Pith Number

pith:BVZE2YXN

pith:2026:BVZE2YXNDHB42FBYT4Y3OREEXT

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Adversarial Robustness of NTK Neural Networks

Yuxuan Hou

NTK neural networks achieve the minimax optimal rate for adversarial regression in Sobolev spaces when trained with gradient flow and early stopping.

arxiv:2604.25965 v2 · 2026-04-28 · stat.ML · cs.LG

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\pithnumber{BVZE2YXNDHB42FBYT4Y3OREEXT}

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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

NTK neural networks, trained via gradient flow with early stopping, can achieve the minimax optimal rate for adversarial regression in Sobolev spaces.

C2weakest assumption

The derivation assumes the standard nonparametric regression model with Sobolev smoothness and that the NTK training dynamics are exactly captured by the kernel gradient flow in the infinite-width limit.

C3one line summary

NTK networks achieve minimax optimal adversarial regression rates in Sobolev spaces with early stopping, but minimum-norm interpolants are vulnerable.

Receipt and verification

First computed	2026-06-09T01:05:18.206200Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d724d62ed19c3cd14389f31b74484bcea51fd167142374443070494fce026f9

Aliases

arxiv: 2604.25965 · arxiv_version: 2604.25965v2 · doi: 10.48550/arxiv.2604.25965 · pith_short_12: BVZE2YXNDHB4 · pith_short_16: BVZE2YXNDHB42FBY · pith_short_8: BVZE2YXN

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BVZE2YXNDHB42FBYT4Y3OREEXT \
  | 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: 0d724d62ed19c3cd14389f31b74484bcea51fd167142374443070494fce026f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ce242ea5fc3205372b8a2c92350a11603b3c1e59435d8043210698f1d41f04c",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-04-28T04:49:31Z",
    "title_canon_sha256": "e4ea70ddfbef381a88ce2d327d0aef15c1cd9b7a2d394114de4403f486bc4e2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25965",
    "kind": "arxiv",
    "version": 2
  }
}