Paper Citation Record · LEDGER

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness

As of 19 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 1 inbound Pith citation observation for arXiv:2502.08532.

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

pith.paper-citation-record.v1
2502.08532 v2

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-08T04:56:54.620345Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-28T13:17:11.219557Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T00:46:24.654519Z

Reference resolution

16 of 16 outbound references displayed

verified exact1
verified fuzzy4
unresolved9
parse uncertain0
malformed identifier2
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 60591c33-283e-4153-8350-f54728fc65e5 · outbound

This paper cites Thus we can further bound (30): AK ξ(xK)−ξ(x ⋆) ≤ D0 K−1X k=0 a2 k+1 Ak+1.

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Thus we can further bound (30): AK ξ(xK)−ξ(x ⋆) ≤ D0 K−1X k=0 a2 k+1 Ak+1

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:56:54.912770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8ce1e9f8-61c5-4985-8d3f-5b499cb281e6 · outbound

This paper cites Note that in this case as well,H∇2f(x)is a symmetric matrix and it follows from Theorem D.2 that the operatorTδL−1, ¯L−1 is injective for anyδ <1.

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Note that in this case as well,H∇2f(x)is a symmetric matrix and it follows from Theorem D.2 that the operatorTδL−1, ¯L−1 is injective for anyδ <1

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:56:54.879441Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b0d0ba62-37af-4f0e-bcbd-11c0dd21b4e3 · outbound

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

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Heavy-Tailed Class Imbalance and Why Adam Outperforms Gradient Descent on Language Models

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-08T04:56:54.561543Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0637655f-160b-499d-bff0-38b94638158a · outbound

This paper cites Gradient descent with a general cost.

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Gradient descent with a general cost

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-08T04:56:54.572784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 987dc433-f523-4cc0-ac49-7ea355f10d2c · outbound

This paper cites Improved anal- ysis of clipping algorithms for non-convex optimization.

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Improved anal- ysis of clipping algorithms for non-convex optimization

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:56:54.995457Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fc79ba83-3f5c-499f-b16a-f2578e1c4f49 · outbound

This paper cites Therefore, through (Bauschke et al., 2017b, Proposition 11.7) we get thath ∗ is increasing onR +.

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Therefore, through (Bauschke et al., 2017b, Proposition 11.7) we get thath ∗ is increasing onR +

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:56:54.978845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 128affbc-c83a-4ee3-8f62-825c2a71e36b · outbound

This paper cites Using Theorem 1.3 we thus obtain ∇ϕ∗(y) = min(1,∥y∥) sgn(y)and the algorithm becomes: xk+1 =x k −γmin(1/∥∇f(x k)∥, λ)∇f(xk), by pulling the norm inside themin.

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Using Theorem 1.3 we thus obtain ∇ϕ∗(y) = min(1,∥y∥) sgn(y)and the algorithm becomes: xk+1 =x k −γmin(1/∥∇f(x k)∥, λ)∇f(xk), by pulling the norm inside themin

Reference 12

Resolution: malformed identifier; raw_fallback, observed 2026-08-08T04:56:54.946319Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4f6524ae-f603-433c-bfa5-4c24c9f63a1e · outbound

This paper cites an unresolved cited work.

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:56:54.928946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7d051e34-ddda-4d27-9ded-a736b35add37 · outbound

This paper cites an unresolved cited work.

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:56:54.895716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation bc4b7d1b-54d7-443f-8f47-08e60b06c2b6 · outbound

This paper cites an unresolved cited work.

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Unresolved cited work

Reference 42

Resolution: malformed identifier; raw_fallback, observed 2026-08-08T04:56:54.962869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fd8a9e62-d6aa-47de-bd40-78ee1264af13 · outbound

This paper cites Mirror Duality in Convex Optimization.

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Mirror Duality in Convex Optimization

Reference 2012

Resolution: unresolved; no resolver link, observed 2026-08-08T04:56:54.550547Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d9a7425b-0cb6-4533-97d6-ad8458bf34f0 · outbound

This paper cites Mirror and Preconditioned Gradient Descent in Wasserstein Space.

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Mirror and Preconditioned Gradient Descent in Wasserstein Space

Reference 2018

Resolution: verified exact; local_arxiv, observed 2026-08-08T04:56:54.862894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8c9e6964-da6a-406d-b9b1-4b6315c04c33 · outbound

This paper cites Optimizing $(L_0, L_1)$-Smooth Functions by Gradient Methods.

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Optimizing $(L_0, L_1)$-Smooth Functions by Gradient Methods

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-08T04:56:54.578227Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 68ffc6e6-f75d-41be-948d-d456195b48e9 · outbound

This paper cites Methods for Convex $(L_0,L_1)$-Smooth Optimization: Clipping, Acceleration, and Adaptivity.

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Methods for Convex $(L_0,L_1)$-Smooth Optimization: Clipping, Acceleration, and Adaptivity

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-08T04:56:54.545328Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 53871856-5521-4ca3-bda1-151d711e62f5 · outbound

This paper cites and Patrinos, P.

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness and Patrinos, P

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-08T04:56:54.566990Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9536f7ba-5991-4d40-b0e3-f2e3f142869b · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Adam: A Method for Stochastic Optimization

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-08T04:56:54.555901Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 3041039d-a36c-49b7-b4ac-6db03c40086a · inbound

Adaptive Accelerated Mirror Descent in Primal and Dual Spaces cites this paper.

Adaptive Accelerated Mirror Descent in Primal and Dual Spaces Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-07-02T00:46:24.656614Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.