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RAOA: Alternating-Operator Neural Computation with Programmable Radio Propagation

Toshiaki Koike-Akino

arXiv:2610.02683v1cs.LGcs.ETcs.LO

TL;DR

The paper asks whether programmable radio propagation can serve as computational depth rather than only as a channel or one-shot transform. It introduces RAOA, a recurrent alternation of energy-derived problem and mixing updates, and tests it on exact objectives, simulated propagation, and pretrained-model adaptation. Deeper execution often improves exact-instance success, while adapter transfer is strong on WikiText but model-dependent on reasoning tasks.

  • Problem

    The paper asks whether programmable radio paths can be reused as computational depth beyond communication or one-shot analog transforms.

    Source: §1 · p. 1

  • Method

    RAOA alternates energy-derived problem and mixing updates over a persistent state, recomputing the local field after each mix while controls can be tied across passes.

    Source: §1 · p. 2, §3.2 · p. 4

  • Results

    Across independent exact instances, deeper execution with the same two controls often improves success; single-stage adapters recover 93.9–99.2% of shallow-MLP WikiText NLL improvement, while GSM8K transfer remains model-dependent.

    Source: §1 · p. 2, §6 · p. 9

  • Takeaways & Limitations

    The results support recurrent pass depth as a computational resource on the tested exact objectives, with a constrained-propagation bridge and transferable neural interface.

    Source: §7 · p. 9

    The evidence remains operator- and simulation-level: calibrated hardware, measured latency and energy, and higher-order physical realization remain open.

    Source: §6 · p. 9

Abstract

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Can programmable radio propagation serve as computational depth rather than only as a communication channel or one-shot analog transform? We introduce the Radio Alternating Operator Ansatz (RAOA), a recurrent computing architecture that alternates an energy-derived problem update with a mixing update over a persistent latent state. Recomputing the problem field after each mix makes repeated passes compositional even when the same learned controls are reused across depth. We evaluate this idea through exact discrete optimization, constrained programmable-propagation simulation, and pretrained-model adaptation. On discrete objectives, repeated execution can improve solution quality without increasing the learned-control count, and the same formulation handles higher-order interactions directly. A passive phase-only free-space model further shows that the required operators can be approximated by programmable propagation while retaining useful downstream behavior despite realization error. When inserted as a zero-initialized residual adapter, RAOA adapts pretrained language models with WikiText performance close to a matched shallow MLP across three model families, while reasoning-task transfer remains model-dependent. Together, these results connect alternating-operator computation, programmable radio propagation, and neural adaptation within one recurrent framework. The RF realization evidence is simulation-based rather than a hardware demonstration.

1 INTRODUCTION

RAOA asks whether programmable radio propagation can be reused as computational depth, and implements that idea as a recurrent alternation over a persistent state. Tests span exact discrete objectives, simulated constrained propagation, and pretrained-model adaptation.

Motivation

  • Wireless propagation is usually treated as a communication channel followed by digital computation, motivating the question of whether a programmable radio path can instead provide computational depth.Programmable surfaces and physical neural networks make the transfer function itself programmable.Source: §1 · p. 1

Approach

  • RAOA alternates an energy-derived problem pass with a mixing pass over a persistent latent state, recomputing the local field after mixing so tied controls can compose state-dependent transformations.The Transformer adapter uses a zero-initialized residual scale; its radio loop is conceptual, and foundation-model experiments execute the differentiable operator in software.Source: §1 · p. 1, Figure 1 · p. 2

Contribution

  • The paper distinguishes its contribution from prior wave-computation and programmable-metasurface work: it studies temporal problem/mixer alternation with controlled exact-objective tests and pretrained-Transformer insertion.The authors do not claim wave-domain inference, nonlinear computation from programmable scattering, or parameter-independent physical depth as new in isolation.Source: §1 · p. 2

Results

  • On independent instances, extending each instance-specific two-control program from two to 4, 8, and 16 passes increases mean success across four objective families, though matched-depth optimization is inconsistent on partition.Native higher-order fields also avoid the fixed-budget ancilla penalty of the tested exact quadratizations.Source: §1 · p. 2
  • Passive phase-only propagation retains useful Max-Cut behavior despite operator error, while single-stage adapters recover 93.9–99.2% of shallow-MLP WikiText NLL improvement across three Transformer families; GSM8K transfer remains model-dependent.All radio-propagation results are simulated.Source: §1 · p. 2

2 RELATED WORK

Prior work establishes programmable propagation, recurrent and nonlinear wave computation, and wave-domain neural inference. RAOA’s stated distinction is its recurrent feedback over one state with alternating problem/mixer semantics and exact-objective controls.

Wave and metasurface computation

  • Programmable RF and metasurface systems already demonstrate iterative algorithms, in-situ electromagnetic learning, and nonlinear or recurrent wave computation; RAOA does not claim these ingredients as new in isolation.Examples include Tzarouchis et al. (2025), Song et al. (2026), and Hughes et al. (2019).Source: §2 · p. 3

Physical neural networks, nonlinearity, and depth

  • Shared-weight programmable-metasurface depth has been studied, but RAOA focuses instead on feedback over one state, problem/mixer semantics, exact QUBO/HUBO fields, cross-depth control reuse, and Transformer insertion.Hammami et al. (2026) vary structural encoding, coupling, and layer depth.Source: §2 · p. 3

Stacked intelligent metasurfaces and over-the-air neural inference

  • Stacked intelligent metasurfaces and wireless neural layers establish wave-domain inference, whereas RAOA studies repeated temporal feedback reuse for exact optimization and foundation-model adaptation.The cited examples include Huang et al. (2025), Stylianopoulos et al. (2025), and An et al. (2026).Source: §2 · p. 3

Structured iteration and parameter-efficient adaptation

  • RAOA relates architecturally to algorithm unrolling, neural operators, and QAOA, but is classical, real-valued, and trained by backpropagation; adaptation comparisons use LoRA and a shallow MLP.The paper asks how much digital-adapter quality the structured operator retains, not whether it universally dominates.Source: §2 · p. 3

3 RADIO ALTERNATING OPERATOR ANSATZ

RAOA turns programmable propagation into a recurrent computation by alternating problem and mixer passes over a state that persists across stages. The same formulation supports exact objectives and a zero-initialized residual interface to pretrained Transformers.

3.1 FROM PROGRAMMABLE PROPAGATION TO ITERATIVE COMPUTATION

  • A fixed programmed path is linear in its transmitted state, while signal-conditioned programming can create nonlinear maps and feedback adds memory; RAOA composes these ingredients through alternating problem and mixer roles.The paper asks whether these state-dependent updates make repeated programmable passes useful as computational depth, rather than claiming any individual ingredient is new.Source: §3.1 · p. 3, Figure 2 · p. 4

3.2 RAOA UPDATE

  • Each RAOA stage applies an energy-derived problem update and a mixing update, then recomputes the problem field on the new state; tied controls increase execution depth without increasing the two learned scalar controls.A fixed Hadamard-derived orthogonal mixer is used, and the shared update covers learned quadratic/context operators and exact QUBO/HUBO objectives.Source: §3.2 · p. 4
  • Under the stated unsaturated-quadratic surrogate, tied controls expose higher powers of the same stage operator without adding learned controls; this explains how depth can help, not that it must.The full normalized, tanh-saturated recurrence is not polynomial, and the surrogate is structural rather than an exact description of the implemented map.Source: §3.2 · p. 4

3.3 CONCEPTUAL RADIO REALIZATION

  • The proposed physical interpretation reconfigures one programmable path between problem and mixer passes and feeds receiver output back, yielding 2L modeled RF passes for L stages.The operators are effective receiver-plane operators; explicit passive phase-only propagation is tested separately.Source: §3.3 · p. 4

3.4 ZERO-INITIALIZED TRANSFORMER INSERTION

  • The Transformer adapter projects hidden states into the RAOA state and returns its output through a residual scale initialized to zero, preserving model behavior at initialization.The primary 4B experiments use L = 1; the physical loop is conceptual and foundation-model experiments use a differentiable software operator.Source: §3.4 · p. 5

4 EXPERIMENTAL DESIGN

The experimental design separates exact discrete optimization, constrained propagation simulation, and pretrained-model transfer. It varies depth with fixed controls in the discrete studies and uses matched validation-search budgets and parameter counts for adapter comparisons.

Exact discrete optimization

  • Exact discrete optimization evaluates four pairwise and higher-order objective families with enumerated optima across independent instances, depths, and seeds, tying one two-control pair across stages and reusing it across depths.The sweep uses 12 instances per family at n ∈ {8, 12}, L ∈ {1, 2, 4, 8}, and five seeds.Source: §4 · p. 5

Constrained propagation

  • Constrained propagation compiles pairwise Max-Cut and partition operators for n = 8 through 1, 2, or 4 passive phase-only free-space panels, measuring operator error and downstream success.Each panel has 128 elements; the setup excludes trainable amplitude control, dense digital precoding or combining, and a direct path.Source: §4 · p. 5

Foundation models

  • Foundation-model tests use Qwen3-4B, Gemma-3-4B-it, and Phi-4-mini-instruct with single-stage, width-64 RAOA adapters on all text MLP blocks, assessing WikiText and GSM8K transfer.WikiText uses disjoint training and validation data plus a three-seed full-test confirmation; GSM8K schedules are selected on a training-split holdout before official test evaluation.Source: §4 · p. 5

Baselines and controls

  • Frozen, LoRA, RAOA, and shallow bottleneck MLP baselines are compared under equal family-specific validation-search budgets and closely matched trainable parameter counts.The primary foundation-model setup tests transfer rather than large-model depth scaling.Source: §4 · p. 5

5 RESULTS

Across discrete optimization, model adaptation, and propagation simulation, RAOA benefits from repeated execution and shows useful transfer under the tested settings. Results also expose limits: matched-depth optimization can be unstable, model-transfer outcomes vary, and RF evidence is simulated.

5.1 NONLINEAR AND RECURRENT COMPUTATIONAL PRIMITIVES

  • A fixed scalar linear surface has best-fit MSE 2.37 × 10^-2 for x ↦ x^3, while signal-conditioned control reaches numerically zero ideally and 2.4 × 10^-3 under a severe synthetic profile.On delayed multiplication, linear feedback is 49.3% and nonlinear feedback is 100% ideally; these tests isolate primitives, not benchmark performance.Source: §5.1 · pp. 5–6

5.2 DISCRETE OPTIMIZATION WITH ALTERNATING RADIO PASSES

  • At n = 12, reusing two-pass controls through 16 passes raises mean success from 0.367 to 0.980 on 3-SAT and from 0.0158 to 0.175 on Max-Cut.The same monotonic increase appears across all eight family-size groups, without changing the learned controls.Source: §5.2 · p. 6, Figure 3 · p. 6
  • Matched-depth optimization improves all 12 3-SAT instances at both sizes, but at 16 passes partition worsens on 10/12 n = 8 instances and 7/12 n = 12 instances.Freezing the initial local field reduces eight-pass success from 0.985 to 0.483 on 3-SAT, 0.850 to 0.040 on hypergraph Max-Cut, and 0.430 to 0.060 on Max-Cut.Source: §5.2 · pp. 6–7
  • Native higher-order execution avoids the 8–9 ancillas introduced by exact quadratization, which sharply lowers optimum-hit probability under the tested eight-pass, two-control budget.This fixed-budget result does not establish universal HUBO superiority.Source: §5.2 · p. 7, Table 1 · p. 7

5.3 FOUNDATION-MODEL TRANSFER

  • RAOA recovers 96.0%, 99.2%, and 93.9% of shallow MLP WikiText NLL improvement on Qwen, Gemma, and Phi, respectively, but is not the universal winner.LoRA leads on Qwen, while MLP leads on Gemma and Phi; a matched digital recurrent bottleneck also falls between MLP and RAOA on Qwen.Source: §5.3 · p. 7, Table 2 · p. 7
  • The 768-token audit raises Qwen and Gemma exact match by 5.1–8.0 points while reducing cap hits, but does not distinguish RAOA, MLP, and frozen models.Phi was not rerun because adapted 384-token cap-hit rates were mostly below 2%.Source: Table 2 · p. 7, §5.3 · p. 8

5.4 STRUCTURAL EFFICIENCY AND CONSTRAINED PROPAGATION

  • Dense Gemma placement reaches 74.30% GSM8K accuracy, while every-second-layer placement reaches 74.00% with 17 rather than 34 adapted blocks.Extreme two-layer sparsity returns toward frozen performance, indicating a coverage–efficiency trade-off rather than special early-layer sensitivity.Source: §5.4 · p. 8, Figure 4 · p. 8
  • After four-panel compilation, reoptimized Max-Cut success is 0.305 and 0.487 versus ideal 0.428 and 0.686 at 8 and 16 passes, respectively.This is a constrained simulation, not an RF measurement; separate modeled perturbations change Qwen WikiText NLL by only +0.00051 (≈0.019%).Source: §5.4 · pp. 8–9

6 DISCUSSION

The evidence supports recurrent execution depth as a computational resource on tested exact objectives, but optimization does not always exploit added depth. The radio evidence is simulation-level, and neural transfer does not establish language-model depth scaling.

6 DISCUSSION

  • Repeated execution with the same two learned controls often improves success across independent exact instances, while partition distinguishes useful execution depth from successful depth-specific optimization.State-dependent field re-evaluation is the consistent mechanism, whereas mixer benefits depend on the objective.Source: §6 · p. 9
  • The primary 4B study uses one RAOA stage; Qwen depth scaling is flat, and a matched depth-2 recurrent control reaches 2.6727 ± 0.0029 NLL, so transfer is not unique to RAOA recurrence.The 768-token GSM8K audit does not distinguish RAOA, MLP, and frozen models under paired bootstrap.Source: §6 · p. 9
  • The evidence remains operator- and simulation-level, with higher-order realization, calibrated hardware, and measured latency and energy left open.The RF realization is not a hardware demonstration.Source: §6 · p. 9

7 CONCLUSION

RAOA is a task-structured recurrent operator that alternates problem and mixer passes over a persistent state. The paper distinguishes this temporal-feedback organization from prior programmable-wave computation and evaluates it across optimization and neural-adaptation settings.

7 CONCLUSION

  • RAOA uses a persistent-state problem/mixer recurrence and, on tested objectives, supports more modeled passes with tied controls; measured hardware and foundation-model depth scaling remain open.The conclusion also reports a constrained propagation bridge and a zero-initialized single-stage adapter across three Transformer families.Source: §7 · p. 9

A.1 COMPUTATIONAL METAMATERIALS AND PROGRAMMABLE ELECTROMAGNETIC ENVIRONMENTS

  • Prior programmable RF systems already demonstrate closed-loop and iterative computation, while RAOA’s distinct contribution is an explicit recurrent problem/mixer program, tied-depth optimization, and transferable neural interface.RIS work usually targets communication and sensing; RAOA organizes state, task-dependent local fields, and repeated pass types.Source: §A.1 · pp. 12–13

A.2 PHYSICAL NEURAL NETWORKS

  • The work adopts hardware-aware learning but focuses on a radio-specific recurrent operator that composes static, conditioned, and feedback ingredients through alternating passes.The paper frames this as an architectural contribution, not a claim that physical neural networks or programmable propagation are new.Source: §A.2 · p. 13

A.3 NONLINEAR COMPUTATION FROM LINEAR OR WEAKLY NONLINEAR WAVE PHYSICS

  • RAOA’s contribution is not nonlinear computation from linear wave physics, but explicit recurrent state and two pass roles evaluated on exact objectives and pretrained language models.The related work also notes prior nonlinear computation through encoding, modulation, scattering, or recurrence.Source: §A.3 · p. 13

A.4 PROGRAMMABLE-METASURFACE EXPRESSIVITY AND DEPTH

  • Unlike the cited programmable-metasurface expressivity study, RAOA uses temporal feedback over one latent state and tests tied-control depth on exact optimization problems and as a Transformer adapter.The two studies are described as complementary, not as establishing parameter-independent wave depth for the first time.Source: §A.4 · p. 13

A.5 STACKED INTELLIGENT METASURFACES AND ELECTROMAGNETIC NEURAL NETWORKS

  • SIM and related wireless neural systems use spatial or cascaded depth, whereas RAOA evaluates temporal feedback recurrence; the axes could be combined in future hardware.Prior SIM work establishes wave-domain neural inference, which RAOA does not claim as new.Source: §A.5 · p. 14

A.6 STRUCTURED ITERATIVE NETWORKS AND NEURAL OPERATORS

  • RAOA follows structured iteration, using paired problem/mixer passes over a shared classical state rather than a generic dense layer; its QAOA analogy is architectural, not quantum equivalence.The method uses real-valued state, tanh saturation, modeled radio passes, and standard backpropagation.Source: §A.6 · p. 14

A.7 PARAMETER-EFFICIENT ADAPTATION OF FOUNDATION MODELS

  • Adapter comparisons are mixed rather than universally ranked: LoRA leads on Qwen WikiText, while MLP leads on Gemma and Phi WikiText and Phi GSM8K.The short Qwen and Gemma reasoning audit makes RAOA, MLP, and frozen accuracy nearly indistinguishable at paired-bootstrap resolution.Source: §A.7 · p. 14

B.2 FIXED-CONTROL MODELED-PASS SWEEP

The appendix examines fixed-control depth, native higher-order optimization, propagation mechanisms, and adapter implementation. Its results show objective- and seed-dependent depth benefits, alongside explicit limits on what simulated propagation and the conceptual illustration establish.

B.2 FIXED-CONTROL MODELED-PASS SWEEP

  • Two learned controls are shared across depths, while 3-SAT-8 rises from 0.617 success at two passes to 0.980 at eight and 1.000 for all five runs at eight passes.Max-Cut-8 and hypergraph Max-Cut also improve through eight passes, but deeper outcomes can be seed-sensitive; partition can worsen with added depth.Source: §B.2 · p. 15, Table 5 · p. 16

B.3 NATIVE HIGHER-ORDER OBJECTIVES VERSUS QUADRATIZATION

  • At eight modeled RF passes, native 3-SAT reaches 0.989 success versus 0.161 after quadratization, and native hypergraph Max-Cut reaches 0.830 versus 0.119.Quatratization expands the 3-SAT instance from 8 to 17 variables and hypergraph Max-Cut from 8 to 16; the comparison is at fixed RAOA budget, not matched state dimension.Source: §B.3 · p. 16, Table 6 · p. 16

C CONCEPTUAL SYSTEM VIEWS

  • The appendix-only AI-generated system image provides qualitative intuition about propagation, control, feedback, repeated passes, and Transformer insertion, not experimental evidence.Quantitative plots are generated programmatically from frozen numerical results.Source: Figure 5 · p. 18

D EXPRESSIVITY HIERARCHY: FORMULATION AND CONTROLLED EVIDENCE

  • Static propagation with fixed H and Φ is linear in the transmitted signal, whereas signal-conditioned surface control can produce nonlinear end-to-end maps.For the cubic task, the ideal signal-conditioned reference has numerically zero error; under the severe synthetic profile, MSE is approximately 2.4 × 10−3 versus 2.57 × 10−2 for the static surface.Source: §D.1 · p. 18, §D.2 · p. 18

D.3 FEEDBACK INTRODUCES STATE AND TEMPORAL COMPUTATION

  • In the delayed-product reference, linear feedback reaches 49.3% accuracy while nonlinear feedback reaches 100% under the ideal software model.The example tests an additional temporal/nonlinear mechanism, not a general reservoir-computing benchmark.Source: §D.3 · p. 19

D.4 RAOA ADDS ITERATIVE MODELED-PASS DEPTH

  • RAOA’s tied program reuses two learned controls while increasing modeled RF passes, but whether optimization exploits added depth depends on objective and seed.The reported expansion studies Max-Cut, partition, 3-SAT, and hypergraph Max-Cut with exact optima.Source: §D.4 · p. 19

E.1 GENERAL RAOA STATE UPDATE

  • The local field is derived from a differentiable energy and context; the foundation-model specialization truncates the multilinear energy at order two, while exact discrete studies use known spin polynomials.Three- and four-body terms enter through products in the local field, but this is a phenomenological software representation, not evidence of arbitrary many-body RF realization; positive global energy rescaling should leave the ideal trajectory essentially unchanged.Source: §E.1 · p. 19, §E.2 · p. 19

E.3 RESIDUAL TRANSFORMER INSERTION AND PARAMETER COUNT

  • The adapter initializes from a context projection, runs RAOA stages, and adds the projected final state as a residual; its zero-initialized scale preserves the pretrained model exactly at insertion.The appendix also specifies a parameter-count expression and synthetic impairment profiles, not device measurements.Source: §E.3 · p. 20, Table 7 · p. 20

F THEORETICAL PROPERTIES OF RAOA

The theoretical analysis characterizes how tied controls can compose across repeated passes, how dynamic field recomputation affects composition, and what bounds apply to scale invariance, descent, and approximation error.

F THEORETICAL PROPERTIES OF RAOA

  • With tied controls, depth generates a block-Krylov-type span of powers of one matrix, potentially enlarging composed computation without increasing the two controls.Strict subspace growth is not guaranteed once the relevant minimal polynomial saturates.Source: F THEORETICAL PROPERTIES OF RAOA · pp. 20–21
  • Dynamic field re-evaluation permits polynomial degree up to (d−1)L, whereas a frozen initial field has degree at most d−1.For cubic and quartic energies, the dynamic bound is 2L and 3L before saturation; these are surrogate results, not exact degree claims for full RAOA.Source: F THEORETICAL PROPERTIES OF RAOA · p. 21
  • Positive global energy rescaling is removed exactly when ϵ = 0 and differs from exact invariance only by an O(ϵ) term when ϵ > 0.For an energy with L_E-Lipschitz gradient, the pre-saturation problem step strictly descends when 0 < η < 2/L_E and the gradient is nonzero.Source: F THEORETICAL PROPERTIES OF RAOA · pp. 21–22
  • For full RAOA stage F, including final tanh, finite inputs enter D = [−1, 1]^m; with stage error at most δ and F Lipschitz constant K on D, same-start recurrences have error at most Lδ for K = 1 or δ/(1 − K) for K < 1.The proposition does not assert that the implemented stage is contractive; it bounds accumulation of known stage-wise approximation error over finite depth.Source: F THEORETICAL PROPERTIES OF RAOA · p. 22
  • Together, the propositions explain tied-control composition, dynamic-field effects, suppression of positive global energy scale, and conditions under which imperfect operators may remain useful.These are explanations of empirical observations, not universal guarantees.Source: F THEORETICAL PROPERTIES OF RAOA · p. 22

G.1 WIKITEXT ARCHITECTURE TRANSFER

Across the supplied experiments, RAOA transfers to WikiText, language-model depth gains are not established, and discrete optimization results depend on objective and optimization stability. The GSM8K long-cap audit also changes how small canonical differences should be read.

G.1 WIKITEXT ARCHITECTURE TRANSFER

  • RAOA captures 96.0%, 99.2%, and 93.9% of the shallow MLP NLL gain over frozen Qwen, Gemma, and Phi, respectively.The reported percentages measure recovery of MLP improvement, not statistical equivalence.Source: §G.1 · p. 22

G.2 QWEN3-4B VALIDATION-ONLY RAOA DEPTH DIAGNOSTIC

  • The Qwen validation depth diagnostic is non-monotonic, with only a 0.00366 NLL range across L = 1, 2, and 4; it does not establish a language-model depth benefit.The selected primary L = 1 comparison is treated as an operator-transfer experiment.Source: §G.2 · p. 22

G.3 MATCHED DIGITAL RECURRENT QWEN CONTROL

  • The parameter-matched Qwen recurrent control recovers about 98.0% of the shallow MLP improvement over frozen, narrowing the interpretation to effective transfer rather than unique advantage over generic recurrence.The comparison does not attach a significance claim to the four-way result.Source: §G.3 · p. 23

G.4 GSM8K FREE-RUNNING REASONING

  • At the 768-token GSM8K audit, Qwen RAOA, MLP, and frozen converge near 88%, while Gemma’s converge near 81%, changing the interpretation of small canonical differences rather than establishing a stable ranking.The paired intervals characterize example sampling conditional on the completed seed ensemble, not full retraining uncertainty.Source: §G.4 · p. 24

G.5 GEMMA RAOA PLACEMENT AND COVERAGE

  • The full-test Gemma placement evaluation reverses the 128-example pilot’s first-two-placement ranking, so the pilot is retained only as a sampling-sensitivity example.The placement study uses one common fixed schedule rather than a primary tuned comparison.Source: §G.5 · p. 24

G.6 MODELED-PASS DEPTH AND HAMILTONIAN NORMALIZATION

  • Across 16 problem, profile, and depth combinations, 15 raw-versus-normalized mean success values are identical; the sole difference is 1.95 × 10−4.This rules out simple global coefficient scale as a sufficient explanation for the partition-depth anomaly.Source: §G.6 · pp. 24–25

G.7 INDEPENDENT-INSTANCE DEPTH AND CROSS-DEPTH CONTROL TRANSFER

  • At L = 8, matched-depth optimization improves 3-SAT on all instances, while partition improves on only 2/12 instances at n = 8 and 5/12 at n = 12.Hypergraph Max-Cut improves on 11/12 and 12/12 instances, respectively; the passage contrasts this with benefits from reusing controls trained at two passes.Source: §G.7 · p. 25
  • 0.5701 versus 0.5689 is the eight-pass ideal four-problem portfolio mean for tied versus untied controls; at sixteen passes it is 0.5659 versus 0.5323.This supports the narrower conclusion that depth effects are not generally explained by adding per-stage controls, not that tying is universally better.Source: §G.7 · p. 25

G.8 MECHANISM ABLATION

The mechanism study identifies field recomputation as the most consistent recurrent contribution, while the propagation study tests its realization under constrained passive phase-only assumptions. The modeled propagation retains useful downstream behavior, but its physical scope is deliberately limited.

G.8 MECHANISM ABLATION

  • Freezing the initial local field drops four-problem mean success from 0.575 for full RAOA to 0.147, while mixer effects vary by objective.The ablation uses a fixed depth of four stages (eight modeled RF passes) and the same optimization schedule across variants.Source: §G.8 · pp. 25–26, Table 16 · p. 26

G.9 RIS PROPAGATION MODEL, GEOMETRY, AND PHYSICAL INTERPRETATION

  • The modeled RIS uses passive unit-amplitude panels and continuous phase control, with geometry-dependent spherical propagation, coherent panel addition, and no direct Tx–Rx term or RIS-to-RIS cascade.The irregular near-planar element clouds are a geometry-constrained operator test, not a specific fabricated-panel design.Source: §G.9 · p. 27
  • Global gain normalization makes the propagation experiment a test of operator-shape approximation, not whether an aperture closes an RF link budget.The model omits effects including element patterns, polarization, coupling, finite-bit control, loss, blockage, and feedback latency; it is not a substitute for full-wave simulation or hardware calibration.Source: §G.9 · p. 28

G.10 PASSIVE PHASE-ONLY PROPAGATION REALIZATION

  • With four panels, Max-Cut success is 0.056, 0.144, 0.305, and 0.487 at 2, 4, 8, and 16 modeled passes, versus ideal values 0.068, 0.195, 0.428, and 0.686.Operator approximation error decreases with panel count; two-control reoptimization retains about 71% of ideal mean success at eight and sixteen passes, with large geometry variability at sixteen.Source: §G.10 · p. 28, Table 17 · p. 28

G.11 MODELED RF ROBUSTNESS

The robustness study evaluates ideal-trained and domain-randomized RAOA on WikiText under four modeled profiles. Ideal-trained RAOA remains nearly invariant to the severe modeled perturbation, while domain-randomized training is slightly worse.

G.11 MODELED RF ROBUSTNESS

  • +0.000511 NLL is the change for ideal-trained RAOA under the severe profile relative to ideal evaluation.The tested profiles are modeled perturbations, not measured RF impairments.Source: §G.11 · p. 29, Figure 6 · p. 29
  • Domain-randomized training is about 0.00274–0.00285 NLL worse than ideal-trained RAOA under every modeled profile.The reported evidence supports near-invariance to this perturbation family, not a benefit from impairment-aware training.Source: §G.11 · p. 29

H DETAILED LIMITATIONS AND CLAIM BOUNDARIES

The discussion records assumptions, negative findings, and boundaries on the paper’s physical-realization, optimization, and adaptation claims.

H DETAILED LIMITATIONS AND CLAIM BOUNDARIES

  • The phase-only free-space study is a simulation, not measured hardware, and supports no measured claim about energy efficiency, throughput, latency, or closed-loop robustness.It omits measured antenna responses, calibration, synchronization, converter nonidealities, feedback delay, oscillator drift, mutual coupling, and end-to-end control latency.Source: H DETAILED LIMITATIONS AND CLAIM… · p. 29
  • The compiler tests one constrained pairwise setting, not arbitrary operator synthesis: it uses 1, 2, or 4 passive panels with 128 phase-only elements each and leaves substantial residual matrix error.More panels reduce operator error and recover more Max-Cut behavior, but deep executions show geometry variability.Source: H DETAILED LIMITATIONS AND CLAIM… · pp. 29–30
  • Higher-order local fields are executed directly in software; constrained phase-only compilation covers only pairwise operators, so higher-order physical realization remains open.The fixed-budget comparison is against tested exact quadratizations and isolates representation and ancilla burden, not universal solver superiority.Source: H DETAILED LIMITATIONS AND CLAIM… · p. 30
  • Exact-objective tests use four families at n ∈{8, 12} with optima available by enumeration; they are not a scaling study and claim no asymptotic complexity or advantage over mature solvers.Success probabilities and tied-control usefulness may change for larger n, denser constraints, or different objective ensembles.Source: H DETAILED LIMITATIONS AND CLAIM… · p. 30
  • Additional execution can help shallow-trained controls, but matched-depth optimization is not monotonic, and extra stage-specific controls do not systematically resolve instability.Mixer effects also depend on the objective: removing or replacing the Hadamard mixer is nearly neutral on 3-SAT and hypergraph Max-Cut, harmful on Max-Cut, and beneficial on the low partition baseline; freezing the initial field causes the dominant degradation.Source: H DETAILED LIMITATIONS AND CLAIM… · p. 30
  • Theoretical propositions explain finite-depth composition in explicit surrogate regimes, but do not establish global convergence, monotonic objective decrease, or optimality of deep RAOA.The local descent inequality applies to the pre-saturation problem step, not the complete problem/mixer stage.Source: H DETAILED LIMITATIONS AND CLAIM… · p. 30
  • Foundation-model experiments establish transfer across three pretrained Transformer families, not depth benefits or unique attribution of adaptation gains to RAOA’s alternating structure.The frozen-schedule Qwen depth diagnostic is essentially flat across L = 1, 2, 4; the matched Qwen depth-2 recurrent baseline reaches 2.6727 ± 0.0029 full-test NLL, numerically between the shallow MLP and RAOA.Source: H DETAILED LIMITATIONS AND CLAIM… · pp. 30–31
  • Parameter matching does not match compute or hardware budgets, and the reported sample sizes do not establish universality across problem distributions or pretrained models.The paper retains mixed or negative controls, including unstable matched-depth partition optimization, a non-universal Hadamard mixer, and a flat frozen-schedule foundation-model depth diagnostic.Source: H DETAILED LIMITATIONS AND CLAIM… · p. 31

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