Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-19T11:57:25.711490Z
Paper Citation Record · LEDGER
As of 14 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2506.00158.
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 2026-05-19T11:57:25.711490Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
41 of 41 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation b85c0328-b635-4852-a650-49dba2a17621 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States In Proceedings of the 2016 ACM SIGSAC conference on computer and communications security
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 10e15b2e-9ca7-4c89-a381-37cfe644ca04 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Advances in Neural Information Processing Systems 35 (2022), 3788–3800
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation ab6867f0-3fc1-47cf-bae3-924fe5618ddd · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Unresolved cited work
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation c19a63b6-97ea-42fb-825d-68dd27296713 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States It's Our Loss: No Privacy Amplification for Hidden State DP-SGD With Non-Convex Loss
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 1ceb12fd-4bde-4ff0-8352-5ef2ee2d0f64 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Privacy Loss of Noisy Stochastic Gradient Descent Might Converge Even for Non-Convex Losses
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation d008f391-215a-43a9-9020-73d43390113e · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Advances in neural information processing systems 31 (2018)
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 70395572-609a-4ccd-be86-5ad009a66823 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Tighter Privacy Auditing of DP-SGD in the Hidden State Threat Model
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation fd1ce97e-64ba-4993-ba5d-d2da25567196 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Advances in Neural Information Processing Systems 34 (2021), 14771–14781
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation e20341a5-9967-4ed7-9ac4-87e9338e337f · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States IEEE Transactions on Information Theory 61, 5 (2015), 2788–2806
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation c62f73c7-5684-438f-9fe1-3fdc8047ce7a · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States In Theory of Cryptography: Third Theory of Cryptography Conference, TCC 2006, New York, NY, USA, March 4-7
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 9b5411a3-dfcc-45cd-b16f-abaa6f94b2d1 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States In 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation e58f03c2-6318-4651-919f-116b690abe95 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Probability and Mathematical Statistics 30, 2 (2010), 339–351
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 3d82fa76-ef21-41a1-8faa-86ef1e528634 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States A Short Note on Concentration Inequalities for Random Vectors with SubGaussian Norm
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 47ffcb48-f505-4195-8fb6-25bc1cadc34a · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Scaling Laws for Neural Language Models
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation bd804d40-0149-4db5-885d-4e607cb9467a · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Privacy of the last iterate in cyclically-sampled DP-SGD on nonconvex composite losses
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation e950c7b2-765f-4696-b44f-04dc8376a704 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Differentially Private Zeroth-Order Methods for Scalable Large Language Model Finetuning
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation ce283280-6b45-45f0-887d-c6802b08dc41 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Unresolved cited work
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 9c5589e1-685a-4ecd-b741-880525f9bf0d · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States In 2017 IEEE 30th computer security foundations symposium (CSF)
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 08049848-d47f-49ed-b494-84c6d2c07953 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States R\'enyi Differential Privacy of the Sampled Gaussian Mechanism
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 7494c136-aa3d-4dde-95a7-00ff209fef92 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Foundations of Computational Mathematics 17, 2 (2017), 527–566
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 401c0b04-a438-4ec7-a530-8edfa01e00aa · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Modern Stochastics: Theory and Applications 10, 2 (2023), 211–228
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 78180ed0-9e43-4e95-8615-4bb5e3b5e5cb · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States The Last Iterate Advantage: Empirical Auditing and Principled Heuristic Analysis of Differentially Private SGD
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation f988bea5-4287-49a5-ba27-77e5a5c13c18 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Private Fine-tuning of Large Language Models with Zeroth-order Optimization
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 2afb66f4-6e96-491e-802f-548ee633979e · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Introduction to the non-asymptotic analysis of random matrices
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation ecc8f071-6a8b-466a-ada6-2978ca2a703c · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Advances in Neural Information Processing Systems 35 (2022), 703–715
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 355bdc7f-b618-4c55-b8f9-454d86cc74d8 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States In International Workshop on Federated Learning in the Age of Foundation Models in Conjunction with NeurIPS 2023
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 7a028a60-8e87-499c-80f7-fe4d7559d930 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States In The Twelfth International Conference on Learning Representations
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation d90faab3-5bec-4f26-a1d4-1058e1a3d191 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States We set the radius of the projected set to be R = 1, smooth constant M = 1, strongly convex constant m = 0.9, and the clipped norm ∆ = 1
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation faa7904a-1f5e-43af-8153-545f5a41c6a7 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States 12 A.4 Proof of Theorem 3.1 The proof is quite standard in the DP literature (i.e., based on the analysis of Mironov (2017))
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 2c8c842f-b884-4ae8-8c0b-a101c8a4bc3b · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States In the meanwhile, the Lipschitz constant c of the first order gradient update map ϕ is as follows: If ℓi are M-smooth and m-strongly convex, then if η K ≤ 1 M we have c = 1 − ηm K
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 9a0b5c05-3682-468d-88e7-98eca9bc82f1 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Additionally, for simplicity we choose βt = 1/2
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 2dba13f7-0c11-40e3-93d4-d2f90de19fc6 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Unresolved cited work
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 4f0ed731-c97a-4eea-9c6d-8385607b9eed · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States (65) Note that Sα can be computed in practice with a numerically stable procedure for precise computa- tion Mironov (2017)
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 1a7f165f-329b-4dcf-8630-1f40c0951224 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Unresolved cited work
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 79e0d4f9-316c-4f39-84f6-05f8ddcfc3ee · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States In practice, Sα(q, σ) is computed via numerical integral for the tightest possible privacy accounting
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation eaf978fa-db0d-4cee-b574-130472494980 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States The averaged loss function is twice differentiable with −H ⪯ ∇2L(w; D) ⪯ H for any w ∈ Rd, and its minimum is finite
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 75af8f3f-52ba-4862-b3c5-d9046ea24fdd · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States (88) where (a) is due to M-smoothness and the elementary inequality (a + b)2 ≤ 2a2 + 2b2
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation edb1ea3e-daa9-4d0d-b4ef-b7144b038653 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States (101) If we further assume that |¯ℓ(w)| ≤ B for any w
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 7ac41693-7552-4a9c-923d-5b6c2b29a93b · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Lemma B.3
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 3b48343d-79cb-47eb-87f4-67b6284f360f · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Since W1 (d) = Z2 for Z ∼ N (0, 1), by the lower bound of the Q-function, it holds that P {W1 ≥ κ1} = P {|Z| ≥ √κ1} = 2 · Q (√κ1) ≥ √κ1 1 + κ1 e−κ1/2 √ 2π
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 913bf4f4-4d7b-4a6a-877e-db94b00fc725 · outbound
Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Then w⊥ 2 2 = R2 z2 1 Pd j=2 z2 j Pd j=1 z2 j 2 ≤ R2 z2 1 Pd j=1 z2 j Pd j=1 z2 j 2 = r2 z2 1Pd j=1 z2 j ≜ B, where B ∼ Beta 1 2 , d−1 2
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
No inbound Pith citation observations are available.