Paper Citation Record · LEDGER

Gradient Multi-Normalization for Stateless and Scalable LLM Training

As of 22 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 3 inbound Pith citation observations for arXiv:2502.06742.

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

pith.paper-citation-record.v1
2502.06742 v1

Coverage vector

measured 51 of 51 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-08T14:37:23.819526Z

measured 54 of 54 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:35:40.221296Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-13T05:52:21.848754Z

Reference resolution

51 of 51 outbound references displayed

verified exact0
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External citation measurements

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Outbound references

Observation b08ad4a5-16fe-4a52-8ad6-c06e6506952c · outbound

This paper cites Layer Normalization.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Layer Normalization

Reference 1

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Observation f122e6d1-83f1-4c54-b2a7-b5a8d3177886 · outbound

This paper cites Iterative bregman projections for regularized transportation problems.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Iterative bregman projections for regularized transportation problems

Reference 2

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Observation 4b0d4c41-37f0-483c-943c-122dde9a1987 · outbound

This paper cites Old Optimizer, New Norm: An Anthology.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Old Optimizer, New Norm: An Anthology

Reference 3

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Observation 4a520790-e2ea-4bb8-8431-e9247760aaaa · outbound

This paper cites signsgd: Compressed optimisation for non-convex problems.

Gradient Multi-Normalization for Stateless and Scalable LLM Training signsgd: Compressed optimisation for non-convex problems

Reference 4

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Observation 2c1c0c26-fcb7-4c9e-abc0-a04d482caf08 · outbound

This paper cites Proximal alternating linearized minimization for nonconvex and nonsmooth problems.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Proximal alternating linearized minimization for nonconvex and nonsmooth problems

Reference 5

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Observation 8c2f0518-867a-4c4a-9849-f4602c19c6fa · outbound

This paper cites Distributed optimization and statistical learning via the alternating direction method of multipliers.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Distributed optimization and statistical learning via the alternating direction method of multipliers

Reference 6

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Observation 6cf160a8-e1af-4778-b2c9-83d0377eb545 · outbound

This paper cites Stochastic spectral descent for restricted boltzmann machines.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Stochastic spectral descent for restricted boltzmann machines

Reference 7

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Observation bbf7d13b-7496-4394-bab7-87a183480732 · outbound

This paper cites and Pock, T.

Gradient Multi-Normalization for Stateless and Scalable LLM Training and Pock, T

Reference 8

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Observation 4299bd35-014a-4e46-b469-d40de0536ef7 · outbound

This paper cites Fira: Can we achieve full-rank training of llms under low-rank constraint?, 2024 b.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Fira: Can we achieve full-rank training of llms under low-rank constraint?, 2024 b

Reference 10

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This paper cites Symbolic discovery of optimization algorithms.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Symbolic discovery of optimization algorithms

Reference 11

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This paper cites and Mehta, H.

Gradient Multi-Normalization for Stateless and Scalable LLM Training and Mehta, H

Reference 12

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Observation bed42d3e-476b-4ee1-bf47-18a02c229b59 · outbound

This paper cites On hilbert’s metric for simplices.

Gradient Multi-Normalization for Stateless and Scalable LLM Training On hilbert’s metric for simplices

Reference 13

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Observation 7bf6bb02-4816-494e-a22a-7d422156ceb6 · outbound

This paper cites The Llama 3 Herd of Models.

Gradient Multi-Normalization for Stateless and Scalable LLM Training The Llama 3 Herd of Models

Reference 14

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Gradient Multi-Normalization for Stateless and Scalable LLM Training Unresolved cited work

Reference 15

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This paper cites and Lorenz, J.

Gradient Multi-Normalization for Stateless and Scalable LLM Training and Lorenz, J

Reference 16

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Observation 0a3d308f-309a-4bda-8ce9-3dee363a3b86 · outbound

This paper cites Eigenvalue-corrected natural gradient based on a new approximation.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Eigenvalue-corrected natural gradient based on a new approximation

Reference 17

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Observation f3a89ebb-4335-405f-ac92-2ae195999eb1 · outbound

This paper cites Shampoo: Preconditioned Stochastic Tensor Optimization.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Shampoo: Preconditioned Stochastic Tensor Optimization

Reference 18

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Observation bbb83fe5-3150-4ccf-81ac-2e61517b0bdc · outbound

This paper cites Flora: Low-Rank Adapters Are Secretly Gradient Compressors.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Flora: Low-Rank Adapters Are Secretly Gradient Compressors

Reference 19

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Observation 6d529124-8416-4357-8a69-f4d6d4058af4 · outbound

This paper cites Beyond convexity: Stochastic quasi-convex optimization.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Beyond convexity: Stochastic quasi-convex optimization

Reference 20

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Observation 820b1f11-b874-4e60-a1fb-a7959e808908 · outbound

This paper cites LoRA: Low-Rank Adaptation of Large Language Models.

Gradient Multi-Normalization for Stateless and Scalable LLM Training LoRA: Low-Rank Adaptation of Large Language Models

Reference 21

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This paper cites Iterative normalization: Beyond standardization towards efficient whitening.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Iterative normalization: Beyond standardization towards efficient whitening

Reference 22

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Observation b3245607-4341-4ef3-8480-8707711b816a · outbound

This paper cites Muon: An optimizer for hidden layers in neural networks, 2024.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Muon: An optimizer for hidden layers in neural networks, 2024

Reference 23

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Gradient Multi-Normalization for Stateless and Scalable LLM Training Unresolved cited work

Reference 24

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This paper cites A., Casper, J., Lym, S., McAfee, L., Andersch, M., Shoeybi, M., and Catanzaro, B.

Gradient Multi-Normalization for Stateless and Scalable LLM Training A., Casper, J., Lym, S., McAfee, L., Andersch, M., Shoeybi, M., and Catanzaro, B

Reference 25

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This paper cites Noise Is Not the Main Factor Behind the Gap Between SGD and Adam on Transformers, but Sign Descent Might Be.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Noise Is Not the Main Factor Behind the Gap Between SGD and Adam on Transformers, but Sign Descent Might Be

Reference 26

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This paper cites Heavy-Tailed Class Imbalance and Why Adam Outperforms Gradient Descent on Language Models.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Heavy-Tailed Class Imbalance and Why Adam Outperforms Gradient Descent on Language Models

Reference 27

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Gradient Multi-Normalization for Stateless and Scalable LLM Training Unresolved cited work

Reference 28

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Observation 02956aa1-6bba-4a64-b1e0-378a505245c6 · outbound

This paper cites Towards faster training of global covariance pooling networks by iterative matrix square root normalization.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Towards faster training of global covariance pooling networks by iterative matrix square root normalization

Reference 29

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This paper cites Relora: High-rank training through low-rank updates.

Gradient Multi-Normalization for Stateless and Scalable LLM Training Relora: High-rank training through low-rank updates

Reference 30

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Observation 5897e39f-a8d8-44e2-863d-cbf31763c4dc · outbound

This paper cites SWAN: SGD with Normalization and Whitening Enables Stateless LLM Training.

Gradient Multi-Normalization for Stateless and Scalable LLM Training SWAN: SGD with Normalization and Whitening Enables Stateless LLM Training

Reference 31

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Gradient Multi-Normalization for Stateless and Scalable LLM Training Decomposition through formalization in a product space

Reference 32

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Gradient Multi-Normalization for Stateless and Scalable LLM Training Unresolved cited work

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Gradient Multi-Normalization for Stateless and Scalable LLM Training Zero: Memory optimizations toward training trillion parameter models

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Gradient Multi-Normalization for Stateless and Scalable LLM Training Unresolved cited work

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Gradient Multi-Normalization for Stateless and Scalable LLM Training A relationship between arbitrary positive matrices and doubly stochastic matrices

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Gradient Multi-Normalization for Stateless and Scalable LLM Training and Knopp, P

Reference 37

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Gradient Multi-Normalization for Stateless and Scalable LLM Training Fast differentiable matrix square root and inverse square root

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Gradient Multi-Normalization for Stateless and Scalable LLM Training Unresolved cited work

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Gradient Multi-Normalization for Stateless and Scalable LLM Training LLaMA: Open and Efficient Foundation Language Models

Reference 40

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Gradient Multi-Normalization for Stateless and Scalable LLM Training Functional operators: Measures and integrals, volume 1

Reference 41

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Gradient Multi-Normalization for Stateless and Scalable LLM Training Unresolved cited work

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Gradient Multi-Normalization for Stateless and Scalable LLM Training No More Adam: Learning Rate Scaling at Initialization is All You Need

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Gradient Multi-Normalization for Stateless and Scalable LLM Training Large Batch Training of Convolutional Networks

Reference 45

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Gradient Multi-Normalization for Stateless and Scalable LLM Training Large Batch Optimization for Deep Learning: Training BERT in 76 minutes

Reference 46

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Gradient Multi-Normalization for Stateless and Scalable LLM Training and Sennrich, R

Reference 47

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Gradient Multi-Normalization for Stateless and Scalable LLM Training P., Veit, A., Kim, S., Reddi, S., Kumar, S., and Sra, S

Reference 48

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Gradient Multi-Normalization for Stateless and Scalable LLM Training Adam-mini: Use Fewer Learning Rates To Gain More

Reference 49

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Gradient Multi-Normalization for Stateless and Scalable LLM Training GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection

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Gradient Multi-Normalization for Stateless and Scalable LLM Training Deconstructing What Makes a Good Optimizer for Language Models

Reference 51

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Gradient Multi-Normalization for Stateless and Scalable LLM Training APOLLO: SGD-like Memory, AdamW-level Performance

Reference 52

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Gradient Multi-Normalization for Stateless and Scalable LLM Training write newline

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Pith citing papers

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Low-rank Momentum Factorization for Memory Efficient Training cites this paper.

Low-rank Momentum Factorization for Memory Efficient Training Gradient Multi-Normalization for Stateless and Scalable LLM Training

Reference 54

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Demystifying Manifold Constraints in LLM Pre-training cites this paper.

Demystifying Manifold Constraints in LLM Pre-training Gradient Multi-Normalization for Stateless and Scalable LLM Training

Reference 44

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Observation e25f7357-df6e-4089-bfd0-46d14d6b6413 · inbound

Optimistic Dual Averaging Unifies Modern Optimizers cites this paper.

Optimistic Dual Averaging Unifies Modern Optimizers Gradient Multi-Normalization for Stateless and Scalable LLM Training

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