Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T19:25:24.982987Z
Paper Citation Record · LEDGER
As of 7 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 2 inbound Pith citation observations for arXiv:2507.05966.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T19:25:24.982987Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-06-26T09:08:41.993925Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-04T10:09:44.606239Z
55 of 55 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 35277eaa-d935-45a7-a922-e10106887638 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Lower bounds for non-convex stochastic optimization.Mathematical Programming, 199(1-2):165–214, 2023
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 96dffac1-f544-44e4-86e9-98d132fd80ab · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective SGD with AdaGrad stepsizes: Full adaptivity with high probability to unknown parameters, unbounded gradients and affine variance
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 705886f5-1206-4618-877e-504f020888e5 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Dissecting Adam: The sign, magnitude and variance of stochastic gradients
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation d6b50d4e-acfd-4e70-9c5e-bdbee63f31c4 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective signSGD: Compressed optimisation for non-convex problems
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4fd4a7bd-b944-42a2-8ba6-9538afd26af6 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Gradient convergence in gradient methods with errors.SIAM Journal on Optimization, 10(3):627–642, 2000
Reference 5
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a1448b4a-3e5b-4cff-96dd-c0c1f9f44b13 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Optimization methods for large-scale machine learning.SIAM review, 60(2):223–311, 2018
Reference 6
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 74849577-cce8-4e77-9b24-b06173cb34f3 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Language models are few-shot learners.Advances in neural information processing systems, 33:1877–1901, 2020
Reference 7
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fc0b04f6-4ce8-412b-aecb-1d4f532ff784 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Towards practical Adam: Non-convexity, convergence theory, and mini-batch acceleration.Journal of Machine Learning Research, 23(229):1–47, 2022
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 11d3e333-4110-4097-84c0-8327c374b3d8 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Lion Secretly Solves Constrained Optimization: As Lyapunov Predicts
Reference 9
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 559654b5-1189-44e8-8fa5-21b20f5338ab · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Symbolic Discovery of Optimization Algorithms
Reference 10
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3a3bebb0-c25d-427c-b034-75336438fa83 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization
Reference 11
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 94fadaeb-e8fe-4cfa-9c53-c40e5704f401 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective PaLM: Scaling language modeling with pathways.Journal of Machine Learning Research, 24(240):1– 113, 2023
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation a8cafaca-0910-411d-9072-79e42d722862 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Ro- bustness to unbounded smoothness of generalized signSGD
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e6719adf-27b9-470a-b54b-92e36ae55226 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective A Simple Convergence Proof of Adam and Adagrad
Reference 14
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d9a34d3d-ac87-4bec-91d1-98ccb4585ba9 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective The Llama 3 Herd of Models
Reference 15
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d07053c8-09ea-4b27-a942-b074b378a25f · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Beyond uniform smoothness: A stopped analysis of adaptive SGD
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 5b93e733-4e24-4a03-aed9-f8f51bc75240 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective The power of adaptivity in SGD: Self-tuning step sizes with unbounded gradients and affine variance
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 6ea988f4-e523-4dcb-ab6c-2eef37107b2c · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Deep residual learning for image recognition
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation d96d8d6a-9d75-4bb4-962d-b3334ba293a4 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Neural networks for machine learning lecture 6a overview of mini-batch gradient descent.Cited on, 14(8):2, 2012
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 41b284f3-d020-4db4-bb2f-7fdd13288949 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective High Probability Convergence of Adam Under Unbounded Gradients and Affine Variance Noise
Reference 20
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6a4893c6-141d-457a-bd52-17523901a20d · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective On Convergence of Adam for Stochastic Optimization under Relaxed Assumptions
Reference 21
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 59423576-3cf6-4779-a3d6-1b4818115798 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Parameter-agnostic optimization under relaxed smoothness
Reference 22
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4398f761-50bc-4597-900c-36f816439481 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Non-convex distributionally robust optimization: Non-asymptotic analysis
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation ce223768-7387-4808-95b4-27633856fca0 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Linear convergence of gradient and proximal- gradient methods under the polyak-łojasiewicz condition
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e83368b9-7540-46fa-acf7-1dc72d1cee52 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Adam: A method for stochastic optimization
Reference 25
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5859ac37-9c0d-49ab-a7e2-6da17c984bb0 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Segment Anything
Reference 26
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation aa74ad19-d0b2-4daa-9cd1-f9cf1252fe95 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Imagenet classification with deep convolutional neural networks.Communications of the ACM, 60(6):84–90, 2017
Reference 27
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0e6c8338-7d86-4ed5-b889-518367398210 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Noise Is Not the Main Factor Behind the Gap Between SGD and Adam on Transformers, but Sign Descent Might Be
Reference 28
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 695b4b05-6208-440c-9b30-0ffb1201aa38 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Heavy-Tailed Class Imbalance and Why Adam Outperforms Gradient Descent on Language Models
Reference 29
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 98eeaa30-7d20-440d-a490-6ffef12a0cfc · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Convergence of Adam under relaxed assumptions.Advances in Neural Information Processing Systems, 36, 2023
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 78af7bd9-1972-4135-a700-1b1379f29afd · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective An improved analysis of stochastic gradient descent with momentum.Advances in Neural Information Processing Systems, 33:18261–18271, 2020
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation c666a50c-643a-4d26-8eb0-611140135ec0 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective A convnet for the 2020s
Reference 32
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b2dafb9f-2064-482c-b675-e4896ba17cf1 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Learning transferable visual models from natural language supervision
Reference 33
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5c97f269-0659-4efb-8d09-95bc73b6f490 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective On the convergence of Adam and beyond
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation db976a6c-0f1f-4376-8762-6ef03e8dba9f · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective A direct adaptive method for faster backpropagation learning: The rprop algorithm
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 614c7d1e-603f-4da3-99db-ef483b1037b1 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective 1-bit stochastic gradient descent and its application to data-parallel distributed training of speech DNNs
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 6f05deac-e38b-45e5-9550-8b886c97128f · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective RMSProp converges with proper hyperparameter
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 0bdee0cc-0e89-4cf3-b983-c3ef9374b9ab · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Scalable distributed DNN training using commodity GPU cloud computing
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 5d694ec4-c544-4ced-a699-313f53c5b24a · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Momentum ensures convergence of signSGD under weaker assumptions
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation ba6d9a05-1f48-4624-948d-73fb7e46fc11 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective LLaMA: Open and Efficient Foundation Language Models
Reference 40
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 99f1e25a-dc36-4a05-93ce-c647c55d7089 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Llama 2: Open Foundation and Fine-Tuned Chat Models
Reference 41
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ccbd7f88-9575-47e9-a65b-adb19b0da7d4 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Attention is all you need.Advances in neural information processing systems, 30, 2017
Reference 42
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8f263129-d093-4f15-ad2a-a9d38abc9478 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Convergence of AdaGrad for non-convex objectives: Simple proofs and relaxed assumptions
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 111bb916-7cb6-42ba-9e6a-69d9dd5519d7 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Convergence of AdaGrad for non-convex objectives: Simple proofs and relaxed assumptions
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation c5effdbe-3f6a-4a2d-9c96-7e692818b58a · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective On the Convergence of Adam under Non-uniform Smoothness: Separability from SGDM and Beyond
Reference 45
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0d6c6492-c62e-493a-a3cf-bed39aa2fb0f · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Provable adaptivity of Adam under non-uniform smoothness
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4988bcb3-deb1-4289-acc9-0879ce3e95a6 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Convnext v2: Co-designing and scaling convnets with masked autoencoders
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 7c6d03a7-2de4-4203-a7a9-4740bcf55b6a · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer
Reference 48
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 656af517-df00-4701-a41e-20165d37edcf · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Improved analysis of clipping algorithms for non-convex optimization
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 016ddfac-a4f9-48b5-a061-a9d4439b32e2 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Why gradient clipping accelerates training: A theoretical justification for adaptivity
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation d2556d20-38d5-4809-95ac-bed2b40ba918 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Adam can converge without any modification on update rules.Advances in neural information processing systems, 35:28386–28399, 2022
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 9d9bc7e9-2622-4c46-8652-5032f800f01d · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective Recently, [20] provably demonstrate the convergence rate of vanilla Adam in high probability perspective, but it only works with the stronger coordinate-wise affine variance
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4c749ebe-f963-4b3d-bde8-d55404ebc44e · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective [49] posits that it is also equivalent to an affine form of the gradient norm for the first-order differentiable function
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 8f602a4d-d4a5-4547-9308-c1a510dc039f · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective [30] further extended the linear (L0, L1)-smooth to the generalized polynomial version, and proved that Adam will converged to O poly(lnT) T 1/4 with the weaker assumption
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation ff9b11ab-3777-4ba9-b2ff-005f85315eb2 · outbound
Simple Convergence Proof of Adam From a Sign-like Descent Perspective tX k=1 βt−k 1 (gk − ∇F(xk)) 2 # | {z } T2 + 1 T T−1X t=0 E
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 0ac89055-0f85-475c-a8c2-d8c0a1c99366 · inbound
When and Why SignSGD Outperforms SGD: A Theoretical Study Based on $\ell_1$-norm Lower Bounds Simple Convergence Proof of Adam From a Sign-like Descent Perspective
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 17e2f267-9e45-466b-a6e2-68fe92e9bd80 · inbound
Open Problem: Is AdamW Effective Under Heavy-Tailed Noise? Simple Convergence Proof of Adam From a Sign-like Descent Perspective
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.