Pith Number

pith:RS5AJSYI

pith:2026:RS5AJSYI57JNWB7L7ZXMILAA2V

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Variational inference via Gaussian interacting particles in the Bures-Wasserstein geometry

Giacomo Borghi, Jos\'e A. Carrillo

Interacting Gaussian particles optimize variational inference in the linearized Bures-Wasserstein space.

arxiv:2601.00632 v2 · 2026-01-02 · math.OC

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

Numerical experiments on variational inference tasks demonstrate the algorithm's robustness and superior performance with respect to deterministic gradient-based method in presence of low-dimensional non log-concave targets.

C2weakest assumption

The Linearized Bures-Wasserstein parametrization preserves the key geometric features of the full Bures-Wasserstein geometry while remaining computationally tractable, and the mean-field limit accurately captures the long-time behavior of the finite-particle system.

C3one line summary

Gaussian particles in a linearized Bures-Wasserstein space perform consensus optimization for variational inference and outperform deterministic gradient methods on low-dimensional non-log-concave targets.

References

63 extracted · 63 resolved · 0 Pith anchors

[1] Barycenters in the 2011 · doi:10.1137/100805741

[2] D. Alvarez-Melis, Y. Schiff, and Y. Mroueh. Optimizing functionals on the space of probabilities with input convex neural networks.Transactions on Machine Learning Research, 2022. URL:https://openrevi 2022

[3] L. Ambrosio, N. Gigli, and G. Savar´ e.Gradient Flows in Metric Spaces and in the Space of Probability Measures. Lectures in Mathematics ETH Z¨ urich. Birkh¨ auser, 2. ed edition, 2008. OCLC: 25418128 2008

[4] I. Arasaratnam and S. Haykin. Cubature Kalman filters.IEEE Transactions on Automatic Control, 54(6):1254–1269, 2009.doi:10.1109/TAC.2009.2019800 2009 · doi:10.1109/tac.2009.2019800

[5] On the Bures–Wasserstein Distance Between Positive Definite Matrices 2019 · doi:10.1016/j.exmath.2018.01.002

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:00.329442Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8cba04cb08efd2db07ebfe6ec42c00d57ad4ca3432d371b0d50b3f8af587ae1b

Aliases

arxiv: 2601.00632 · arxiv_version: 2601.00632v2 · doi: 10.48550/arxiv.2601.00632 · pith_short_12: RS5AJSYI57JN · pith_short_16: RS5AJSYI57JNWB7L · pith_short_8: RS5AJSYI

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RS5AJSYI57JNWB7L7ZXMILAA2V \
  | 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: 8cba04cb08efd2db07ebfe6ec42c00d57ad4ca3432d371b0d50b3f8af587ae1b

Canonical record JSON

{
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    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-01-02T10:25:39Z",
    "title_canon_sha256": "cf898d0384e08d6bb34fa1f9e39b616665b78fe482ff20565ec8fb9720f19a52"
  },
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  "source": {
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    "kind": "arxiv",
    "version": 2
  }
}