Pith Number

pith:6FGT2XE2

pith:2026:6FGT2XE2XR3QSQ5F3NNFFZSR4G

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Local Inverse Geometry Can Be Amortized

Aaditya L. Kachhadiya

A learned reverse operator amortizes local inverse geometry so first-order methods match damped Gauss-Newton on nonlinear inverse problems.

arxiv:2605.13068 v1 · 2026-05-13 · cs.LG

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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

We prove that D-IPG is first-order equivalent to damped Gauss-Newton under local pseudoinverse consistency, with deviation controlled by composition error and conditioning.

C2weakest assumption

The learned reverse Jacobian maintains local pseudoinverse consistency with the forward Jacobian along optimization trajectories, which is enforced only by the Jacobian Composition Penalty during training.

C3one line summary

D-IPG uses a trained Deceptron and Jacobian Composition Penalty to deliver first-order equivalent performance to damped Gauss-Newton on nonlinear inverse problems at up to 77x lower inference cost.

References

14 extracted · 14 resolved · 0 Pith anchors

[1] A method for the solution of certain non-linear problems in least squares 1944

[2] Donald W. Marquardt. An algorithm for least-squares estimation of nonlinear parameters. Journal of the Society for Industrial and Applied Mathematics, 11(2):431–441, 1963 1963

[3] Wright.Numerical Optimization 2006

[4] Learning fast approximations of sparse coding 2010

[5] Hoffman, David Pfau, Tom Schaul, Brendan Shillingford, and Nando de Freitas 2016

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:08:58.928357Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f14d3d5c9abc770943a5db5a52e651e19628a52061dbe00d29e0fea982762814

Aliases

arxiv: 2605.13068 · arxiv_version: 2605.13068v1 · doi: 10.48550/arxiv.2605.13068 · pith_short_12: 6FGT2XE2XR3Q · pith_short_16: 6FGT2XE2XR3QSQ5F · pith_short_8: 6FGT2XE2

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6FGT2XE2XR3QSQ5F3NNFFZSR4G \
  | 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: f14d3d5c9abc770943a5db5a52e651e19628a52061dbe00d29e0fea982762814

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60a76c8adbc90184d98f95a57ff3d4b02bf4d1d3efedf030b0e5fabd8cb5b6a6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T06:41:57Z",
    "title_canon_sha256": "33ff503d8fd396dcb614d105ca37454ab4cd62ebda45fd9db140e808a0613158"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13068",
    "kind": "arxiv",
    "version": 1
  }
}