Pith Number

pith:7IRQ65OX

pith:2026:7IRQ65OXOP45BIRQRVKFZJ65BO

not attested not anchored not stored refs pending

Why Adam Can Beat SGD: Second-Moment Normalization Yields Sharper Tails

Ruinan Jin, Shaofeng Zou, Yingbin Liang

Adam achieves δ^{-1/2} high-probability convergence while SGD requires at least δ^{-1} under bounded variance.

arxiv:2603.03099 v8 · 2026-03-03 · cs.LG · cs.AI

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\usepackage{pith}
\pithnumber{7IRQ65OXOP45BIRQRVKFZJ65BO}

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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

we establish the first theoretical separation between the high-probability convergence behaviors of the two methods: Adam achieves a δ^{-1/2} dependence on the confidence parameter δ, whereas corresponding high-probability guarantee for SGD necessarily incurs at least a δ^{-1} dependence.

C2weakest assumption

the classical bounded variance model (a second moment assumption)

C3one line summary

Adam attains a δ^{-1/2} high-probability rate while any SGD guarantee must incur at least δ^{-1} dependence.

Cited by

1 paper in Pith

PowerStep: Memory-Efficient Adaptive Optimization via $\ell_p$-Norm Steepest Descent

Receipt and verification

First computed	2026-05-20T00:04:27.138505Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa230f75d773f9d0a2308d545ca7dd0b86b1fb23693fc287a4ad7f9b6c0ac818

Aliases

arxiv: 2603.03099 · arxiv_version: 2603.03099v8 · doi: 10.48550/arxiv.2603.03099 · pith_short_12: 7IRQ65OXOP45 · pith_short_16: 7IRQ65OXOP45BIRQ · pith_short_8: 7IRQ65OX

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/7IRQ65OXOP45BIRQRVKFZJ65BO \
  | 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: fa230f75d773f9d0a2308d545ca7dd0b86b1fb23693fc287a4ad7f9b6c0ac818

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37fad614f3752adbd3c26905b6c01ceafe6763835bae9c038f13d3743c14338e",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-03-03T15:34:51Z",
    "title_canon_sha256": "708972d8746b4e25e7cb094cb87827ad8dc5954a64875ce651ad1e753f491730"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.03099",
    "kind": "arxiv",
    "version": 8
  }
}