Pith Number

pith:U237QWH5

pith:2026:U237QWH55NINB3E4HXRWQMADN2

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Hyperbolic Latent Space Models for Network Embedding: Model Specification and Bayesian Inference

Anna L. Smith, Catherine A. Calder, Dena Asta, Yiwei Gong

Inferring the temperature parameter in hyperbolic latent space models captures network tree-like topology better than fixing it.

arxiv:2605.11340 v2 · 2026-05-11 · stat.ME

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\pithnumber{U237QWH55NINB3E4HXRWQMADN2}

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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

We demonstrate that temperature is the fundamental parameter governing a network's tree-like topology, and that failing to infer it weakens model expressiveness.

C2weakest assumption

That the hyperbolic geometry with a temperature-modulated distance-to-probability mapping is the correct generative model for the hierarchical structure observed in the networks under study, and that the proposed inference procedures can reliably recover this temperature from finite data.

C3one line summary

A Bayesian hyperbolic latent space model with inferable temperature parameter outperforms fixed-temperature and Euclidean models in network reconstruction by better capturing tree-like topologies.

Receipt and verification

First computed	2026-06-11T01:09:37.585465Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6b7f858fdeb50d0ec9c3de36830036ea9b0e9b5cf13bdfc9e6a6922da8c701d

Aliases

arxiv: 2605.11340 · arxiv_version: 2605.11340v2 · doi: 10.48550/arxiv.2605.11340 · pith_short_12: U237QWH55NIN · pith_short_16: U237QWH55NINB3E4 · pith_short_8: U237QWH5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/U237QWH55NINB3E4HXRWQMADN2 \
  | 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: a6b7f858fdeb50d0ec9c3de36830036ea9b0e9b5cf13bdfc9e6a6922da8c701d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31af9154d08a29412a01b5af89ccfdf618a7709c48ce55a49c20c036e92025d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-11T23:47:25Z",
    "title_canon_sha256": "a0bd4c9e380b23ce6caadf8e2b2470573a63656c1e37b0adec6656816d91abad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11340",
    "kind": "arxiv",
    "version": 2
  }
}