KYMA v2 composition probe — corrected design, PASS — 2026-07-21

Status: run complete. Verdict: PASS (pre-committed contract, 5 seeds). Addresses the two defects diagnosed by the v1 NEGATIVE. Code: src/scpn_quantum_control/benchmarks/kyma_v2/, tests tests/test_kyma_v2_*.py, runner scripts/run_kyma_v2_composition_probe.py, artifact data/kyma_v2_composition_probe/kyma_v2_composition_probe.json. Pre-registration (frozen before the run): .coordination/planning/CEO/KYMA_V2_PROBE_PREREGISTRATION_7f6b_2026-07-21.md. 0 QPU (classical differentiable-Kuramoto probe).

What v1 proved and why v2 exists

v1 (KYMA_TOY_PROBE_PREREGISTRATION_7f6b_2026-07-18.md, commit 2f67de12) returned an honest NEGATIVE and named two design defects that made the probe unable to test the "motifs compose" claim, independent of training quality:

1. The substrate could not realise both relations at once — a single shared symmetric coupling K, conditioned only through an additive frequency drive, cannot be both attractive (in-phase) and frustrated (anti-phase); it plateaued at single-motif R ≈ 0.5/0.4.
2. The target was a linear lookup from the code — a parameter-matched MLP composed it at 100 % with no dynamics, so the ≥ pp-over-MLP bar was structurally unreachable.

The deeper reading (as originally framed): a param-matched MLP composes any separable target whose per-relation state it can also learn — if the MLP learns each relation's state from its single-relation trials and the combining function from the other training conjunctions, it composes with no dynamics. This motivated a θ0-dependent readout so the answer is not a code-lookup.

Refined by the v2.1 ablations (see the Mechanism-correction note under "The two fixes"). The ablations show the decisive property is not that the two relations must interact (a single-relation readout also defeats the MLP), but that each relation's readout is a θ0-dependent achieved phase — a hard nonlinear function of the data the MLP cannot approximate even for one relation, while the substrate integrates it directly.

The two fixes

• Fix 1 — per-relation coupling gating. The code gates the coupling itself, K_eff(code) = K_base + Σ_{r,p} code[r,p]·ΔK[r,p], each ΔK[r,p] masked to cluster-pair p. One substrate now realises in-phase on one pair and anti-phase on a disjoint pair simultaneously.
• Fix 2 — non-separable, data-dependent readout. A passive readout node (no motif) is bridged to one oscillator of a held-out-R1 cluster and one held-out-R2 cluster; its final phase is a θ0-dependent function of the relations' achieved states, quantised into a 4-way label (chance 25 %). The substrate composes because the physics composes; a param-matched MLP must extrapolate to an unseen combination.

Mechanism correction (from the v2.1 ablations, 2026-07-21). The empirical result below is reproduced and unchanged, but the mechanism is more precise than an early framing of this fix suggested. The v2.1 ablation A2 (a separable, single-relation readout — bridge to the R1 cluster only) leaves the substrate ahead of the MLP by +51 pp, so the MLP's failure is not primarily about non-separability / "forcing the relations to interact". The load-bearing difficulty is that the label is a θ0-dependent achieved phase — the circular-mean lock of a cluster's initial phases, a hard nonlinear function of the data that a param-matched feedforward net (and, per v2.1

2, an over-parameterised MLP and a code-conditioned GNN) cannot approximate, while the oscillator

substrate simply integrates the dynamics. The compositional-generalisation claim stands (the substrate composes two learned motifs onto an unseen conjunction); what v2.1 sharpens is why the baselines fail — dynamics-computation, of which composition is one instance. See docs/campaigns/kyma_v2_1_rigor_2026-07-21.md.

Mechanism-only design check (§5, teacher dynamics only — no model, no test-accuracy peeking)

The pre-run sanity check fixed g_sync = 0.5, dt = 0.1, steps = 40, k_bridge = 0.8, n_bins = 4 and rejected two drafted mechanisms before any training (recorded in the pre-registration):

• a uniform ambient coupling strong enough to be non-separable destroys the anti-phase motif (attraction fights frustration) → replaced by a sparse readout bridge touching no motif edge;
• a readout inside a locked cluster is pinned, and one coupled to both clusters of an anti-phase pair sees the two π-apart branches cancel (anti-phase is mean-field-invisible) → replaced by a passive node reading a single coherent branch of each relation.

Frozen diagnostics: realisability R1 = R2 = 1.00, non-separability 0.403 (min over relations; drop-R1 0.403, drop-R2 0.457), class balance max 0.27 — all §5 gates met without lowering any target.

Result (5 seeds, frozen contract)

model	held-out-conjunction accuracy	params
gated student substrate	80.1 % ± 3.0 %	336
parameter-matched non-motif MLP	36.9 % ± 1.5 %	361 (+7.4 %)
chance (most-frequent training class)	24.2 % ± 2.0 %	—

Per-seed substrate: 0.80, 0.75, 0.81, 0.84, 0.80. Margin over MLP +43.1 pp (contract ≥ 20 pp). PASS on all three conditions (≥ 60 % AND ≥ 20 pp over MLP AND above chance), all five seeds.

Selection is task-validity-only (unbiased comparison). The frozen constants (g_sync 0.5, dt 0.1, steps 40, k_bridge 0.8, n_bins 4) were selected on seed 0's teacher-only realisability / non-separability / balance (§5) — using no student or MLP performance — so the substrate-vs-MLP comparison is not biased by the selection: both models train on the same fixed task. The result is stable including vs excluding the selection seed: excluding seed 0, substrate 80.1 % ± 3.4 % (vs 80.1 % ± 3.0 % including it), MLP 37.3 %, margin +42.8 pp (vs +43.1 pp) — the PASS does not depend on the seed the mechanism was tuned on.

J/task (measured, CPU simulation): substrate 4.6 J (high sd — JIT-recompile wall-time noise on the memory-constrained host), MLP 1.3 × 10⁻³ J. The substrate is costlier on CPU simulation; this is reported honestly and is not evidence of frugality — KYMA's frugality claim concerns neuromorphic oscillator hardware, not a CPU Kuramoto simulation, and this number must not be cited for it.

Interpretation (bounded claim — carry verbatim into Part B §1.2.2a)

When the ground truth is compositional phase-locking, the gated oscillator substrate generalises from single-relation trials to an unseen conjunction (80 % over 5 seeds) where a parameter-matched non-motif MLP does not (37 %, a +43 pp gap). Because the ground truth is generated by an oscillator teacher, the task lives in the substrate's hypothesis class, so this is not a claim that oscillators beat MLPs on arbitrary tasks — it is a fair test of the KYMA inductive-bias claim, and the fair-test guarantee rests entirely on the parameter-matched MLP control, so the +43 pp margin is the claim. Nothing forces gradient descent to find a compositional gated solution rather than overfitting the seen conjunctions; that it generalises is the measured evidence. v1 (2f67de12, NEGATIVE) stays the honest baseline — its two defects are exactly what v2's two fixes remove.

Authored by Anulum Fortis & Arcane Sapience (protoscience@anulum.li) Seat: 7f6b