Pith Number

pith:7FT3R4XQ

pith:2026:7FT3R4XQLCTVWR523CFX6J7PK6

not attested not anchored not stored refs resolved

Hierarchical Transformer Preconditioning for Interactive Physics Simulation

Carl Osborne, Crystal Owens, Minghao Guo, Wojciech Matusik

A hierarchical transformer preconditioner solves stiff multiphase Poisson systems up to 28 times faster than standard GPU incomplete factorization.

arxiv:2605.13343 v2 · 2026-05-13 · cs.GR · cs.DC · cs.LG · cs.NA · math.NA

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\usepackage{pith}
\pithnumber{7FT3R4XQLCTVWR523CFX6J7PK6}

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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

On stiff multiphase Poisson systems (up to 100:1 density contrast, N = 1,024-16,384), the solver runs from ~143 to ~21 fps. At N = 8,192, it reaches 17.9 ms/frame, with 2.2x speedup over GPU Jacobi, ~28x over GPU IC/DILU (AMGX multicolor_dilu), and 2.7x over neural SPAI retrained per scale on the same benchmark.

C2weakest assumption

The weak-admissibility H-matrix partition plus highway connections in the transformer are assumed to capture long-range couplings sufficiently for the cosine-Hutchinson objective to produce a preconditioner that improves PCG convergence on irregular spectra without post-hoc tuning.

C3one line summary

A hierarchical transformer preconditioner with H-matrix structure and cosine-Hutchinson training delivers up to 2.7x speedup over prior neural methods on stiff multiphase Poisson systems up to N=16384.

References

3 extracted · 3 resolved · 1 Pith anchors

[1] Swin Transformer: Hierarchical Vision Transformer using Shifted Windows 2021 · arXiv:2103.14030

[2] In Advances in Neural Information Processing Systems 30 (NIPS 2017) 2017

[3] https://arxiv.org/abs/2510.27517 5 2025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:48.366686Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f967b8f2f058a75b47bad88b7f27ef579e869232b8c275fa670ebf8bd73fa033

Aliases

arxiv: 2605.13343 · arxiv_version: 2605.13343v2 · doi: 10.48550/arxiv.2605.13343 · pith_short_12: 7FT3R4XQLCTV · pith_short_16: 7FT3R4XQLCTVWR52 · pith_short_8: 7FT3R4XQ

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/7FT3R4XQLCTVWR523CFX6J7PK6 \
  | 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: f967b8f2f058a75b47bad88b7f27ef579e869232b8c275fa670ebf8bd73fa033

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7be0647020a3e2f740d0c52257ebe1424a07ad4192c39bca638bfe6a4f08e8eb",
    "cross_cats_sorted": [
      "cs.DC",
      "cs.LG",
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GR",
    "submitted_at": "2026-05-13T11:02:27Z",
    "title_canon_sha256": "b84f5f8f42baeca84db57e33ff3c38b3c6033eba735ed50b67230699d01c378f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13343",
    "kind": "arxiv",
    "version": 2
  }
}