Pith Number

pith:HI5THGUT

pith:2026:HI5THGUT2R3FD4HIZHOQGOZUNT

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Trees to Flows and Back: Unifying Decision Trees and Diffusion Models

Sai Niranjan Ramachandran, Suvrit Sra

Decision trees correspond to diffusion processes in limiting regimes and share the Global Trajectory Score Matching optimization principle.

arxiv:2605.00414 v2 · 2026-05-01 · cs.LG · cond-mat.stat-mech · cs.AI

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\pithnumber{HI5THGUT2R3FD4HIZHOQGOZUNT}

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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

establishing a crisp mathematical correspondence between hierarchical decision trees and diffusion processes in appropriate limiting regimes. Our unification reveals a shared optimization principle: Global Trajectory Score Matching (GTSM), for which gradient boosting (in an idealized version) is asymptotically optimal.

C2weakest assumption

The limiting regimes invoked for the correspondence are appropriate and yield a meaningful practical unification without additional unstated assumptions that would break the link between trees and diffusion processes.

C3one line summary

Decision trees and diffusion models are unified through limiting-regime correspondence under Global Trajectory Score Matching, yielding TreeFlow for competitive tabular generation with 2x speedup and DSMTREE for distilling tree logic into neural nets with near-teacher performance.

Receipt and verification

First computed	2026-05-22T01:04:03.843430Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a3b339a93d47651f0e8c9dd033b346cf6878b75d1fd9de402fd14c7e91a42cc

Aliases

arxiv: 2605.00414 · arxiv_version: 2605.00414v2 · doi: 10.48550/arxiv.2605.00414 · pith_short_12: HI5THGUT2R3F · pith_short_16: HI5THGUT2R3FD4HI · pith_short_8: HI5THGUT

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HI5THGUT2R3FD4HIZHOQGOZUNT \
  | 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: 3a3b339a93d47651f0e8c9dd033b346cf6878b75d1fd9de402fd14c7e91a42cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b33c5ffba143746f59c9974d74b22c04a4afefe28cbca74fb46dba396a44ad3",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-01T05:19:54Z",
    "title_canon_sha256": "1fcbb5129569cd4cd1c05e2fccedb889e62a946be1943bd90120c95d1b8965d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.00414",
    "kind": "arxiv",
    "version": 2
  }
}