Pith Number

pith:XPMPOXGZ

pith:2026:XPMPOXGZJZYTJVRAQ7KV3RZVPX

not attested not anchored not stored refs pending

Optimal Recourse Summaries via Bi-Objective Decision Tree Learning

Athanasios Voulodimos, Giorgos Stamou, Ioannis Chatzis, Jason Liartis

SOGAR finds the complete Pareto front of recourse summaries by learning bi-objective decision trees that balance effectiveness against cost.

arxiv:2605.07598 v2 · 2026-05-08 · cs.LG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XPMPOXGZJZYTJVRAQ7KV3RZVPX}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

SOGAR enables post-hoc selection of the desired trade-off without retraining. Using shallow axis-parallel decision trees and sparse leaf actions, SOGAR produces stable, low-cost, and effective recourse summaries that outperform existing approaches across effectiveness and cost metrics.

C2weakest assumption

That shallow axis-parallel decision trees combined with sparse leaf actions are sufficient to produce stable, globally effective recourse summaries without losing critical population structure or requiring more expressive models.

C3one line summary

SOGAR learns Pareto-optimal recourse summaries by solving a bi-objective decision tree problem, yielding stable low-cost effective group actions that outperform prior methods on effectiveness and cost.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-22T01:04:05.286712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbd8f75cd94e7134d62087d55dc7357dd007b0819d29a41ead0cc815ec31cd54

Aliases

arxiv: 2605.07598 · arxiv_version: 2605.07598v2 · doi: 10.48550/arxiv.2605.07598 · pith_short_12: XPMPOXGZJZYT · pith_short_16: XPMPOXGZJZYTJVRA · pith_short_8: XPMPOXGZ

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/XPMPOXGZJZYTJVRAQ7KV3RZVPX \
  | 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: bbd8f75cd94e7134d62087d55dc7357dd007b0819d29a41ead0cc815ec31cd54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "272cccac106c6881dc3d9c8908e9388f678cc3090dc80116987cd7eb941cc6f5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-08T11:16:40Z",
    "title_canon_sha256": "6b8225d65541a0c737c88378358b7d5ee437b5496515c0f6257d45f335279765"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.07598",
    "kind": "arxiv",
    "version": 2
  }
}