Pith Number

pith:POD4KESH

pith:2025:POD4KESHONUXTHTJ7FM2DG4LNB

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Radial Compensation: Fixing Radius Distortion in Chart-Based Generative Models on Riemannian Manifolds

Marios Papamichalis, Regina Ruane

Within isotropic scalar-Jacobian azimuthal charts no base distribution preserves geodesic-radial likelihoods, chart-invariant radial Fisher information, and tangent-space isotropy unless it takes the specific Radial Compensation form.

arxiv:2511.14056 v2 · 2025-11-18 · cs.LG · cs.AI · cs.IT · math.DG · math.IT · stat.ML

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\pithnumber{POD4KESHONUXTHTJ7FM2DG4LNB}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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Claims

C1strongest claim

Within isotropic, scalar-Jacobian azimuthal charts, no base distribution can simultaneously preserve geodesic-radial likelihoods, chart-invariant radial Fisher information, and tangent-space isotropy unless it has a specific form, which we call Radial Compensation (RC).

C2weakest assumption

The analysis holds only inside the class of isotropic, scalar-Jacobian azimuthal charts; outside this class the impossibility result and the necessity of the RC form may not apply.

C3one line summary

Radial Compensation derives a specific tangent-space base distribution that preserves geodesic-radial likelihoods and chart-invariant Fisher information while maintaining isotropy, decoupling statistical modeling from numerical chart choice in manifold generative models.

References

29 extracted · 29 resolved · 1 Pith anchors

[1] Heli Ben-Hamu, Samuel Cohen, Joey Bose, Brandon Amos, Maximillian Nickel, Aditya Grover, Ricky T. Q. Chen, and Yaron Lipman. Matching normalizing flows and probability paths on manifolds. In Proceedin 2022

[2] Joey Bose, Ariella Smofsky, Renjie Liao, Prakash Panangaden, and William L. Hamilton. Latent variable modelling with hyperbolic normalizing flows. InProceedings of the 37th International Conference on 2020

[3] Ricky T. Q. Chen and Yaron Lipman. Flow matching on general geometries. InInternational Conference on Learning Representations (ICLR), 2024. URLhttps://openreview.net/pdf?id=Zc02qfR3GN 2024

[4] HVQ-VAE: Variational auto-encoder with hyperbolic vector quantization.Computer Vision and Image Understanding, 258:104392, 2025 2025

[5] Hyper- spherical variational auto-encoders 2018

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:10:11.811582Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b87c512477369799e69f959a19b8b6870c1d7c1db53b8a0e2605edec272ff3d

Aliases

arxiv: 2511.14056 · arxiv_version: 2511.14056v2 · doi: 10.48550/arxiv.2511.14056 · pith_short_12: POD4KESHONUX · pith_short_16: POD4KESHONUXTHTJ · pith_short_8: POD4KESH

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/POD4KESHONUXTHTJ7FM2DG4LNB \
  | 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: 7b87c512477369799e69f959a19b8b6870c1d7c1db53b8a0e2605edec272ff3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "488ebf88d76278ac174ee21a7f4b357e2d652d61afd638b704c98061cb0488e0",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.IT",
      "math.DG",
      "math.IT",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-11-18T02:15:25Z",
    "title_canon_sha256": "0e89bc3f2429a0331c6ae3826998500ae5cea868df62c9308e7f12b945aacdb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.14056",
    "kind": "arxiv",
    "version": 2
  }
}