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Paper Citation Record · LEDGER

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States

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.

pith.paper-citation-record.v1
2506.00158 v3

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-19T11:57:25.711490Z

measured 41 of 41 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+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

41 of 41 outbound references displayed

  • verified exact7
  • verified fuzzy25
  • unresolved4
  • parse uncertain0
  • malformed identifier1
  • metadata mismatch4

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b85c0328-b635-4852-a650-49dba2a17621 · outbound

This paper cites In Proceedings of the 2016 ACM SIGSAC conference on computer and communications security.

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

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raw_fallback, observed 2026-05-19T12:03:03.774099Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:e0a778bb4815c3f7c6a7a5148113549536d94cf070bdd3afe31882c47bdaa7c7

Observation 10e15b2e-9ca7-4c89-a381-37cfe644ca04 · outbound

This paper cites Advances in Neural Information Processing Systems 35 (2022), 3788–3800.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Advances in Neural Information Processing Systems 35 (2022), 3788–3800

Reference 2

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raw_fallback, observed 2026-05-19T12:02:17.644999Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:32b0503adab2092a75dbdaed14a8ea935709e3c8a7368c588a74f2ca285d29ec

Observation ab6867f0-3fc1-47cf-bae3-924fe5618ddd · outbound

This paper cites an unresolved cited work.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Unresolved cited work

Reference 3

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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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:91c0ea5ca4581caa25d05acee8f13a9345b8cf8f0eb5aede528830df90ca927d

Observation c19a63b6-97ea-42fb-825d-68dd27296713 · outbound

This paper cites It's Our Loss: No Privacy Amplification for Hidden State DP-SGD With Non-Convex Loss.

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

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arxiv_id, observed 2026-05-19T12:02:16.863645Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:d6dfdefea358648bcacaa2c4c1a594c0c816360c8a7568bb69fe32a67b4fb86b

Observation 1ceb12fd-4bde-4ff0-8352-5ef2ee2d0f64 · outbound

This paper cites Privacy Loss of Noisy Stochastic Gradient Descent Might Converge Even for Non-Convex Losses.

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

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verified exact
arxiv_id, observed 2026-05-19T12:02:16.833773Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:d9706e3e509c667a6998530f6f4fc399ebf93905c1295a74a571bad67ad3974d

Observation d008f391-215a-43a9-9020-73d43390113e · outbound

This paper cites Advances in neural information processing systems 31 (2018).

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Advances in neural information processing systems 31 (2018)

Reference 6

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raw_fallback, observed 2026-05-19T12:02:17.634682Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:d939dae31a034966909042377bcb54d04879983f6ab726917a7f34f5a814aaf2

Observation 70395572-609a-4ccd-be86-5ad009a66823 · outbound

This paper cites Tighter Privacy Auditing of DP-SGD in the Hidden State Threat Model.

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

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verified exact
arxiv_id, observed 2026-05-19T12:02:16.845915Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:a919c88490502cdea2266aca7469953896214923c748644626f321d4307a2951

Observation fd1ce97e-64ba-4993-ba5d-d2da25567196 · outbound

This paper cites Advances in Neural Information Processing Systems 34 (2021), 14771–14781.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Advances in Neural Information Processing Systems 34 (2021), 14771–14781

Reference 8

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raw_fallback, observed 2026-05-19T12:03:03.789280Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:5b724ade0f36ee803c9c20daa3764aa867b29dabc648f497958786f5f8ebdb86

Observation e20341a5-9967-4ed7-9ac4-87e9338e337f · outbound

This paper cites IEEE Transactions on Information Theory 61, 5 (2015), 2788–2806.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States IEEE Transactions on Information Theory 61, 5 (2015), 2788–2806

Reference 9

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raw_fallback, observed 2026-05-19T12:02:17.636577Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:9d0bc1adf39790c4ab17f34dcd08968d8c30d49f80dd3750579cc39b2a5c92c8

Observation c62f73c7-5684-438f-9fe1-3fdc8047ce7a · outbound

This paper cites In Theory of Cryptography: Third Theory of Cryptography Conference, TCC 2006, New York, NY, USA, March 4-7.

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

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raw_fallback, observed 2026-05-19T12:03:03.779049Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:23932341da0e82ce1872fe6c6a52f520815e5547a300ed966a80c0657f69b7a7

Observation 9b5411a3-dfcc-45cd-b16f-abaa6f94b2d1 · outbound

This paper cites In 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS).

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

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raw_fallback, observed 2026-05-19T12:03:03.775892Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:c48b0db7349b9a8ca5d523b01feaaeecd74df470bb9de93f0fbcf28e1191b696

Observation e58f03c2-6318-4651-919f-116b690abe95 · outbound

This paper cites Probability and Mathematical Statistics 30, 2 (2010), 339–351.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Probability and Mathematical Statistics 30, 2 (2010), 339–351

Reference 12

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raw_fallback, observed 2026-05-19T12:03:03.763813Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:cc354f691d8b9ce8bf6ceb604367a1d5f007d8731d4a6bfb80ed3b7101a5b640

Observation 3d82fa76-ef21-41a1-8faa-86ef1e528634 · outbound

This paper cites A Short Note on Concentration Inequalities for Random Vectors with SubGaussian Norm.

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

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local_arxiv, observed 2026-05-19T12:02:16.851855Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:e0404ed4013bdaba40088ecb9fe6a9413f987eae6d6202adf3561675a73043e6

Observation 47ffcb48-f505-4195-8fb6-25bc1cadc34a · outbound

This paper cites Scaling Laws for Neural Language Models.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Scaling Laws for Neural Language Models

Reference 14

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local_arxiv, observed 2026-05-19T12:02:16.842859Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:df2e50f7552727ba3bd555d34a20567fb8f8383e5cc0829c150b8ea8b6bbc4bd

Observation bd804d40-0149-4db5-885d-4e607cb9467a · outbound

This paper cites Privacy of the last iterate in cyclically-sampled DP-SGD on nonconvex composite losses.

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

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arxiv_id, observed 2026-05-19T12:02:16.857860Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:8c1c596305c154296fef03701489504dccbe2d0216ef36b8e03aca301e087545

Observation e950c7b2-765f-4696-b44f-04dc8376a704 · outbound

This paper cites Differentially Private Zeroth-Order Methods for Scalable Large Language Model Finetuning.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Differentially Private Zeroth-Order Methods for Scalable Large Language Model Finetuning

Reference 16

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arxiv_id, observed 2026-05-19T12:02:16.839782Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:2a8e2377012e6f963cfe4ad8a5634f6de4761b3c0f9265572110bc28743efb57

Observation ce283280-6b45-45f0-887d-c6802b08dc41 · outbound

This paper cites an unresolved cited work.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Unresolved cited work

Reference 17

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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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:1d1c6ab6b77179395400aa064dbc8dc318b34a34a8ecc0359e0b008f71745c10

Observation 9c5589e1-685a-4ecd-b741-880525f9bf0d · outbound

This paper cites In 2017 IEEE 30th computer security foundations symposium (CSF).

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States In 2017 IEEE 30th computer security foundations symposium (CSF)

Reference 18

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raw_fallback, observed 2026-05-19T12:03:03.785191Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:5354c91d2c9bcd128b40701758b8d32898438b00a36379b262020fec75216b3f

Observation 08049848-d47f-49ed-b494-84c6d2c07953 · outbound

This paper cites R\'enyi Differential Privacy of the Sampled Gaussian Mechanism.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States R\'enyi Differential Privacy of the Sampled Gaussian Mechanism

Reference 19

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arxiv_id, observed 2026-05-19T12:02:16.860826Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:2acaca270c821e50087cb89eba9e3ea9c6b94dd8af17ae224a35278e24898034

Observation 7494c136-aa3d-4dde-95a7-00ff209fef92 · outbound

This paper cites Foundations of Computational Mathematics 17, 2 (2017), 527–566.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Foundations of Computational Mathematics 17, 2 (2017), 527–566

Reference 20

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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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:abb812be8bda28483afaa10611edc585804ffd2364d2c3d21f28a9719ec0ef47

Observation 401c0b04-a438-4ec7-a530-8edfa01e00aa · outbound

This paper cites Modern Stochastics: Theory and Applications 10, 2 (2023), 211–228.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Modern Stochastics: Theory and Applications 10, 2 (2023), 211–228

Reference 21

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:f1b402de1cbbff678d070559f3f907501a761e399f199de1a87a7b8ac8d594bc

Observation 78180ed0-9e43-4e95-8615-4bb5e3b5e5cb · outbound

This paper cites The Last Iterate Advantage: Empirical Auditing and Principled Heuristic Analysis of Differentially Private SGD.

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

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arxiv_id, observed 2026-05-19T12:02:16.836885Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:913556751c9f2db99ed5a3079984c2303e353fc8e20481ce49a8073f645016ef

Observation f988bea5-4287-49a5-ba27-77e5a5c13c18 · outbound

This paper cites Private Fine-tuning of Large Language Models with Zeroth-order Optimization.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Private Fine-tuning of Large Language Models with Zeroth-order Optimization

Reference 23

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arxiv_id, observed 2026-05-19T12:02:16.854897Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:3976b2f6d02043c4fca4e54f10d2225a28036e31bd8fdd2b3162b770d7c8e27f

Observation 2afb66f4-6e96-491e-802f-548ee633979e · outbound

This paper cites Introduction to the non-asymptotic analysis of random matrices.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Introduction to the non-asymptotic analysis of random matrices

Reference 24

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local_arxiv, observed 2026-05-19T12:02:16.848833Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:683b99a4a51956ab9e23c4a9a28c208ff4f2df9f5e55ad8e6c8fa9ba4ffeb13e

Observation ecc8f071-6a8b-466a-ada6-2978ca2a703c · outbound

This paper cites Advances in Neural Information Processing Systems 35 (2022), 703–715.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Advances in Neural Information Processing Systems 35 (2022), 703–715

Reference 25

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raw_fallback, observed 2026-05-19T12:02:17.611248Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:249e6504678e1fbd5fddee99e8dc72031ccdbe057f4514c9b693bddccb540d8e

Observation 355bdc7f-b618-4c55-b8f9-454d86cc74d8 · outbound

This paper cites In International Workshop on Federated Learning in the Age of Foundation Models in Conjunction with NeurIPS 2023.

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

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raw_fallback, observed 2026-05-19T12:02:17.628327Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:b45147959ded519a082c83c999e92735d1a384bf6f4aa245e68d1326108c2d86

Observation 7a028a60-8e87-499c-80f7-fe4d7559d930 · outbound

This paper cites In The Twelfth International Conference on Learning Representations.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States In The Twelfth International Conference on Learning Representations

Reference 27

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raw_fallback, observed 2026-05-19T12:03:03.787381Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:5cdbc5c23e6816b8f1555ff9782faedf75c191360a18bc15b09b482afee6bc0a

Observation d90faab3-5bec-4f26-a1d4-1058e1a3d191 · outbound

This paper cites 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.

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

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raw_fallback, observed 2026-05-19T12:03:03.776274Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:583794ace19d7459f21d15379b447451ac5ec002b496b554cea846956ed66f61

Observation faa7904a-1f5e-43af-8153-545f5a41c6a7 · outbound

This paper cites 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)).

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

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raw_fallback, observed 2026-05-19T12:02:17.638590Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:01b35b9805c3206658054159081eb2bd46cd8dae6b0e4cbb552449c6c8ce39d5

Observation 2c8c842f-b884-4ae8-8c0b-a101c8a4bc3b · outbound

This paper cites 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.

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

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raw_fallback, observed 2026-05-19T12:03:03.771733Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:40f8ea2c2252342bf2f470a5d27fae2071050104fbe798a37d85b12ce4d2e790

Observation 9a0b5c05-3682-468d-88e7-98eca9bc82f1 · outbound

This paper cites Additionally, for simplicity we choose βt = 1/2.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Additionally, for simplicity we choose βt = 1/2

Reference 31

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raw_fallback, observed 2026-05-19T12:02:17.624434Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:4ad88e938d01125e9a7028e02dd35e736e413d2e965ec55c624e83acde530c05

Observation 2dba13f7-0c11-40e3-93d4-d2f90de19fc6 · outbound

This paper cites an unresolved cited work.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Unresolved cited work

Reference 32

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unresolved
raw_fallback, observed 2026-05-19T12:02:17.640902Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:7cd60f8809ce449fd205f582c63b8f19efb3aad734d0be8b61409c303ba39fe7

Observation 4f0ed731-c97a-4eea-9c6d-8385607b9eed · outbound

This paper cites (65) Note that Sα can be computed in practice with a numerically stable procedure for precise computa- tion Mironov (2017).

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

Resolution
verified fuzzy
raw_fallback, observed 2026-05-19T12:02:17.632542Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:5325bc40fc95ce33c8aaf9938dec9040ad5d5f982e5cbf7a8f6756cba7dda0f9

Observation 1a7f165f-329b-4dcf-8630-1f40c0951224 · outbound

This paper cites an unresolved cited work.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Unresolved cited work

Reference 34

Resolution
unresolved
raw_fallback, observed 2026-05-19T12:02:17.626162Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:c3b6c214c4d229c86453a306baae86dfb16b4df90c9d50e4244b0c9883cca63e

Observation 79e0d4f9-316c-4f39-84f6-05f8ddcfc3ee · outbound

This paper cites In practice, Sα(q, σ) is computed via numerical integral for the tightest possible privacy accounting.

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

Resolution
verified fuzzy
raw_fallback, observed 2026-05-19T12:03:03.785684Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:12176f2da5817ead1133f2526ef45376d4c0d471caf1edfaad5f712228fa5573

Observation eaf978fa-db0d-4cee-b574-130472494980 · outbound

This paper cites The averaged loss function is twice differentiable with −H ⪯ ∇2L(w; D) ⪯ H for any w ∈ Rd, and its minimum is finite.

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

Resolution
verified fuzzy
raw_fallback, observed 2026-05-19T12:02:17.613195Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:0ef61f0f1469d0703ddeef031b650fbeffbed98711718e4d6aae04e63a45d273

Observation 75af8f3f-52ba-4862-b3c5-d9046ea24fdd · outbound

This paper cites (88) where (a) is due to M-smoothness and the elementary inequality (a + b)2 ≤ 2a2 + 2b2.

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

Resolution
verified fuzzy
raw_fallback, observed 2026-05-19T12:02:17.615916Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:602696b66600f8616dc64faa6a86f99cc13f998b9f151eba17a896edfaf83c80

Observation edb1ea3e-daa9-4d0d-b4ef-b7144b038653 · outbound

This paper cites (101) If we further assume that |¯ℓ(w)| ≤ B for any w.

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

Resolution
malformed identifier
raw_fallback, observed 2026-05-19T12:02:17.630456Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:0c7c9fde063ac205526cfb5c9068a15170028ac7f06c54f038c3b46ae4822755

Observation 7ac41693-7552-4a9c-923d-5b6c2b29a93b · outbound

This paper cites Lemma B.3.

Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States Lemma B.3

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-05-19T12:03:03.766512Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:d637e40bd7f7933b5702bdb950a0bfe125978349af2cb213dbec011d63e1c19d

Observation 3b48343d-79cb-47eb-87f4-67b6284f360f · outbound

This paper cites 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.

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

Resolution
verified fuzzy
raw_fallback, observed 2026-05-19T12:02:17.618396Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:98c552b6abe547305a40a5d210091c5568b6af9033c68f42d4b3c89c59981068

Observation 913bf4f4-4d7b-4a6a-877e-db94b00fc725 · outbound

This paper cites 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.

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

Resolution
verified fuzzy
raw_fallback, observed 2026-05-19T12:03:03.782799Z

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.

source=pdf_text observed=2026-05-19T11:57:25.711490Z digest=sha256:c9bce7b747250f012f80320c141803b12293dee3e1c43556412545fd5d7e3c03

Pith citing papers

No inbound Pith citation observations are available.