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CAMOS: Coupled Oscillatory State-Space Model for Multimodal Clinical Time-Series

Maxx Richard Rahman, Mostafa Hammouda, Wolfgang Maass

arXiv:2609.39484v1stat.MLcs.AI

TL;DR

Multimodal clinical time series are irregular and incomplete, yet linear state-space models leave their transitions unchanged when modalities are missing. CAMOS places availability-gated coupling inside oscillator dynamics, making transitions depend on which measurements were taken. On ADNI, it outperforms uncoupled oscillatory models and clinical fusion models across staging, landmark prediction, and longitudinal forecasting.

  • Problem

    Existing linear state-space approaches mask absent modalities in inputs but leave transitions availability-independent, despite coupled clinical processes and informative joint availability.

    Source: §1 · pp. 1–2

  • Method

    CAMOS places availability-gated intermodal coupling inside oscillator dynamics, making its transition operator depend on which modalities were measured.

    Source: §1 · p. 2

  • Results

    CAMOS outperforms uncoupled oscillatory state-space models and clinical fusion models on ADNI same-visit staging, landmark prediction, and longitudinal forecasting.

    Source: §1 · p. 2, §7 · p. 9

  • Takeaways & Limitations

    The paper concludes that multimodal clinical missingness belongs in the transition operator, not only in the forcing term.

    Source: §7 · p. 9

    The theorem concerns a single linear layer and does not establish that deep networks cannot represent availability interactions or distinguish CAMOS from nonlinear fusion encoders.

    Source: §4.3 · p. 5

Abstract

from arXiv · show

Longitudinal clinical cohorts are multimodal, irregularly sampled and pervasively incomplete: in ADNI, positron emission tomography and cerebrospinal fluid assays are absent from roughly half of all visits. Linear state-space models handle irregular sampling gracefully but treat a missing modality by masking the input, leaving the transition operator untouched. We prove that this is a representational limitation: the latent state of any linear state-space layer whose transition operator does not depend on the availability pattern is an additive function of the availability indicators, so no such layer can represent an interaction between two modalities being jointly present or jointly absent. We propose CAMOS, which gives each modality a bank of second-order oscillators coupled through a matrix that sits inside the differential equation and is gated by availability, so the transition operator itself becomes a function of which measurements were taken. Coupling invalidates the analysis of uncoupled oscillatory models, and we restore it: a per-channel Gershgorin budget makes the effective stiffness positive definite uniformly over all $2^M$ availability patterns and all gaps, an energy argument charges amplification to availability transitions rather than sequence length, and a channel factorization preserves exact associative parallel scans. On ADNI, CAMOS outperforms uncoupled oscillatory state-space models and clinical fusion models on same-visit staging, landmark prediction and longitudinal forecasting, and under zero-shot transfer to OASIS-3 it is the only model that avoids collapse to the majority class.

1 INTRODUCTION

CAMOS makes latent transitions depend on which modalities are observed, addressing the additive limitation of availability-independent linear state-space layers while preserving exact associative parallel scans. On ADNI and OASIS-3, it outperforms uncoupled oscillatory SSMs and clinical fusion models across three clinical prediction tasks.

1 INTRODUCTION

  • In ADNI, imaging and cognitive testing are common while amyloid PET and cerebrospinal fluid assays are rarer, despite the coupled progression of Alzheimer’s pathology.The paper frames irregular sampling and modality-specific missingness as central challenges for tracking the disease cascade (Hardy & Selkoe, 2002; Jack et al., 2010; 2013; Petersen et al., 2010).Source: §1 · p. 1
  • Availability-independent linear state-space layers make latent state additive in modality availability, so one modality’s effect cannot depend on another’s presence at a different step.Post-temporal multimodal fusion also cannot let one modality shape another’s trajectory across a long gap.Source: §1 · p. 2
  • CAMOS gates a coupling matrix inside modality-specific oscillator dynamics, making the transition depend on the availability pattern and removing the additive obstruction.Its channel-wise factorization preserves exact associative parallel scans.Source: §1 · p. 2
  • CAMOS outperforms uncoupled oscillatory SSMs and clinical fusion models on ADNI and OASIS-3 for same-visit staging, landmark prediction, and longitudinal forecasting.Source: §1 · p. 2

2 RELATED WORK

Prior state-space and clinical fusion approaches address structured dynamics, irregular sampling, or missing modalities, but the cited work does not combine availability-gated cross-modal coupling with continuous-time second-order dynamics. CAMOS is distinguished from these families by the aspects of their modeling that the passages identify as absent or different.

Structured, oscillatory and coupled state-space models

  • S4, S5, LRU and Mamba use structured or selective state matrices solved by FFT or associative scans (Gu et al., 2020; 2022; Smith et al., 2023; Orvieto et al., 2023; Gu & Dao, 2024; Dao & Gu, 2024).Source: §2 · p. 2
  • LinOSS discretizes second-order oscillators; LinOSS-IM and LinOSS-IMEX differ in integration scheme, while D-LinOSS decouples damping from frequency (Rusch & Rus, 2025; Boyer et al., 2025).These models are direct parents of CAMOS and its primary baselines.Source: §2 · p. 2
  • These state-space models use monolithic inputs, leaving modality partitions invisible to shared dynamics and representing no modality driving another; Coupled Mamba instead couples discrete first-order chains.Its discrete recurrence lacks a natural meaning for irregular gaps, unlike a continuous-time second-order system.Source: §2 · p. 2

Irregular sampling and missing modalities

3 PROBLEM FORMULATION

Section 3 formalizes irregular multimodal visits with explicit availability indicators and defines three clinical prediction targets. Availability is treated as a model input, not merely as a mask on measurements.

3 PROBLEM FORMULATION

  • Each subject has visits at strictly increasing times, with positive year-based gaps, and each modality has a feature vector and binary measurement-availability indicator.A modality’s feature vector is undefined and never read when that modality is unavailable.Source: §3 · p. 3
  • The tasks are same-visit ordinal staging, three-year MCI-to-AD progression prediction, and longitudinal forecasting scored only for measured future modalities.Staging predicts CN, MCI, or AD; progression is binary; forecasting targets future modality values.Source: §3 · p. 3
  • The model uses the availability sequence a_1:N as a genuine input rather than merely masking modality features.The formulation also defines a binary availability pattern, a stacked latent width, a gate matrix, and static subject covariates.Source: §3 · p. 3

4 PROPOSED CAMOS MODEL

CAMOS stacks gated coupled-oscillator blocks between an encoder and three task heads, with availability controlling the oscillator dynamics. Its coupling and discretization are designed to remain stable across availability patterns and irregular visit gaps.

4.5 DEEP BLOCKS, WITHIN-VISIT ATTENTION AND TASK HEADS

  • CAMOS places gated coupled-oscillator blocks between an encoder and three task heads, and evaluates the recurrence with an associative scan of O(log N) depth.Within-visit attention uses an availability bias; heads support staging, landmark prediction, and longitudinal forecasting, whose loss is masked to observed targets.Source: §4 · p. 3, §4.5 · pp. 6–7

4.1 INPUT ENCODERS

  • Static covariates initialize oscillator states through a two-layer GELU perceptron, while modality inputs are projected to shared width and forcing is gated by availability.The initialization encodes baseline demographics through oscillator phase and amplitude rather than an additive readout offset.Source: §4.1 · pp. 3–4

4.2 COUPLED MULTIMODAL OSCILLATORS, AND WHY THE COUPLING MUST BE BUDGETED

  • Symmetric, channel-factorized coupling mixes modalities within latent channels, and a per-channel Gershgorin budget keeps effective stiffness positive definite under every availability pattern.The budget is imposed on ungated coupling; availability gating can shrink, but not enlarge, off-diagonal row sums.Source: §4.2 · pp. 4–5

4.3 AVAILABILITY GATING AND WHAT INPUT MASKING CANNOT REPRESENT

  • Input-masked linear state-space layers produce only additive availability effects, whereas CAMOS gates coupling inside the recurrence to represent joint-availability interactions.A symmetric availability gate also isolates an unobserved modality from the others while allowing its own state to evolve.Source: §4.3 · p. 5

4.4 STABLE DISCRETIZATION ON THE IRREGULAR VISIT GRID

  • Implicit discretization supports arbitrary visit gaps, while an energy bound charges amplification to availability transitions rather than sequence length.The transition is strictly contractive uniformly in the gap and availability pattern; energy is non-increasing while availability remains constant.Source: §4.4 · p. 6

5 EXPERIMENTS

Experiments evaluate CAMOS on multimodal ADNI and OASIS-3 cohorts and compare it with oscillatory state-space and clinical fusion baselines. On 3-year MCI-AD landmark prediction, CAMOS is significantly better than the best baseline on both datasets.

5 EXPERIMENTS

  • ADNI includes four modalities and static covariates, while OASIS-3 includes imaging, genetics, and cognition; only normalization statistics are refit for OASIS-3.Visits are retained for subjects with at least three diagnosed visits and one fully observed modality per visit; a modality is available only when all its features are recorded.Source: §5 · p. 7
  • Comparisons use uncoupled LinOSS-IM and LinOSS-IMEX to isolate coupling, plus MedFuse and DrFuse adapted with per-modality gated recurrent encoders over visits.For LinOSS, unobserved features are zero-filled and availability and time gaps are supplied as channels; the gap also sets each discretization interval.Source: §5 · p. 7
  • CAMOS is significantly better than the best baseline on 3-year MCI-AD landmark prediction on ADNI and OASIS-3.The table caption reports significance at †p < 0.01 or ∗p < 0.05 using a two-sided Welch’s t-test.Source: Table 2 · p. 8

6 RESULTS

CAMOS improves ADNI staging, landmark prediction, and longitudinal forecasting, and retains staging performance under zero-shot transfer to OASIS-3. Ablations attribute its gains to implicit discretization, cross-modal coupling, and availability gating working together.

Same-visit Staging

  • On ADNI, CAMOS improves accuracy over DrFuse by 0.0502 and macro F1 by 0.0436; on OASIS-3, it raises macro F1 from 0.3253 to 0.5557.On OASIS-3, CAMOS also raises macro recall from 0.3558 to 0.5261 and exceeds majority-class accuracy; the baselines are close to single-class prediction.Source: §6 · p. 8

Landmark Prediction

  • On ADNI, CAMOS improves AUROC from 0.9386 to 0.9611 and AUPRC from 0.7689 to 0.8687 over DrFuse; on OASIS-3, AUPRC rises from 0.4185 to 0.7894.On ADNI, AUROC spans only 0.9134 to 0.9611 across five models, while AUPRC spans 0.6900 to 0.8687; on OASIS-3, AUROC is 0.9600 for CAMOS versus 0.9560 for LinOSS-IMEX. AUPRC is the more relevant summary for precision-limited trial enrichment.Source: §6 · p. 8

Longitudinal forecasting

  • On ADNI, CAMOS attains the lowest MAE and RMSE on all four modalities, with the largest MAE reductions in genetics (0.7535 → 0.4088) and CSF (0.7676 → 0.5906).The same ordering holds zero-shot on OASIS-3: CAMOS reduces genetics MAE from 0.7875 to 0.2847, clinical-measures MAE from 0.5775 to 0.3756, and imaging MAE from 0.7664 to 0.7333.Source: §6 · p. 8, Figure 2 · p. 9

Relative improvements over baselines

  • On ADNI, switching from implicit to implicit-explicit discretization lowers macro F1 from 0.7790 to 0.653 and AUPRC from 0.8687 to 0.8063, while raising forecasting MAE by 39.8% (sparse) and 25.5% (dense).The implicit scheme is stable for every gap, whereas the implicit-explicit scheme is unstable once ∆t^2 nν > 4. Removing cross-modal coupling raises MAE by 7.7% (sparse) and 8.1% (dense) and lowers AUPRC to 0.8193; it also lowers staging macro F1 by 2.3 points and landmark AUPRC by 4.9 points.Source: §6 · pp. 8–9

Ablation studies

  • Without availability gating, coupling lowers landmark AUPRC to 0.7916 and raises forecasting MAE by 11.2% (sparse) and 11.4% (dense); asymmetric gating restores much of this loss but yields staging F1 of 0.7532.Removing the availability gate lowers AUROC to 0.9531 and AUPRC to 0.8296 while leaving staging F1 at 0.7804 and forecasting MAE at 0.5016 (sparse) and 0.4014 (dense), essentially unchanged. The gate also keeps the unobserved OASIS-3 CSF oscillator isolated rather than entering it as a zero-filled input block; only full gating performs well across all tasks.Source: §6 · p. 9

7 CONCLUSION … C.5 PROOF OF PROPOSITION 6

CAMOS places modality availability in the transition operator, enabling interactions between availability patterns while retaining stability and exact parallel scans. The paper reports gains across ADNI tasks and zero-shot OASIS-3, alongside clinical-use limitations and reproducibility materials.

7 CONCLUSION

  • CAMOS outperforms uncoupled oscillatory state-space and clinical fusion models on ADNI staging, landmark prediction, and forecasting, and alone avoids majority-class collapse on zero-shot OASIS-3.The ablations attribute these gains to implicit discretization and coupling.Source: §7 · p. 9

C.2 PROOF OF LEMMA 2

  • A per-channel Gershgorin budget keeps effective stiffness positive definite across all 2^M availability patterns and gaps, while the energy bound charges amplification to availability transitions.A channel-block matrix family preserves exact associative scans with O(M^2) overhead.Source: §7 · p. 9, §C.2 · p. 15

AI USE STATEMENT

  • Generative AI was used only for language editing, not for experimental results, numerical values, or theoretical claims and proofs.The authors take responsibility for the manuscript and its artifacts.Source: AI USE STATEMENT · p. 10

ETHICS STATEMENT

  • CAMOS is presented as a research instrument, not a decision-support tool, because cohorts are unrepresentative, probabilities are uncalibrated, and availability may reflect access to care.Subgroup evaluation, calibration, and performance audits conditional on availability are prerequisites for clinical claims; no new human-subject data were collected.Source: ETHICS STATEMENT · p. 10

REPRODUCIBILITY STATEMENT

  • The authors provide an anonymized code repository with implementation, cohort preprocessing, and evaluation pipelines; qualified researchers can obtain datasets from their original providers.The paper points to tables and appendices for hyperparameters, configurations, feature definitions, preprocessing, labels, assumptions, and proofs.Source: REPRODUCIBILITY STATEMENT · p. 10

C.3 PROOF OF PROPOSITION 3

  • Under symmetric gating, removing a modality decouples its block; the asymmetric gate can instead produce a non-symmetric, block-triangular stiffness matrix.The proof uses the block structure of the gated coupling and transition operators.Source: §C.3 · p. 15

C.4 PROOF OF THEOREM 5

  • For a single linear state-space layer, input-only gating yields an additive availability statistic with no cross-modal interactions, whereas CAMOS represents interactions inside its recurrence.The theorem does not rule out interactions reconstructed by nonlinear readouts or representation-level fusion.Source: Figure 4 · p. 15, §C.4 · p. 16

C.5 PROOF OF PROPOSITION 6

  • At fixed availability with no forcing, the energy dissipates; for slow clinical modes it remains above 0.90 at roughly 10 visits, one-year gaps, and μ ≈ 0.02.High-frequency modes are damped more strongly at long gaps, the cost of unconditional stability.Source: §C.5 · p. 16

C.6 PROOF OF THEOREM 7

The proof characterizes how availability-dependent coupling shapes energy growth, cross-modal transfer, and normal modes. It shows that transfer depends on the sampling gap and that modalities exchange information through connected components of the gated coupling graph.

C.6 PROOF OF THEOREM 7

  • Unchanged availability steps have energy factor one, so energy amplification is charged to availability transitions rather than sequence length.The proof also establishes monotonicity when availability does not change.Source: §C.6 · pp. 16–17
  • With fixed P, the input-to-state bound controls energy growth under forcing.The proof applies an energy inequality using the forcing norm at each step.Source: §C.6 · p. 17
  • Cross-modal transfer of a previous state is largest at intermediate gaps and vanishes at long gaps.For two modalities, the transfer is unimodal in the gap.Source: §C.6 · p. 17
  • For each channel and availability pattern, unforced dynamics decompose into M harmonic modes; cross-modal transfer vanishes across disconnected gated-graph components and is generically nonzero within a component.Coupling shifts modal stiffness eigenvalues from their uncoupled values by at most γ.Source: §C.6 · p. 18

D PARALLEL EVALUATION, COMPLEXITY AND EXPRESSIVITY · E DENSE AND LOW-RANK COUPLINGS · F ALGORITHMS

CAMOS preserves efficient parallel evaluation through channel-block structure while making coupling availability-dependent; denser coupling can weaken stability constraints and sharply increase scan cost. The section also distinguishes the gating-driven expressivity gain from the model’s inheritance of uncoupled-layer universality.

D PARALLEL EVALUATION, COMPLEXITY AND EXPRESSIVITY

  • Channel-block structure is closed under scan-combine multiplication and contains each transition operator, so associative scans retain the cheap factorized family.The scan returns all visit states in ⌈log2 N⌉ sequential rounds; the forward-pass listings specify GCO-layer and per-subject CAMOS procedures.Source: D PARALLEL EVALUATION, COMPLEXITY AND… · p. 18, E DENSE AND LOW-RANK COUPLINGS · p. 20
  • Θ(NdM^3) work, ⌈log2 N⌉ sequential depth, and Θ(NdM^2) scan memory characterize a GCO layer; coupling adds Θ(M^2) work overhead over uncoupled oscillatory layers.Within-visit attention adds Θ(NM^2d) at constant depth; for M = 4 and d = h = 64, 384 of about 2.8 × 10^5 parameters belong to coupling (0.14%).Source: D PARALLEL EVALUATION, COMPLEXITY AND… · pp. 18–19
  • Setting coupling to zero recovers an uncoupled oscillatory layer and its universality within continuous causal operators; the representational gain instead comes from availability gating.With all modalities observed, a symmetric coupled system is orthogonally equivalent to an uncoupled one; gating acts in the modality basis and does not commute with the diagonalizing rotation.Source: D PARALLEL EVALUATION, COMPLEXITY AND… · p. 19

E DENSE AND LOW-RANK COUPLINGS

  • For dense symmetric coupling, ∥C∥2 ≤ (1 − ϵ)λmin(A) guarantees λmin(P(a)) ≥ ϵλmin(A) > 0 for every availability pattern.Enforcement requires spectral normalization and power iteration each training step; standard α ∼ U([0, 1]) initialization can make the admissible coupling collapse.Source: E DENSE AND LOW-RANK COUPLINGS · p. 19
  • Dense coupling makes scan cost Θ(d^2) higher than channel-factored coupling, about 4000 times per layer at d = 64.The transition inverse becomes dense at Θ(d^3M^3), and scan combines require dense 2m × 2m products.Source: E DENSE AND LOW-RANK COUPLINGS · p. 19
  • Low-rank-plus-diagonal coupling reduces parameters from d^2 to dρ per block but does not reduce scan cost because multiplication can triple the non-diagonal rank at each combine.After a full scan, the carried operator’s rank can reach N log2 3ρ, so Woodbury inversion at individual steps does not preserve the low-rank structure through the scan.Source: E DENSE AND LOW-RANK COUPLINGS · p. 19
  • Grouping channels into blocks of size ρ interpolates between channel-factored and dense coupling, with cost Θ(Ndρ^2M^3); ρ = 1 recovers channel factoring.Source: E DENSE AND LOW-RANK COUPLINGS · p. 19

G IMPLEMENTATION DETAILS

The implementation specifies a shared validation-search protocol and evaluation metrics, alongside the numerical and input-handling choices used to make CAMOS and its baselines comparable and stable.

G IMPLEMENTATION DETAILS

  • All models used the same validation grid and trial budget; selection optimized the unweighted mean of staging macro-F1, landmark AUROC, and one minus normalized forecasting MAE.Models were implemented in PyTorch 2.3 and trained on one NVIDIA A100 40GB GPU; CAMOS used a Blelloch associative scan and batched float32 Cholesky solves. Evaluation also reported staging accuracy, macro-F1, precision, recall and specificity; landmark AUROC and AUPRC; and per-modality forecasting MAE and RMSE over observed targets.Source: G IMPLEMENTATION DETAILS · p. 20
  • A positive frequency shift avoids near-zero initial frequencies that would leave many channels without a coupling budget and unable to recover.The admissible coupling is proportional to the minimum frequency of each channel pair.Source: G IMPLEMENTATION DETAILS · p. 20
  • With epsilon=0.2 and the Table 4 initialization, the conditioning bound is below 200 independently of the time gap, keeping float32 Cholesky solves practical.The coupling budget prevents I + delta_t^2 P from becoming near-singular at long gaps, when the model is most needed.Source: G IMPLEMENTATION DETAILS · p. 21
  • Baseline inputs zero-fill unobserved measurements and append availability and time-gap channels; MedFuse and DrFuse use per-modality gated recurrent encoders over visits.This gives MedFuse and DrFuse the same temporal information as the state-space models rather than a single pooled vector.Source: G IMPLEMENTATION DETAILS · p. 21

H DATASET CONSTRUCTION … I.3 LONGITUDINAL FORECASTING WITH ALL THE BASELINES

Across staging, landmark prediction, and forecasting, CAMOS is compared with twelve baselines on ADNI and zero-shot OASIS-3, with results varying across tasks and cohorts. The paper also specifies procedure-level modality availability and rules for cohort construction and task labels.

H DATASET CONSTRUCTION

  • A modality is available only when all its features are recorded at a visit, matching procedure-level acquisition such as whole CSF or PET panels.Subjects need at least three diagnosed visits and at least one fully observed modality per retained visit; continuous features are robust z-scored using training-split statistics, and volumetric MRI is divided by intracranial volume before normalization.Source: H DATASET CONSTRUCTION · pp. 21–22
  • Staging uses recorded diagnoses mapped to CN, MCI, and AD; landmark labels mark AD within three years after the first MCI diagnosis or require three years of follow-up without conversion.Subjects censored before three years without conversion are excluded from landmark prediction, and MCI-to-CN reversions remain in staging with their recorded labels.Source: H DATASET CONSTRUCTION · p. 22
  • OASIS-3 uses the same modalities, nearest available measures for features without exact ADNI counterparts, and refitted normalization statistics, with no model retraining.This is a zero-shot evaluation.Source: H DATASET CONSTRUCTION · p. 22

I EXTENDED RESULTS

  • The extended comparison covers twelve baselines from four model families on both cohorts, reporting means over five seeds using subject-level splits.The families are uncoupled oscillatory SSMs, general and coupled SSMs, irregular-time and missing-value models, and clinical fusion models.Source: I EXTENDED RESULTS · p. 22

I.1 STAGING WITH ALL THE BASELINES

  • CAMOS exceeds all twelve baselines on every ADNI staging metric and is the only model retaining discrimination among three stages under OASIS-3 transfer.OASIS-3 baseline accuracy ranges from 0.6263 to 0.7525, while every baseline has macro F1 and macro recall below 0.44; DrFuse has 1/3 recall and 2/3 specificity.Source: §I.1 · p. 22, Table 6 · p. 23

I.2 LANDMARK PREDICTION WITH ALL THE BASELINES

  • On ADNI, landmark AUROC spans 0.8795–0.9611 and AUPRC 0.6187–0.8687; mTAN leads baseline AUPRC at 0.7750 but ranks third on AUROC.On OASIS-3, baseline AUPRC spans 0.0801–0.5982 at AUROC 0.7896–0.9560; baseline AUPRC standard deviations reach ±0.188 versus ±0.009 for CAMOS.Source: §I.2 · pp. 22–23, Figure 5 · p. 23, Table 7 · p. 24

I.3 LONGITUDINAL FORECASTING WITH ALL THE BASELINES

  • On ADNI forecasting, CAMOS separates from the best baselines by 0.115 MAE on CSF and 0.106 on genetics.Baselines cluster within 0.112 MAE on CSF and, aside from S5, Mamba, and Coupled Mamba, within 0.091 on genetics.Source: §I.3 · p. 23, Table 8 · p. 24
  • On OASIS-3 forecasting, CAMOS reaches 0.3756 MAE on clinical measures and 0.2847 on genetics, versus baseline minima of 0.6569 and 0.7711.Its imaging MAE is 0.7333 against 0.7705 for the best baseline; eleven of twelve baselines cluster within 0.041 MAE on imaging and 0.039 on clinical measures.Source: §I.3 · pp. 23–24, Table 9 · p. 24

I.4 ABLATION STUDIES ON OASIS-3

Under zero-shot transfer to OASIS-3, the ablation ordering matches ADNI: IMEX is most damaging, while the other variants have smaller, statistically unresolved margins. The asymmetric gate showed no divergence despite breaking the symmetry required by Lemma 2.

I.4 ABLATION STUDIES ON OASIS-3

  • IMEX lowered macro F1 from 0.5573 to 0.4880 and raised forecasting MAE by 7.3%, 56.1%, and 119.1% on imaging, clinical measures, and genetics, respectively.Table 10 repeats the Section 6 ablations under zero-shot transfer.Source: §I.4 · p. 25
  • Removing the gate was the next most damaging change; removing coupling or replacing the symmetric product with the asymmetric gate cost less.The ablation ordering matches ADNI.Source: §I.4 · p. 25
  • Only the IMEX effect was resolved at this sample size: margins for the three non-IMEX variants were smaller than seed standard deviations of up to ±0.034 macro F1 and ±0.112 AUPRC.The asymmetric gate breaks the symmetry required by Lemma 2, but no divergence was observed, making the guarantee a safeguard rather than a practical necessity at this scale.Source: §I.4 · p. 25

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