Pith Number

pith:6CCSBAYX

pith:2026:6CCSBAYXO2TOT63PTWOFGPMCLO

not attested not anchored not stored refs pending

Aitchison Embeddings for Learning Compositional Graph Representations

Chrysoula Kosma, Giannis Nikolentzos, Michail Chatzianastasis, Nikolaos Nakis, Panagiotis Promponas

Graph nodes represented as simplex compositions yield intrinsically interpretable embeddings that reflect archetype trade-offs and remain coherent under component restriction.

arxiv:2605.00716 v2 · 2026-05-01 · cs.LG · cs.SI

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\pithnumber{6CCSBAYXO2TOT63PTWOFGPMCLO}

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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

Nodes are represented as simplex-valued compositions and embedded via isometric log-ratio (ILR) coordinates, which preserve Aitchison distances while enabling unconstrained optimization in Euclidean space. This yields intrinsically interpretable embeddings whose geometry reflects relative trade-offs among archetypes and supports coherent behavior under component restriction.

C2weakest assumption

Many networks naturally admit a role-mixture view, where nodes are best described as mixtures over latent archetypal factors.

C3one line summary

Graph nodes are embedded as simplex compositions via ILR coordinates to yield intrinsically interpretable representations that preserve Aitchison geometry and enable subcompositional analysis.

Cited by

1 paper in Pith

Rank Is Not Capacity: Spectral Occupancy for Latent Graph Models

Receipt and verification

First computed	2026-05-29T01:04:37.517623Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f08520831776a6e9fb6f9d9c533d825b862a4660f77c5f8f0cc1d32547bbc24b

Aliases

arxiv: 2605.00716 · arxiv_version: 2605.00716v2 · doi: 10.48550/arxiv.2605.00716 · pith_short_12: 6CCSBAYXO2TO · pith_short_16: 6CCSBAYXO2TOT63P · pith_short_8: 6CCSBAYX

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/6CCSBAYXO2TOT63PTWOFGPMCLO \
  | 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: f08520831776a6e9fb6f9d9c533d825b862a4660f77c5f8f0cc1d32547bbc24b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2dc96d4fed758ddfa549971a85e214915d5aed92217db23712b69394cc08824e",
    "cross_cats_sorted": [
      "cs.SI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-01T15:05:23Z",
    "title_canon_sha256": "cf2caade1bec5fddfdac2248cfd5bdf97a73e9d884dc2c31ebe9f3a47ea9d2ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.00716",
    "kind": "arxiv",
    "version": 2
  }
}