Paper Citation Record · LEDGER

Geometrically Principled Randomized Optimization for Efficient LLM Training

As of 23 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2510.01878.

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

pith.paper-citation-record.v1
2510.01878 v2

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T12:51:27.845880Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

43 of 43 outbound references displayed

verified exact1
verified fuzzy0
unresolved42
parse uncertain0
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External citation measurements

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Outbound references

Observation d5ddae9b-63f9-4526-ab8e-ae827fa5765b · outbound

This paper cites write newline.

Geometrically Principled Randomized Optimization for Efficient LLM Training write newline

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:23.511881Z

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Observation 989674e2-44cd-4f93-9f39-c5d5a4f56aeb · outbound

This paper cites Subtrack++ : Gradient subspace tracking for scalable LLM training.

Geometrically Principled Randomized Optimization for Efficient LLM Training Subtrack++ : Gradient subspace tracking for scalable LLM training

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:23.619747Z

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Unavailable: canonical work link unavailable.

Observation 4426c383-0fdd-4e15-9931-efe734ef867a · outbound

This paper cites Online Identification and Tracking of Subspaces from Highly Incomplete Information.

Geometrically Principled Randomized Optimization for Efficient LLM Training Online Identification and Tracking of Subspaces from Highly Incomplete Information

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:23.833099Z

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Unavailable: canonical work link unavailable.

Observation d99a8bc5-f360-49ce-90e5-bffef50882bc · outbound

This paper cites an unresolved cited work.

Geometrically Principled Randomized Optimization for Efficient LLM Training Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:23.942912Z

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Observation 42eba02a-e7f4-4cc5-84f1-0ba0b2530fce · outbound

This paper cites signSGD: Compressed Optimisation for Non-Convex Problems.

Geometrically Principled Randomized Optimization for Efficient LLM Training signSGD: Compressed Optimisation for Non-Convex Problems

Reference 5

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Observation ec4a981e-58ca-4f2d-bf38-13754d5410f1 · outbound

This paper cites Dynamic Subspace Estimation with Grassmannian Geodesics.

Geometrically Principled Randomized Optimization for Efficient LLM Training Dynamic Subspace Estimation with Grassmannian Geodesics

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:24.210521Z

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Observation 56615a3b-c3ec-4bac-aef0-b40ebefed901 · outbound

This paper cites Greedy low-rank gradient compression for distributed learning with convergence guarantees, 2025 a.

Geometrically Principled Randomized Optimization for Efficient LLM Training Greedy low-rank gradient compression for distributed learning with convergence guarantees, 2025 a

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:24.353072Z

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Observation d3bd95b4-13f5-45cb-a5c6-65401fc54bf9 · outbound

This paper cites Fira: Can we achieve full-rank training of LLM s under low-rank constraint?, 2025 b.

Geometrically Principled Randomized Optimization for Efficient LLM Training Fira: Can we achieve full-rank training of LLM s under low-rank constraint?, 2025 b

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:24.469621Z

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Observation 492caf4a-0197-4d20-8ce6-a06365f669e8 · outbound

This paper cites A memory efficient randomized subspace optimization method for training large language models.

Geometrically Principled Randomized Optimization for Efficient LLM Training A memory efficient randomized subspace optimization method for training large language models

Reference 9

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Observation 3d5cee29-5fde-445f-b9e2-27e70ba48aaa · outbound

This paper cites Qlora: Efficient finetuning of quantized llms.

Geometrically Principled Randomized Optimization for Efficient LLM Training Qlora: Efficient finetuning of quantized llms

Reference 10

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Observation 7781a580-788f-45f9-b6ac-e85b35fad7de · outbound

This paper cites Gradient Descent Happens in a Tiny Subspace.

Geometrically Principled Randomized Optimization for Efficient LLM Training Gradient Descent Happens in a Tiny Subspace

Reference 11

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Observation d698031b-8d77-4aac-950e-d36cb0ad7f5a · outbound

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

Geometrically Principled Randomized Optimization for Efficient LLM Training Flora: Low-Rank Adapters Are Secretly Gradient Compressors

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:24.931840Z

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Observation 8522e0e6-0882-4834-822d-f9d839d8a124 · outbound

This paper cites Subspace optimiztion for large language models with convergence guarantees, 2025.

Geometrically Principled Randomized Optimization for Efficient LLM Training Subspace optimiztion for large language models with convergence guarantees, 2025

Reference 13

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Observation 9cbd9066-b2d0-4b91-9aa3-68ebf869e8f9 · outbound

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

Geometrically Principled Randomized Optimization for Efficient LLM Training LoRA: Low-Rank Adaptation of Large Language Models

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:25.077452Z

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Observation c380c0bc-7622-4b41-93ec-11ecb2949cb3 · outbound

This paper cites From Low Rank Gradient Subspace Stabilization to Low-Rank Weights: Observations, Theories, and Applications.

Geometrically Principled Randomized Optimization for Efficient LLM Training From Low Rank Gradient Subspace Stabilization to Low-Rank Weights: Observations, Theories, and Applications

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:25.155303Z

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Observation a69a6658-e3be-4235-93cd-8941691a0965 · outbound

This paper cites Fast online low-rank tensor subspace tracking by CP decomposition using recursive least squares from incomplete observations.

Geometrically Principled Randomized Optimization for Efficient LLM Training Fast online low-rank tensor subspace tracking by CP decomposition using recursive least squares from incomplete observations

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:25.239364Z

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Observation d5417c77-347c-41a0-b719-166692296813 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Geometrically Principled Randomized Optimization for Efficient LLM Training Adam: A Method for Stochastic Optimization

Reference 17

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Observation 7cc56b29-0149-4627-a9f8-6ec1316c84be · outbound

This paper cites ReLoRA: High-Rank Training Through Low-Rank Updates.

Geometrically Principled Randomized Optimization for Efficient LLM Training ReLoRA: High-Rank Training Through Low-Rank Updates

Reference 18

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Observation dac99b14-4c84-47ac-8e71-d092dae2894d · outbound

This paper cites Memory-efficient LLM training with online subspace descent.

Geometrically Principled Randomized Optimization for Efficient LLM Training Memory-efficient LLM training with online subspace descent

Reference 19

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Observation 82c7a648-b295-4695-a3d7-6540a70d6ac7 · outbound

This paper cites BAdam: A Memory Efficient Full Parameter Optimization Method for Large Language Models.

Geometrically Principled Randomized Optimization for Efficient LLM Training BAdam: A Memory Efficient Full Parameter Optimization Method for Large Language Models

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:25.634720Z

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Observation 4cf8c801-3916-417f-b237-c55c460bdd19 · outbound

This paper cites VeLoRA: Memory Efficient Training using Rank-1 Sub-Token Projections.

Geometrically Principled Randomized Optimization for Efficient LLM Training VeLoRA: Memory Efficient Training using Rank-1 Sub-Token Projections

Reference 21

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Observation 8f158026-f139-4e40-9f92-a55456bf3c81 · outbound

This paper cites MicroAdam: Accurate Adaptive Optimization with Low Space Overhead and Provable Convergence.

Geometrically Principled Randomized Optimization for Efficient LLM Training MicroAdam: Accurate Adaptive Optimization with Low Space Overhead and Provable Convergence

Reference 22

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Observation 3552efa4-8be1-4205-98fa-b1d15ec007f4 · outbound

This paper cites Grass: Compute Efficient Low-Memory LLM Training with Structured Sparse Gradients.

Geometrically Principled Randomized Optimization for Efficient LLM Training Grass: Compute Efficient Low-Memory LLM Training with Structured Sparse Gradients

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:25.889874Z

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Observation c4d11c80-29ce-46d3-bb6f-08a658ac40fc · outbound

This paper cites LISA: Layerwise Importance Sampling for Memory-Efficient Large Language Model Fine-Tuning.

Geometrically Principled Randomized Optimization for Efficient LLM Training LISA: Layerwise Importance Sampling for Memory-Efficient Large Language Model Fine-Tuning

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:25.950349Z

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Observation 74101232-d61f-486d-aeb6-dcfaf44f90be · outbound

This paper cites BlockLLM: Memory-Efficient Adaptation of LLMs by Selecting and Optimizing the Right Coordinate Blocks.

Geometrically Principled Randomized Optimization for Efficient LLM Training BlockLLM: Memory-Efficient Adaptation of LLMs by Selecting and Optimizing the Right Coordinate Blocks

Reference 25

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Observation f5378656-d0b7-4d58-8be3-79efa4eeec93 · outbound

This paper cites Tied- L o RA : Enhancing parameter efficiency of L o RA with weight tying.

Geometrically Principled Randomized Optimization for Efficient LLM Training Tied- L o RA : Enhancing parameter efficiency of L o RA with weight tying

Reference 26

Resolution: verified exact; doi, observed 2026-08-04T12:53:28.615558Z

Source-reported events for the cited work

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Observation 70b9db0f-3aa8-4823-9dc2-29f8594c5e75 · outbound

This paper cites LDA dam: Adaptive optimization from low-dimensional gradient statistics.

Geometrically Principled Randomized Optimization for Efficient LLM Training LDA dam: Adaptive optimization from low-dimensional gradient statistics

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:26.170579Z

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Observation 9f63228f-05f1-4404-95b5-336a40a2c9e9 · outbound

This paper cites Identifying Policy Gradient Subspaces.

Geometrically Principled Randomized Optimization for Efficient LLM Training Identifying Policy Gradient Subspaces

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:26.253702Z

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Observation 106f3610-b82b-47b3-bda8-9ae1a85372a6 · outbound

This paper cites Does SGD really happen in tiny subspaces? In The Thirteenth International Conference on Learning Representations, 2025.

Geometrically Principled Randomized Optimization for Efficient LLM Training Does SGD really happen in tiny subspaces? In The Thirteenth International Conference on Learning Representations, 2025

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:26.370212Z

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Observation 39aa6c97-ea8e-4285-b4f5-96d4d61ae888 · outbound

This paper cites Llama 2: Open Foundation and Fine-Tuned Chat Models.

Geometrically Principled Randomized Optimization for Efficient LLM Training Llama 2: Open Foundation and Fine-Tuned Chat Models

Reference 30

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Observation ab3e1090-b895-457f-96a7-364cefe9d59d · outbound

This paper cites Chain of LoRA: Efficient Fine-tuning of Language Models via Residual Learning.

Geometrically Principled Randomized Optimization for Efficient LLM Training Chain of LoRA: Efficient Fine-tuning of Language Models via Residual Learning

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:26.589123Z

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Observation 762cb517-eaed-4fc7-9f09-c74450685c1e · outbound

This paper cites COAP: Memory-Efficient Training with Correlation-Aware Gradient Projection.

Geometrically Principled Randomized Optimization for Efficient LLM Training COAP: Memory-Efficient Training with Correlation-Aware Gradient Projection

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:26.656570Z

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Observation d41bf984-20dc-48d2-85d8-d840a18665c1 · outbound

This paper cites Invariant low-dimensional subspaces in gradient descent for learning deep matrix factorizations.

Geometrically Principled Randomized Optimization for Efficient LLM Training Invariant low-dimensional subspaces in gradient descent for learning deep matrix factorizations

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:26.695139Z

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Observation e159d8d5-d9dd-45b4-ab09-c797a82e28ea · outbound

This paper cites Compressible dynamics in deep overparameterized low-rank learning & adaptation.

Geometrically Principled Randomized Optimization for Efficient LLM Training Compressible dynamics in deep overparameterized low-rank learning & adaptation

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:26.708620Z

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Observation 9915ddb9-ec98-43f5-852f-aaac70eeae3f · outbound

This paper cites Global Convergence of a Grassmannian Gradient Descent Algorithm for Subspace Estimation.

Geometrically Principled Randomized Optimization for Efficient LLM Training Global Convergence of a Grassmannian Gradient Descent Algorithm for Subspace Estimation

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:26.788589Z

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Observation 340eb668-c159-443d-9338-b10923264495 · outbound

This paper cites Adam-mini: Use Fewer Learning Rates To Gain More.

Geometrically Principled Randomized Optimization for Efficient LLM Training Adam-mini: Use Fewer Learning Rates To Gain More

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:26.952238Z

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Observation c481b0b1-2fcf-41e0-add3-2a3b461ebd59 · outbound

This paper cites GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection.

Geometrically Principled Randomized Optimization for Efficient LLM Training GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:27.103592Z

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Observation b1c3a37b-2c5e-43af-a6be-8bf5131f3b4a · outbound

This paper cites Adapprox: Adaptive Approximation in Adam Optimization via Randomized Low-Rank Matrices.

Geometrically Principled Randomized Optimization for Efficient LLM Training Adapprox: Adaptive Approximation in Adam Optimization via Randomized Low-Rank Matrices

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:27.244782Z

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Observation 17c8cba1-b950-42e7-87c1-9f2477ed13d0 · outbound

This paper cites APOLLO: SGD-like Memory, AdamW-level Performance.

Geometrically Principled Randomized Optimization for Efficient LLM Training APOLLO: SGD-like Memory, AdamW-level Performance

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:27.373729Z

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Unavailable: canonical work link unavailable.

Observation 605f6ef2-9754-4d8c-828c-85dbaa968e77 · outbound

This paper cites FRUGAL : Memory-efficient optimization by reducing state overhead for scalable training.

Geometrically Principled Randomized Optimization for Efficient LLM Training FRUGAL : Memory-efficient optimization by reducing state overhead for scalable training

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:27.541776Z

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Observation 86ba1130-7d90-4a33-b820-e6080fd11e0e · outbound

This paper cites @esa (Ref.

Geometrically Principled Randomized Optimization for Efficient LLM Training @esa (Ref

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:27.650349Z

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Observation eaa652d2-e7fa-4e9b-85d0-aa0ea915467e · outbound

This paper cites an unresolved cited work.

Geometrically Principled Randomized Optimization for Efficient LLM Training Unresolved cited work

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:27.766772Z

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Unavailable: canonical work link unavailable.

Observation 07c08ce2-2331-4ffa-8d9f-cf1ca8ce4f3b · outbound

This paper cites These findings explain both the strengths and weaknesses of existing randomized and structured approaches, and motivate our proposed algorithms.

Geometrically Principled Randomized Optimization for Efficient LLM Training These findings explain both the strengths and weaknesses of existing randomized and structured approaches, and motivate our proposed algorithms

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-04T12:51:27.845880Z

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Pith citing papers

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