Pith Number

pith:6EAOJO5K

pith:2025:6EAOJO5KX57JMFUMH3PQLA3ZLI

not attested not anchored not stored refs resolved

Higher-order Linear Attention

Quanquan Gu, Yifan Zhang, Zhen Qin

Higher-order Linear Attention captures second-order interactions in linear time with a constant-size state.

arxiv:2510.27258 v3 · 2025-10-31 · cs.LG · cs.AI · cs.CL

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\usepackage{pith}
\pithnumber{6EAOJO5KX57JMFUMH3PQLA3ZLI}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

In the second-order case, HLA maintains a constant-size state and computes per-token outputs in linear time without materializing any n × n matrices.

C2weakest assumption

That compact prefix sufficient statistics exist and suffice to realize the desired higher-order interactions while preserving the causal streaming property and exact equivalence to the serial recurrence.

C3one line summary

Higher-order Linear Attention realizes second-order and higher interactions in linear-time causal attention via constant-size state and associative scans.

References

18 extracted · 18 resolved · 12 Pith anchors

[1] Titans: Learning to Memorize at Test Time · arXiv:2501.00663

[2] Atlas: Learning to optimally memorize the context at test time

[3] Rethinking Attention with Performers 2009 · arXiv:2009.14794

[4] Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality · arXiv:2405.21060

[5] Mamba: Linear-Time Sequence Modeling with Selective State Spaces · arXiv:2312.00752

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:33.709679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f100e4bbaabf7e96168c3edf0583795a1bd95f1bbea284a29d54ba0703d7a59d

Aliases

arxiv: 2510.27258 · arxiv_version: 2510.27258v3 · doi: 10.48550/arxiv.2510.27258 · pith_short_12: 6EAOJO5KX57J · pith_short_16: 6EAOJO5KX57JMFUM · pith_short_8: 6EAOJO5K

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/6EAOJO5KX57JMFUMH3PQLA3ZLI \
  | 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: f100e4bbaabf7e96168c3edf0583795a1bd95f1bbea284a29d54ba0703d7a59d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6621ca0d78c7a98bc0d561bec1b1e67ec62dc6611e6cad8853988c691a0c70cc",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CL"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-10-31T07:54:37Z",
    "title_canon_sha256": "f0bfc303a838b5982ad5d513662834d6f5995deadb1e423399ed1b9128751e38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.27258",
    "kind": "arxiv",
    "version": 3
  }
}