and H.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Cutkosky and H

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.147349Z

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Observation 985fccad-a970-4938-b504-d31826e01d93 · outbound

This paper cites Cutkosky and H.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Cutkosky and H

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.250308Z

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Observation 1d1c7ef1-bfb7-4495-ba29-15c046ffce0d · outbound

This paper cites D'Angelo, M.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise D'Angelo, M

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.222967Z

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Observation 96042cf4-a9ec-465d-8c63-7552bbe78880 · outbound

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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.282539Z

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Observation ae69909b-3193-4439-90a5-225649408a93 · outbound

This paper cites When do spectral gradient updates help in deep learning?arXiv preprint arXiv:2512.04299.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise When do spectral gradient updates help in deep learning?arXiv preprint arXiv:2512.04299

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.645209Z

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Observation cc677852-a68f-4e08-af1c-b2fe9e15d57b · outbound

This paper cites Defazio, X.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Defazio, X

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.167993Z

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Observation d87daf04-9a71-41c7-b46f-3775315523ef · outbound

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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.156691Z

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Observation 32de5bfe-6801-4cff-8fe6-9855b5097a18 · outbound

This paper cites Nemotron-CLIMB: CLustering-based Iterative Data Mixture Bootstrapping for Language Model Pre-training.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Nemotron-CLIMB: CLustering-based Iterative Data Mixture Bootstrapping for Language Model Pre-training

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-07-01T14:55:48.649402Z

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Observation 99487f41-1434-4195-a7f3-a6a67cb5ba46 · outbound

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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.149795Z

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Observation 49dd3ea7-2b83-4243-9d76-66c0c2782522 · outbound

This paper cites Dragutinovi \'c and R.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Dragutinovi \'c and R

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.214947Z

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Observation bc2f25e1-1f68-469d-8994-261112784dfd · outbound

This paper cites Du and W.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Du and W

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.689012Z

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Observation e63645ad-0333-442f-a521-951b5802eb57 · outbound

This paper cites Duchi, E.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Duchi, E

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.219501Z

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Observation 13ddb3d1-db03-4875-8ef8-a601927adf37 · outbound

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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.248459Z

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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.192620Z

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Observation e0fe70fc-c40d-42d0-adb5-9cbee2800550 · outbound

This paper cites Ghadimi and G.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Ghadimi and G

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.195937Z

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Observation 20d4c39e-b69e-4ce7-942a-cb0d32500948 · outbound

This paper cites Glorot and Y.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Glorot and Y

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.240704Z

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Observation 94a89203-bab6-47e8-8c97-668d44ffb2d6 · outbound

This paper cites Goldfarb, Y.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Goldfarb, Y

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.126336Z

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Observation 0ec55bbe-6eae-4873-9ebe-e746c7e33e4a · outbound

This paper cites Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, et al.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, et al

Reference 40

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.669061Z

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Observation f85b10ef-83d2-428f-b9b9-0dbbafd526e9 · outbound

This paper cites Gonon, A.-A.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Gonon, A.-A

Reference 41

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.672491Z

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Observation 942d05cf-9cb6-40e2-9581-7a915ac0b6e2 · outbound

This paper cites Gorbunov, A.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Gorbunov, A

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.212972Z

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Observation fa561397-e2e2-47eb-b74b-4f58c9c90535 · outbound

This paper cites The Implicit Bias of Adam and Muon on Smooth Homogeneous Neural Networks.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise The Implicit Bias of Adam and Muon on Smooth Homogeneous Neural Networks

Reference 43

Resolution: metadata mismatch; local_arxiv, observed 2026-07-01T14:55:48.675184Z

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Observation 21863c30-0798-485f-9893-2d7efb25a6d4 · outbound

This paper cites Grosse and J.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Grosse and J

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.177488Z

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Observation b542172d-d147-44ea-8dac-d5e65c8008a0 · outbound

This paper cites Gu and Z.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Gu and Z

Reference 45

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.683365Z

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Observation 3aac95e2-c337-49f0-b684-33bc9d575fa0 · outbound

This paper cites Gupta, T.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Gupta, T

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.172792Z

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Observation 97738d80-caf6-4da9-badd-88cf9351201b · outbound

This paper cites Gurbuzbalaban, U.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Gurbuzbalaban, U

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.175258Z

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Observation f0146bed-666f-4e53-b58f-95521c7d8309 · outbound

This paper cites Low-rank Orthogonalization for Large-scale Matrix Optimization with Applications to Foundation Model Training.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Low-rank Orthogonalization for Large-scale Matrix Optimization with Applications to Foundation Model Training

Reference 48

Resolution: verified exact; local_arxiv, observed 2026-07-01T14:55:48.680826Z

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Observation 09da8aeb-8f5c-4423-a0d2-2b88ed5e7065 · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 49

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.200381Z

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Observation d80baeff-a564-4cab-b5b9-06f64b0c9901 · outbound

This paper cites Henry, P.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Henry, P

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.198236Z

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Observation c5200ee9-ad93-44f9-a10f-7d23976c3feb · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 51

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.227059Z

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Observation 235bd6f8-2926-498f-ad40-0b0d0c4da1ed · outbound

This paper cites Hochreiter and J.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Hochreiter and J

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.302403Z

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Observation 45628ea2-593d-4c1d-9942-751f1fb0a7b7 · outbound

This paper cites Hsu and S.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Hsu and S

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.094375Z

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Observation 7f9c81ae-da99-4528-882d-b6161cea12a6 · outbound

This paper cites LiMuon: Light and Fast Muon Optimizer for Large Models.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise LiMuon: Light and Fast Muon Optimizer for Large Models

Reference 54

Resolution: verified exact; local_arxiv, observed 2026-07-01T14:55:48.662853Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5f3ad602-6316-4233-8316-2e77ee096b79 · outbound

This paper cites H \"u bler, I.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise H \"u bler, I

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.139657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 69dad6a9-98b1-4d6a-8c84-0e8a7f944128 · outbound

This paper cites Ioffe and C.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Ioffe and C

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.274896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 157d2085-701d-464c-bc21-cd64bc8210d9 · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 57

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.284766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 8cf21659-189a-4f0c-9c8d-da47237a156e · outbound

This paper cites Jiang, D.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Jiang, D

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.268038Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation cf45b86a-7681-46cd-a8b5-f30557cc1deb · outbound

This paper cites 94% on CIFAR-10 in 3.29 Seconds on a Single GPU.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise 94% on CIFAR-10 in 3.29 Seconds on a Single GPU

Reference 59

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.648154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c9ca10ba-960f-4841-8490-58cb9dea0dbd · outbound

This paper cites Jordan, Y.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Jordan, Y

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.257367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 33cc99c1-e344-41c1-ae87-ba165ee86d21 · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 61

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.217488Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3493effe-29ab-4a11-9d06-86e3618592c4 · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 62

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.269774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation fc609079-d638-4e47-9c86-5ff7a0350027 · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 63

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.242595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1ed47fd0-f1a6-4444-9a2a-c646d0de3d85 · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 64

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.255540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a48fa612-1c17-4b82-9c88-de12dc58630e · outbound

This paper cites Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 65

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.633794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 01c2bf41-e1ee-46c1-a508-3a1d1876df5a · outbound

This paper cites Krizhevsky.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Krizhevsky

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.277446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 260146a6-958a-4f39-b77c-45b468bf64a5 · outbound

This paper cites Krizhevsky, I.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Krizhevsky, I

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.259070Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 039e0d93-a2b5-4ffb-9a16-f829eb02c7b6 · outbound

This paper cites Kunstner and F.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Kunstner and F

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.132909Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b0b9a0f5-2607-42fb-abc9-906bd50fc6c0 · outbound

This paper cites Kunstner, J.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Kunstner, J

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.123023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1976cbdc-e332-4bbe-9abf-4a83c381bb91 · outbound

This paper cites Kunstner, A.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Kunstner, A

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.154406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 12227eaa-8651-4ab6-9503-f8743f51ba0f · outbound

This paper cites Large, Y.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Large, Y

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.163666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 89185c06-a796-4ffc-a379-25af06a63ed1 · outbound

This paper cites ArXiv Preprint: 2505.21799 , Year =.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise ArXiv Preprint: 2505.21799 , Year =

Reference 72

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.641062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 03cae06d-c947-4e34-b8f1-00fa2f99bd6d · outbound

This paper cites LeCun, L.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise LeCun, L

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.204526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ae13a8cf-1f91-4bac-8693-738816bd74d3 · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 74

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.185595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e1a2d1f0-eb99-4a69-9a6d-72a8cc4e0348 · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 75

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.229031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 61eacf10-5fab-4f83-8737-4d8d37798a98 · outbound

This paper cites A Note on the Convergence of Muon.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise A Note on the Convergence of Muon

Reference 76

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.651364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6b31444a-bf34-4a03-88f7-5d5884e7c255 · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 77

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.202456Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 368ba23b-c153-4ad2-b1ea-0889a737a3ed · outbound

This paper cites Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds

Reference 78

Resolution: verified exact; local_arxiv, observed 2026-07-01T14:55:48.655002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f42306e0-94d3-4326-9de2-9833f3ff5688 · outbound

This paper cites Normuon: Making muon more efficient and scalable.arXiv preprint arXiv:2510.05491.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Normuon: Making muon more efficient and scalable.arXiv preprint arXiv:2510.05491

Reference 79

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.622519Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 40c85e73-8832-41fb-883f-bd2ddc3c322f · outbound

This paper cites Muon is Scalable for LLM Training.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Muon is Scalable for LLM Training

Reference 80

Resolution: verified exact; local_arxiv, observed 2026-07-01T14:55:48.630939Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 44a88f49-535b-4d72-82f9-01a1ad67b13f · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 81

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.210957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 46dc839a-8372-4847-9cb9-03e062e00258 · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 82

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.129551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 15b68725-e887-476c-a000-d19347a9df8d · outbound

This paper cites ArXiv Preprint: 2508.07473 , Year =.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise ArXiv Preprint: 2508.07473 , Year =

Reference 83

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.602369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 812cfa34-c3a1-4535-8a44-3d016e42234a · outbound

This paper cites Liu and Z.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Liu and Z

Reference 84

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.105194Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 861ee0d1-1365-45b6-a1e8-c9bfc675211b · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 85

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.098017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4d170533-06b0-496b-81a1-16c4ef97e228 · outbound

This paper cites Loshchilov and F.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Loshchilov and F

Reference 86

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.041774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6f78b53d-165b-4f23-bacd-4d50a5d12aef · outbound

This paper cites Charles H Martin and Christopher Hinrichs.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Charles H Martin and Christopher Hinrichs

Reference 87

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.657372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b9fb6c30-5f9b-4ebd-b675-5e88274e2f0a · outbound

This paper cites Martens and R.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Martens and R

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.026646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5a357483-9c5c-4774-ae7f-ea22e7e4186c · outbound

This paper cites Morwani, I.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Morwani, I

Reference 89

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.084355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4c504a5a-74c8-4bf8-a320-390a2c6b529b · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 90

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.189049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 82b11952-2f03-4a94-a332-81187d70c0fe · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 91

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.238630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b5e058d8-3c33-45f5-b753-81fe1e4c200f · outbound

This paper cites Muonall: Muon variant for efficient finetuning of large language models.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Muonall: Muon variant for efficient finetuning of large language models

Reference 92

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.607785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 30028358-cef4-4e56-ae16-14aeb34b90b5 · outbound

This paper cites Muon Does Not Converge on Convex Lipschitz Functions.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Muon Does Not Converge on Convex Lipschitz Functions

Reference 93

Resolution: verified exact; local_arxiv, observed 2026-07-01T14:55:48.678250Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ba5182d3-8dfe-4b58-875b-8669ccf81db3 · outbound

This paper cites Pethick, P.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Pethick, P

Reference 94

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.081234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f2477fa5-706c-44e0-9ea2-7cbe4666ee86 · outbound

This paper cites Pethick, W.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Pethick, W

Reference 95

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.087587Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e6270319-4915-4476-b002-55890aa16f93 · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 96

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.306302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e7161dc0-66e9-423d-aed7-3ad5f2070bfb · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 97

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.111762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1537cd41-6e2e-4b39-88c2-7a030be7dc12 · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 98

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.182824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f3792ccf-8cae-403d-a79d-da1e200cf9e8 · outbound

This paper cites an unresolved cited work.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Unresolved cited work

Reference 99

Resolution: unresolved; raw_fallback, observed 2026-07-08T04:24:33.145052Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 99c40e55-e691-4ffb-85eb-1922c9244c8e · outbound

This paper cites Ren and D.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Ren and D

Reference 100

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T04:24:33.262738Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Coverage vector

Reference resolution

Outbound references

Pith citing papers