Pith Number

pith:R7BCWP37

pith:2026:R7BCWP37ECGZDXQZV7SQJQGYXO

not attested not anchored not stored refs pending

Decision-Focused Learning via Tangent-Space Projection of Prediction Error

Junhyeong Lee, Sangjin Jin, Yongjae Lee

The regret gradient equals the prediction error projected onto the tangent space of active constraints and scaled by local curvature.

arxiv:2605.01361 v2 · 2026-05-02 · cs.LG

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\pithnumber{R7BCWP37ECGZDXQZV7SQJQGYXO}

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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

the regret gradient admits a closed-form geometric characterization, equivalent to the prediction error projected onto the tangent space of active constraints, scaled by local curvature

C2weakest assumption

under standard regularity with locally stable active constraints

C3one line summary

Regret gradients in DFL are the tangent-space projection of prediction error scaled by curvature, enabling efficient direct computation without differentiating through solvers.

Receipt and verification

First computed	2026-05-20T01:06:09.575779Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8fc22b3f7f208d91de19afe504c0d8bb9fb69bd50eb5db9db3a4ea42446552c5

Aliases

arxiv: 2605.01361 · arxiv_version: 2605.01361v2 · doi: 10.48550/arxiv.2605.01361 · pith_short_12: R7BCWP37ECGZ · pith_short_16: R7BCWP37ECGZDXQZ · pith_short_8: R7BCWP37

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/R7BCWP37ECGZDXQZV7SQJQGYXO \
  | 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: 8fc22b3f7f208d91de19afe504c0d8bb9fb69bd50eb5db9db3a4ea42446552c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e1da7c7205cc484b24c83ffa9287baeea543716dce7292a5c5abe5b93cdba58",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-02T10:10:16Z",
    "title_canon_sha256": "852e7d258e107a38363639d4c2a3d5387880a81c75ce0a7657c7959e785f24c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.01361",
    "kind": "arxiv",
    "version": 2
  }
}