Pith Number

pith:SOYTDBV7

pith:2026:SOYTDBV75CBW5JF5PTL5ET4HZX

not attested not anchored not stored refs resolved

HodgeCover: Higher-Order Topological Coverage Drives Compression of Sparse Mixture-of-Experts

Christine Allen-Blanchette, Dongzhe Zheng, Tao Zhong

Hodge decomposition of KL merge barriers on a 2-complex isolates the harmonic kernel that blocks joint merging of expert triples in sparse MoE layers.

arxiv:2605.13997 v1 · 2026-05-13 · cs.LG · cs.AI · cs.CL

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\pithnumber{SOYTDBV75CBW5JF5PTL5ET4HZX}

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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

Hodge-decomposing the edge-barrier signal isolates the kernel exactly; HodgeCover greedily covers the harmonic-critical edges and triplet-critical triangles and leads on the aggressive-compression frontier of the hybrid axis while uniquely balancing retained mass across all four Hodge components.

C2weakest assumption

That the KL merge barriers placed on edges and faces of the 2-complex faithfully capture the joint mergeability of expert triples, so that the harmonic kernel of the resulting Laplacian precisely identifies the irreducible cycles that block compression.

C3one line summary

HodgeCover isolates the harmonic kernel of a simplicial Laplacian on an expert 2-complex to identify irreducible merge cycles and selects experts for aggressive compression, matching or exceeding baselines on open-weight MoE models.

References

77 extracted · 77 resolved · 16 Pith anchors

[1] Higher order learning with graphs 2006

[2] Hypergraph convolution and hypergraph attention.Pattern Recognition, 110:107637, 2021 2021

[3] Higher-order organization of complex networks 2016

[4] Piqa: Reasoning about physical common- sense in natural language 2020

[5] Weisfeiler and lehman go topological: Message passing simplicial networks 2021

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:13.191504Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93b13186bfe8836ea4bd7cd7d24f87cdfcd70123fc0a9ec3b6018ca3baf12e52

Aliases

arxiv: 2605.13997 · arxiv_version: 2605.13997v1 · doi: 10.48550/arxiv.2605.13997 · pith_short_12: SOYTDBV75CBW · pith_short_16: SOYTDBV75CBW5JF5 · pith_short_8: SOYTDBV7

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SOYTDBV75CBW5JF5PTL5ET4HZX \
  | 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: 93b13186bfe8836ea4bd7cd7d24f87cdfcd70123fc0a9ec3b6018ca3baf12e52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f7c3bb7b66767c553622d267ffa75beaca3b62164c5f4e8576e4bdbd6279ae6",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CL"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T18:07:12Z",
    "title_canon_sha256": "74fa471528886affbcd1279ef6a0c91f0aeaa8274ffcf9e242c8722eafaa74f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13997",
    "kind": "arxiv",
    "version": 1
  }
}