Pith Number

pith:JJFHEDZ6

pith:2026:JJFHEDZ67ZT4BU37PDTXTAW3GL

not attested not anchored not stored refs pending

Communication Dynamics Neural Networks: FFT-Diagonalized Layers for Improved Hessian Conditioning at Reduced Parameter Count

Lurong Pan

Block-circulant layers with FFT diagonalization make the population Hessian exactly the identity under pre-whitening while using one-Bth the parameters of a dense layer.

arxiv:2605.08171 v2 · 2026-05-04 · cs.LG · cs.AI

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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

Under input pre-whitening, the population Hessian condition number satisfies kappa = 1 exactly, with the empirical condition number bounded by 1+O(sqrt(B/N)) on N samples (Theorem 2). A CDLinear MLP at B = 4 achieves 97.50% +/- 0.23% test accuracy with 2,380 parameters versus 98.15% +/- 0.47% for a parameter-matched dense MLP at 8,970 parameters.

C2weakest assumption

That the block-circulant restriction with block size B = 2l+1 preserves sufficient expressivity for the target task and that input pre-whitening can be performed without destroying the data distribution or introducing new instabilities.

C3one line summary

CDLinear layers achieve population Hessian condition number exactly 1 under pre-whitening, deliver 3.8x parameter reduction versus dense layers at 0.65% accuracy cost, and show 310x better empirical conditioning on an MLP.

Receipt and verification

First computed	2026-06-10T00:08:26.733774Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a4a720f3efe67c0d37f78e77982db32ddd2821fbe9f67a2e0df75dcec71f8db

Aliases

arxiv: 2605.08171 · arxiv_version: 2605.08171v2 · doi: 10.48550/arxiv.2605.08171 · pith_short_12: JJFHEDZ67ZT4 · pith_short_16: JJFHEDZ67ZT4BU37 · pith_short_8: JJFHEDZ6

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JJFHEDZ67ZT4BU37PDTXTAW3GL \
  | 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: 4a4a720f3efe67c0d37f78e77982db32ddd2821fbe9f67a2e0df75dcec71f8db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ca56caa532581ed27cbfeb6b331f7eaec22a19a488124a6df3b303b62102080",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-04T23:43:09Z",
    "title_canon_sha256": "25731c91f095d62d79e002cecd272829678ad7403dd582acbe889ea1eae1fc5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.08171",
    "kind": "arxiv",
    "version": 2
  }
}