Paper Citation Record · LEDGER

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping

As of 12 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 1 inbound Pith citation observation for arXiv:2412.19529.

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

pith.paper-citation-record.v1
2412.19529 v4

Coverage vector

measured 55 of 55 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T00:23:05.364651Z

measured 56 of 56 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-13T05:34:48.195468Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-13T05:37:19.252093Z

Reference resolution

55 of 55 outbound references displayed

verified exact1
verified fuzzy29
unresolved25
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0fc28118-baf3-49a6-b1eb-9b8ff1e4a8eb · outbound

This paper cites write newline.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping write newline

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.160353Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 24bcfccf-0945-4922-83e1-30dc3419e7ef · outbound

This paper cites Lower bounds for non-convex stochastic optimization.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Lower bounds for non-convex stochastic optimization

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.165327Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d3ad11f4-6b02-432f-9a2e-524cc9b75066 · outbound

This paper cites Optimization methods for large-scale machine learning.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Optimization methods for large-scale machine learning

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.170048Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc9be62a-f9e0-4c6e-9034-0fac49ad27a5 · outbound

This paper cites Extrapolation and interpolation of quasi-linear operators on martingales.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Extrapolation and interpolation of quasi-linear operators on martingales

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:06.005562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a04d6d5b-be21-48a0-9ad1-7c5435dcad12 · outbound

This paper cites Martingale transforms.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Martingale transforms

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.994834Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ad4242fa-2a07-4bc1-be10-f72ca3ff91d1 · outbound

This paper cites Lower bounds for finding stationary points i.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Lower bounds for finding stationary points i

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.983749Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2b4ca97b-f132-46bd-9581-fe7ede0f56e8 · outbound

This paper cites Generalized-smooth nonconvex optimization is as efficient as smooth nonconvex optimization.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Generalized-smooth nonconvex optimization is as efficient as smooth nonconvex optimization

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.971418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ad5105ba-d011-475e-91a7-7c4bba9741f7 · outbound

This paper cites Robustness to unbounded smoothness of generalized signsgd.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Robustness to unbounded smoothness of generalized signsgd

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.960483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2c750b12-965d-46cb-9e03-0e660ef42e10 · outbound

This paper cites Momentum improves normalized SGD.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Momentum improves normalized SGD

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.949463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a16ab0f0-9084-4c36-aa29-4531ae374c28 · outbound

This paper cites High-probability bounds for non-convex stochastic optimization with heavy tails.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping High-probability bounds for non-convex stochastic optimization with heavy tails

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.938843Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 80b17b9a-bb29-414c-9873-9c2b50e97c26 · outbound

This paper cites On the intergrability of the martingale square function.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping On the intergrability of the martingale square function

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.928488Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation afd19ac1-36ca-4c2c-8f98-181502c26e4b · outbound

This paper cites Adaptive subgradient methods for online learning and stochastic optimization.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Adaptive subgradient methods for online learning and stochastic optimization

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.206190Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58aea4d7-3ec7-4d56-8a4e-71a109f52808 · outbound

This paper cites Beyond uniform smoothness: A stopped analysis of adaptive sgd.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Beyond uniform smoothness: A stopped analysis of adaptive sgd

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.911746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 35ad4cc9-880d-4bf3-8011-0a57d2d20282 · outbound

This paper cites Stochastic first-and zeroth-order methods for nonconvex stochastic programming.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Stochastic first-and zeroth-order methods for nonconvex stochastic programming

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.213244Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6c1cbb4-d6d2-4e45-a082-e09f526ac253 · outbound

This paper cites High-probability convergence for composite and distributed stochastic minimization and variational inequalities with heavy-tailed noise.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping High-probability convergence for composite and distributed stochastic minimization and variational inequalities with heavy-tailed noise

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.895550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 75b954ad-2c0f-4a4a-a7f2-e71bf02b0ded · outbound

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

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Beyond convexity: Stochastic quasi-convex optimization

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.220660Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee49d851-ff89-406e-a56a-2afb4caed0c7 · outbound

This paper cites Revisiting Convergence of AdaGrad with Relaxed Assumptions.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Revisiting Convergence of AdaGrad with Relaxed Assumptions

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.225264Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a407fcb-ee45-407f-bae5-678c604665f2 · outbound

This paper cites From Gradient Clipping to Normalization for Heavy Tailed SGD.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping From Gradient Clipping to Normalization for Heavy Tailed SGD

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.229100Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8ee79d4f-0f3a-4261-827b-e32fd7b80bba · outbound

This paper cites Parameter-agnostic optimization under relaxed smoothness.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Parameter-agnostic optimization under relaxed smoothness

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.879086Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 77125654-26d1-4b33-8fa1-ae009d22de61 · outbound

This paper cites Non-convex distributionally robust optimization: Non-asymptotic analysis.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Non-convex distributionally robust optimization: Non-asymptotic analysis

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.868128Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 46a386e5-9403-452e-a034-af1360ef99b3 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Adam: A Method for Stochastic Optimization

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.240285Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 638ce608-afd1-4407-9a37-5c6c522e82ea · outbound

This paper cites Convergence and efficiency of subgradient methods for quasiconvex minimization.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Convergence and efficiency of subgradient methods for quasiconvex minimization

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.857095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5fa88c4b-f563-4aae-bc01-ea316aca6af1 · outbound

This paper cites Accelerated zeroth-order method for non-smooth stochastic convex optimization problem with infinite variance.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Accelerated zeroth-order method for non-smooth stochastic convex optimization problem with infinite variance

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.845941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ebd65b1a-f0c5-4cf6-a42e-a3ce8600a10e · outbound

This paper cites First-order and stochastic optimization methods for machine learning.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping First-order and stochastic optimization methods for machine learning

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.250868Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0ca87c4-de89-4b4b-af29-4e7be5e90b01 · outbound

This paper cites The Power of Normalization: Faster Evasion of Saddle Points.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping The Power of Normalization: Faster Evasion of Saddle Points

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.255061Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 132f5c5f-bb67-4e2a-80ea-35306b4bf7d1 · outbound

This paper cites Convex and non-convex optimization under generalized smoothness.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Convex and non-convex optimization under generalized smoothness

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.828707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e3645a8f-7a53-4e4c-978f-e0e5c03231de · outbound

This paper cites Convergence of adam under relaxed assumptions.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Convergence of adam under relaxed assumptions

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.817103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 81e46ea8-f965-42e2-9c13-137eec65ac64 · outbound

This paper cites High-probability bound for non-smooth non-convex stochastic optimization with heavy tails.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping High-probability bound for non-smooth non-convex stochastic optimization with heavy tails

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.806122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 9b9e4e8e-941d-4737-9bfa-7d0161702bc8 · outbound

This paper cites Stochastic Nonsmooth Convex Optimization with Heavy-Tailed Noises: High-Probability Bound, In-Expectation Rate and Initial Distance Adaptation.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Stochastic Nonsmooth Convex Optimization with Heavy-Tailed Noises: High-Probability Bound, In-Expectation Rate and Initial Distance Adaptation

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.269460Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 011f68f0-915a-4656-ba06-fdcf2690a83b · outbound

This paper cites Near-Optimal Non-Convex Stochastic Optimization under Generalized Smoothness.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Near-Optimal Non-Convex Stochastic Optimization under Generalized Smoothness

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-11T00:23:05.562657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 80e220e5-3bbd-4626-8174-1ce74974eca4 · outbound

This paper cites Breaking the lower bound with (little) structure: Acceleration in non-convex stochastic optimization with heavy-tailed noise.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Breaking the lower bound with (little) structure: Acceleration in non-convex stochastic optimization with heavy-tailed noise

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.795062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8c848301-a694-4ceb-a6c3-bd1c76924c35 · outbound

This paper cites Brendan McMahan and Matthew J.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Brendan McMahan and Matthew J

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.783834Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 95a200f2-69dc-4234-98d9-d6fb1b0aa4cd · outbound

This paper cites Convergence of gradient descent on separable data.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Convergence of gradient descent on separable data

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.773141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 339e4444-5c6e-4323-ac52-d31237d0a8d7 · outbound

This paper cites Lectures on convex optimization, volume 137.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Lectures on convex optimization, volume 137

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.287926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fd650228-1fa1-4104-994f-d706340f71d2 · outbound

This paper cites Minimization methods for nonsmooth convex and quasiconvex functions.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Minimization methods for nonsmooth convex and quasiconvex functions

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.291488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e66b33ec-86c6-4d0d-a181-cb0598653329 · outbound

This paper cites Improved convergence in high probability of clipped gradient methods with heavy tailed noise.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Improved convergence in high probability of clipped gradient methods with heavy tailed noise

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.747536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 62e710e2-5c40-4598-b580-5d1b39161451 · outbound

This paper cites Breaking the heavy-tailed noise barrier in stochastic optimization problems.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Breaking the heavy-tailed noise barrier in stochastic optimization problems

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.735972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5b44bcd0-0498-4aee-ab37-f4294002ddf1 · outbound

This paper cites On equivalence of martingale tail bounds and deterministic regret inequalities.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping On equivalence of martingale tail bounds and deterministic regret inequalities

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.725144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1f43cce4-4eeb-450d-bbb9-3781d43cb2a0 · outbound

This paper cites A stochastic approximation method.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping A stochastic approximation method

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.307200Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 262ab119-b5b0-4809-9591-85ae4bcf5d8f · outbound

This paper cites High-probability bounds for stochastic optimization and variational inequalities: the case of unbounded variance.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping High-probability bounds for stochastic optimization and variational inequalities: the case of unbounded variance

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.707260Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 13d035c6-4109-4359-8599-e2fe27fa8e5d · outbound

This paper cites On the Heavy-Tailed Theory of Stochastic Gradient Descent for Deep Neural Networks.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping On the Heavy-Tailed Theory of Stochastic Gradient Descent for Deep Neural Networks

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.314264Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d6f61eb8-111b-476c-acda-1c1211037043 · outbound

This paper cites A tail-index analysis of stochastic gradient noise in deep neural networks.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping A tail-index analysis of stochastic gradient noise in deep neural networks

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.696259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0afb4bcc-8ae6-46d0-b042-7fc16b8c506d · outbound

This paper cites Gradient normalization provably benefits nonconvex sgd under heavy-tailed noise.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Gradient normalization provably benefits nonconvex sgd under heavy-tailed noise

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.321472Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d1a17774-fafa-4920-8f77-1e7301bea51e · outbound

This paper cites Lecture 6.5-rmsprop: Divide the gradient by a running average of its recent magnitude.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Lecture 6.5-rmsprop: Divide the gradient by a running average of its recent magnitude

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.325034Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30285a24-ec49-4c23-acc5-adf26fa2ae50 · outbound

This paper cites Convergence of adagrad for non-convex objectives: Simple proofs and relaxed assumptions.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Convergence of adagrad for non-convex objectives: Simple proofs and relaxed assumptions

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.679329Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3ea02deb-cf8d-4a4e-acb3-1c5831536187 · outbound

This paper cites On the Convergence of Adam under Non-uniform Smoothness: Separability from SGDM and Beyond.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping On the Convergence of Adam under Non-uniform Smoothness: Separability from SGDM and Beyond

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.332066Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 807b14e1-fd80-477c-832e-25c3c34487bf · outbound

This paper cites Large Batch Training of Convolutional Networks.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Large Batch Training of Convolutional Networks

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.335736Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b9e8fe4-1f53-4c19-af55-00a91c1fa4b4 · outbound

This paper cites Large Batch Optimization for Deep Learning: Training BERT in 76 minutes.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Large Batch Optimization for Deep Learning: Training BERT in 76 minutes

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.339526Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dc5a44f9-b838-4056-9a91-5a5472e3f179 · outbound

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

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Improved analysis of clipping algorithms for non-convex optimization

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.343597Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 41ec6a0c-d5c0-421d-b1dd-170400ff3825 · outbound

This paper cites Why gradient clipping accelerates training: A theoretical justification for adaptivity.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Why gradient clipping accelerates training: A theoretical justification for adaptivity

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.662393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1e9764ac-5c63-4251-b2a9-30925eb9bfb2 · outbound

This paper cites Why are adaptive methods good for attention models? Advances in Neural Information Processing Systems, 33: 0 15383--15393, 2020 c.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Why are adaptive methods good for attention models? Advances in Neural Information Processing Systems, 33: 0 15383--15393, 2020 c

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.350245Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b318596c-0bea-45b7-889a-c199c38b5511 · outbound

This paper cites Parameter-free regret in high probability with heavy tails.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Parameter-free regret in high probability with heavy tails

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.645301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 60e2cdf6-d79d-4105-89e5-052ddd30fd9d · outbound

This paper cites @esa (Ref.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping @esa (Ref

Reference 53

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.357279Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e5e25932-8001-4f9d-a7f1-8691e04d1534 · outbound

This paper cites an unresolved cited work.

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping Unresolved cited work

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-11T00:23:05.360942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e6d7eb5e-8a71-4dee-8029-dab6d8102179 · outbound

This paper cites denotes the set of natural numbers (excluding 0 ).

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping denotes the set of natural numbers (excluding 0 )

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:23:05.621655Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

Observation 411c530c-4a62-4b55-a653-5c317d1eed7e · inbound

Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives cites this paper.

Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping

Reference 42

Resolution: verified exact; arxiv_id, observed 2026-05-13T05:37:19.253844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.