---
title: Can a leaf-sized network hold the four-ply search's ordering?
family: lifetime-objective
summary: Trains the smallest network that could run inside a search leaf on the exact values the four-ply search gives every sibling move, and asks whether it ranks those moves the way the search does.
status: completed
evidence: task-record only
reads: diagnostic
---

Train the smallest network that could run inside a search leaf on the exact
values the four-ply search gives every sibling move, and ask whether it ranks
those moves the way the search does.

<EvidenceLabel status="completed" evidence="task-record only" reads="diagnostic" />

<Callout tone="warn">
The held-out panel this probe is scored on had already been opened once, by the
earlier afterstate experiment that produced the labels. Reading it a second
time makes this a diagnostic, not evidence about fresh positions. The
preregistration said so before the run, and a pass would only have licensed a
confirmation on new labels.
</Callout>

## Why anyone expected this to work

The [search-guided self-play](/learn/glossary) loop needs a learned board
evaluator that does two things at once: agree with the
[depth-4 search](/learn/concepts/expectimax) about which column is best, and
cost about a microsecond, because the search asks that question hundreds of
thousands of times per decision. The earlier attempt used a 3.4-million-parameter
convolutional network, which is far too slow for a leaf and, as it turned out,
agreed with the search on the best column only 37.5% of the time
(result RS-20260821T104500Z-77d21e90) — worse than the one-ply search's 48.6%.

The one model class that *is* cheap enough for a leaf is the
[NNUE](/learn/glossary)-shaped network from
[learned-leaf](/approaches/lifetime-objective/learned-leaf): 8,902 binary
features looked up and summed, then two small dense layers. It had only ever
been trained to predict how long a game would last, never on the search's own
sibling values. The probe asks whether feature-space saturation on one target
says anything about ranking on another. The designer's prior was about 8% for
a pass.

## How it works

1. **Inputs.** Every row of the existing label file is one sibling move's
   resulting board (after the drop and any clears), the visible next disc, and
   the moves until the next rise, under one of five chance
   [strata](/learn/concepts/expectimax), together with the exact value the
   pinned depth-4 search assigns it. 291,890 rows over 8,639 root positions;
   6,551 roots are the training fold and 2,088 the validation ("calibration")
   fold, exactly as the afterstate experiment wrote them.
2. **Student.** `leaf_features.py` from learned-leaf (imported, not copied)
   turns each board into 135 active features; the network is
   EmbeddingBag(8902, 64) with a bias, ReLU, Linear(64, 32), ReLU, Linear(32, 1):
   571,905 parameters.
3. **Per-move score.** As in the comparator's `d4q.py`, a move's score is the
   average over the five strata of the immediate score change plus the
   student's value of the resulting board.
4. **Loss, within each root.** A listwise softmax cross-entropy against the
   search's values (softened at 0.18 times the root's value spread, the
   [d4-q-clone](/approaches/value-policy-learning/d4-q-clone) convention), a
   gap-weighted pairwise margin, and a 0.1-weight mean-squared anchor on the
   standardised value. Adam at 1e-3, 256 roots per batch, 30 epochs.
5. **Selection and reading.** Five initialisation seeds (0xA52E01 to 0xA52E05).
   The seed with the best validation top-1 is chosen, and only then is the
   3,030-root held-out panel read — once — and reported for all five seeds,
   split into two halves by a hash of each root's origin game. The metrics
   (top-1, top-2, pairwise agreement, normalised regret) are the functions of
   `d4q.py`, imported.

## What happened

It failed clearly. The selected seed agreed with the depth-4 search on the best
column about 30% of the time on the held-out positions — below the convolutional
network it was meant to replace, and below the one-ply search. Every one of the
three preregistered thresholds failed in both half-folds, for every seed.

<ResultSummary id="RS-20260823T194142Z-946e3cd1" />

<TechnicalDetails title="Numbers and records">

Result record `RS-20260823T194142Z-946e3cd1`, run `RUN-20260823T193853Z-5abd7c95`,
experiment `EX-20260823-nnue-d4q-ordering-probe-0ca09bb1`, theory
`TH-20260823-nnue-class-holds-d4-ordering-c7b397a5`. Artifacts under
`runs/RUN-20260823T191900Z-b9f8f80d/probe/` (`train.log`, `metrics.json`,
`model-seed*.pt`, `commands.log`, `leaf-check.log`).

Selected seed 0xA52E02 (validation top-1 0.3281). Held-out, half-fold 1 / 2:
top-1 0.2960 / 0.3011 (gate: at least 0.60); pairwise 0.6266 / 0.6259 (at least 0.78);
normalised regret 0.3354 / 0.3379 (at most 0.13). Pooled top-1 across the five seeds
ranged from 0.2987 to 0.3135. Comparators from RS-20260821T104500Z-77d21e90:
afterstate CNN 0.375, exact D1 0.486, exact D2 0.568.

Validation top-1 peaked at 0.352 to 0.359 between epochs 5 and 10 for every seed
and then fell while the training loss kept falling; the protocol fixed 30 epochs
and the final-epoch model was used. Even the best epoch is far below the gate.

Exported through the existing `export_leaf.py` and timed with `leaf-check`
(single thread, 400,000 evaluations): 1.27 microseconds per state. The student
is leaf-affordable; it just does not know the ordering.

Total wall time 166 s on 8 CPU threads; no GPU. Run validity valid, outcome
fail, recorded at the lowest result tier (the schema has no diagnostic tier)
because the panel had already been read once.

</TechnicalDetails>

## What this taught us, and what is still open

A leaf-sized NNUE student of this size trained on the existing successor-closed
depth-4 labels does not hold the search's ordering; the self-play loop cannot be
unblocked in its leaf form by this route, and its redesign goes to the
larger-student question. This rejects only the tested configuration: 64/32
hidden units, these loss weights, 30 fixed epochs, 6,551 training roots. Whether
a wider NNUE, early stopping, or far more labelled roots would change the
picture is untested here; the fact that every seed overfits after about ten
epochs suggests the label volume, not only the model, is binding.