Pith Number

pith:AWP4YKGS

pith:2024:AWP4YKGS72BW3GXMW4LNZSIXJ3

not attested not anchored not stored refs pending

Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences

Benjamin J. Zhang, Markos A. Katsoulakis, Ziyu Chen

Equivariant vector fields enable score-based generative models to learn group-invariant distributions without data augmentation.

arxiv:2410.01244 v2 · 2024-10-02 · stat.ML · cs.LG · math.PR

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Claims

C1strongest claim

one can learn the score of a symmetrized distribution using equivariant vector fields without data augmentations through the analysis of the optimality and equivalence of score-matching objectives. This also provides practical guidance that one does not have to augment the dataset as long as the vector field or the neural network parametrization is equivariant.

C2weakest assumption

The data distribution is exactly group-invariant and the symmetry group is known in advance so that an exactly equivariant vector field can be constructed; the improved d1 bound and the HJB equivalence both rest on this premise (abstract, paragraphs on improved d1 bound and HJB analysis).

C3one line summary

Equivariant SGMs achieve improved Wasserstein-1 generalization bounds on group-invariant distributions and learn the symmetrized score via equivariant vector fields without augmentation, with non-equivariant models incurring a quantifiable model-form error.

Cited by

1 paper in Pith

SymDrift: One-Shot Generative Modeling under Symmetries

Receipt and verification

First computed	2026-06-30T01:17:20.567791Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

059fcc28d2fe836d9aecb716dcc9174ecd3eed40b3a918822a2cb013d0b41f92

Aliases

arxiv: 2410.01244 · arxiv_version: 2410.01244v2 · doi: 10.48550/arxiv.2410.01244 · pith_short_12: AWP4YKGS72BW · pith_short_16: AWP4YKGS72BW3GXM · pith_short_8: AWP4YKGS

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AWP4YKGS72BW3GXMW4LNZSIXJ3 \
  | 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: 059fcc28d2fe836d9aecb716dcc9174ecd3eed40b3a918822a2cb013d0b41f92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3e76177c1ad4fb5620334875c4f8b76877e9f0d120abfebce4e269ab89f436c",
    "cross_cats_sorted": [
      "cs.LG",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2024-10-02T05:14:28Z",
    "title_canon_sha256": "27d556e01d8b157f9908df21ad78bd166c06bcf13b9cc3feca19063bc210afd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.01244",
    "kind": "arxiv",
    "version": 2
  }
}