Pith Number

pith:HFWLFTPA

pith:2026:HFWLFTPABDP6CVXZ7QUH6QDUWY

not attested not anchored not stored refs pending

Trade-off Functions for DP-SGD with Subsampling based on Random Shuffling: Tight Upper and Lower Bounds

Marten van Dijk, Murat Bilgehan Ertan

DP-SGD with random shuffling subsampling yields tight closed-form trade-off function bounds that converge to the ideal 1-a diagonal under suitable epoch scaling.

arxiv:2605.06259 v2 · 2026-05-07 · cs.LG · cs.CR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HFWLFTPABDP6CVXZ7QUH6QDUWY}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Our analysis covers the regime σ ≥ √(3/ln M) ... yielding transparent and interpretable closed-form bounds. ... if E=c_M²M with c_M→0, then the E-fold composed trade-off function satisfies f⊗E(a)→1-a uniformly in a∈[0,1] with δ having only an O(√E) dependency.

C2weakest assumption

The central claims rest on the regime restriction σ ≥ √(3/ln M) together with the applicability of the Berry-Esseen theorem to the relevant sum of bounded random variables arising from the shuffling process; if this concentration regime does not hold or the approximation error exceeds the claimed tightness, the explicit bounds and the uniform convergence to the diagonal fail.

C3one line summary

Tight closed-form bounds via Berry-Esseen show DP-SGD with random shuffling achieves near-ideal privacy (trade-off close to 1-a) for σ ≥ √(3/ln M) and large M, with δ linear in epochs restricting E to O(√M) and an asymptotic O(√E) δ under E = c_M²M.

Receipt and verification

First computed	2026-05-26T02:04:12.267396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

396cb2cde008dfe156f9fc287f4074b63128e894e3ea7e2dccd435f4ba407d6e

Aliases

arxiv: 2605.06259 · arxiv_version: 2605.06259v2 · doi: 10.48550/arxiv.2605.06259 · pith_short_12: HFWLFTPABDP6 · pith_short_16: HFWLFTPABDP6CVXZ · pith_short_8: HFWLFTPA

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HFWLFTPABDP6CVXZ7QUH6QDUWY \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 396cb2cde008dfe156f9fc287f4074b63128e894e3ea7e2dccd435f4ba407d6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2eac22f204432efc8fbcc82ea461acfdca96d1b238dde4aefbe65c740c658e2",
    "cross_cats_sorted": [
      "cs.CR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-07T13:35:43Z",
    "title_canon_sha256": "e36567464a8e832011d452488ceb86102818409229023d4e6b79b3d9f5923b54"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.06259",
    "kind": "arxiv",
    "version": 2
  }
}