pith:YA77ZUE3
Topo-GS: Continuous Volumetric Embedding of High-Dimensional Data via Topological Gaussian Splatting
Topo-GS repurposes 3D Gaussian Splatting to cast high-dimensional projections as continuous volumetric reconstructions driven by local geometric constraints.
arxiv:2605.17011 v1 · 2026-05-16 · cs.GR · cs.CV · cs.LG
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\pithnumber{YA77ZUE3ZVKUG2VUZPQEQZGUNZ}
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Record completeness
Claims
we introduce Topo-GS, a framework that repurposes 3D Gaussian Splatting (3DGS) to cast multidimensional projection as a meshless volumetric reconstruction process... driven by local geometric constraints... solving orthogonal Procrustes targets... aligning the spatial covariance of each Gaussian to the local tangent space... topology-aware strategy that tailors the loss formulation to preserve either continuous 1D trajectories or cohesive 2D surfaces.
That enforcing As-Rigid-As-Possible priors via orthogonal Procrustes alignment of Gaussian covariances to local tangent spaces, combined with topology-specific loss tailoring, will produce faithful continuous volumetric representations without introducing new artifacts or losing fidelity compared to discrete baselines.
Topo-GS repurposes 3D Gaussian Splatting with local geometric constraints and topology-aware losses to produce continuous volumetric embeddings of high-dimensional data.
References
Formal links
Receipt and verification
| First computed | 2026-05-20T00:03:35.837953Z |
|---|---|
| Builder | pith-number-builder-2026-05-17-v1 |
| Signature | Pith Ed25519
(pith-v1-2026-05) · public key |
| Schema | pith-number/v1.0 |
Canonical hash
c03ffcd09bcd55436ab4cbe04864d46e61feac879b36880c37cf8f0d39bd4dad
Aliases
· · · · ·Agent API
Verify this Pith Number yourself
curl -sH 'Accept: application/ld+json' https://pith.science/pith/YA77ZUE3ZVKUG2VUZPQEQZGUNZ \
| 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: c03ffcd09bcd55436ab4cbe04864d46e61feac879b36880c37cf8f0d39bd4dad
Canonical record JSON
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