# Study Documentation Detailed description of every study behind the manuscript "Relevance-Aware Semantic Multiple Access via Meta-Learned User-Wise Cross-Attention": the question each study answers, the exact setup, the procedure, the metrics, the key results, and the artifact paths. All studies run on a single NVIDIA RTX A4500 (PyTorch 2.10, CUDA 12.8), seed 42, and write raw JSON results consumed only by `experiments/make_figures.py`. **Common system model** (all `experiments/` studies, matching the manuscript's received-signal model): single superimposed uplink y = sum_v |h_v| e^{j dphi_v} (e_v (.) m_v) + n over one d=64-dimensional frame; fixed {0,1} disjoint transmit block masks (d/U coordinates per user, identical for every compared scheme); per-rail noise std = sqrt(mean|y_tx|^2 / SNR); U=4 users and the HIGH/LOW/MIX scenarios of the manuscript unless stated. The decoder-side masks are separate learned soft masks in [0,1]^d initialized at the block pattern. Training is the manuscript's first-order meta-training aggregated over SNR tasks {0,4,...,20} dB, Adam 1e-3 (mask logits 0.1), 250-300 epochs, batch 64; evaluation uses 150-200 Monte Carlo batches of 64 per point. --- ## E1 — Comparison fairness against optimal linear receivers - **Question.** Is the d/U subspace ceiling of orthogonal access an artifact of weak comparison schemes, and how much of the UWCA gain is mere dimensionality rather than relevance exploitation? - **Setup.** For each scenario the true relevance matrix B (B_uv = beta_u beta_v for a shared scene, else 0) and the per-realization channel magnitudes are formed. Receivers evaluated on the *same* received frame: `uwca` (trained), `ofdma`, `sfdma`, `noma` (full-band power-domain SIC, powers 0.40/0.30/0.20/0.10), `lmmse_blind` (closed-form Wiener with cross-covariances zeroed), `lmmse_genie` (closed form with true B and channel gains, the manuscript's Proposition on optimal linear receivers), and `tdma_proj` (random orthonormal 16-dim projection per user — an arbitrary orthogonal partition). - **Key results.** lmmse_blind = OFDMA at every SNR in all scenarios (SER 0.509 vs 0.508 @10 dB HIGH), and tdma_proj and SFDMA coincide with them — the ceiling binds every correlation-blind receiver. HIGH @20 dB: blind 0.327 -> UWCA 0.110 -> genie 0.044, so UWCA recovers 77% of the blind-to-genie gap without side information. LOW: genie = blind (nothing to exploit), UWCA within 0.02 SER. - **Artifacts.** `experiments/e1_fair_baselines.py` -> `experiments/data/e1_fair_baselines.json` -> `fig/fig_fair.pdf` (manuscript Fig. 3). Trained checkpoints `e1_uwca_{HIGH,LOW,MIX}.pt` (reused by E4/E6). ## E2 — Full complex-baseband phase errors and CSI error - **Question.** Does the multi-user superposition amplify residual phase errors into severe inter-user interference once every leakage path is simulated explicitly? - **Setup.** Complex channel with per-user residual dphi_u ~ N(0, sigma^2), sigma in {0,5,10,15,20,30} deg; both rails simulated. Three decoders: mismatch-trained (never saw phase errors), phase-augmented (trained with sigma ~ U[0,20] deg), and a two-rail variant whose keys/values read [Re;Im]. CSI sweep: amplitude error h_hat = h(1+eps), eps ~ N(0, sigma_h^2), sigma_h up to 0.2, at 10 deg. The learned-mask overlap (mean pairwise cosine) is also measured. - **Key results.** Mismatch-trained @10 dB: SER 0.270 -> 0.291 (20 deg) -> 0.332 (30 deg); @20 dB 0.110 -> 0.127; augmentation and I/Q reading change the curves by less than the Monte Carlo spread. The leakage is second order because it scales with sin(dphi) times the mask overlap (measured 0.26). CSI: UWCA unchanged within 0.004 (it uses no explicit CSI). - **Artifacts.** `experiments/e2_phase_iui.py` -> `experiments/data/e2_phase_iui.json`; `fig/fig_phase2.pdf`. ## E3 — Dynamic user population - **Question.** Does a decoder provisioned for U_max users need retraining when users arrive and depart? - **Setup.** U_max = 8 mask slots (d=64, 8 dims/slot), high-correlation scenario (beta_u = 0.6, one scene). The active set is resampled per frame; inactive users transmit nothing and their softmax scores are masked out (the scheduler announces the active set). Compared: one model trained with the full population always active (never retrained), an activity-sampled model, and per-count models retrained from scratch for |A| in {2,4,6,8}. Metric: mean cosine (the sqrt(1/8)=0.35 subspace ceiling saturates the binary SER at this scale). - **Key results.** The single full-population model sustains fidelity over every active count (c 0.34 -> 0.39 for |A| = 2 -> 8 @10 dB) and matches or exceeds the per-count retrained models (0.33/0.32/0.36/0.39); per-count retraining is counterproductive, since sparse populations train each slot on a fraction of the traffic. - **Artifacts.** `experiments/e3_dynamic_users.py` -> `experiments/data/e3_dynamic_users.json`; `fig/fig_dynusers.pdf`. ## E4 — Symbol-timing offsets and receiver-side realignment - **Question.** How does the decoder behave under asynchronous reception, and what does the standard timing-correction chain restore? - **Setup.** Per-user integer offsets delta_u ~ U{0..Delta} symbols, Delta in {0,1,2,4,8}, shift each user's transmitted block within the frame (edge energy lost). Conditions: uncorrected reception (UWCA and OFDMA), block-wise realignment using pilot-estimated offsets (each user's block region shifted back individually), and realignment with a deliberately impaired estimator (+-1 symbol on 20% of users). - **Key results.** Uncorrected offsets are catastrophic for *every* embedding-level scheme (one symbol: UWCA 0.26 -> 0.73, OFDMA 0.51 -> 0.76), because i.i.d. embedding coordinates fully decorrelate under a one-symbol misalignment — synchronization is a shared physical-layer prerequisite, not a property of the multiple-access mechanism. With realignment the degradation is gradual (0.266 -> 0.304 @Delta=1, 0.455 @Delta=8) and realigned UWCA stays below realigned OFDMA (0.536-0.638) at every offset. The impaired estimator costs 0.14 SER: whole-symbol residuals sacrifice the affected block, so timing must be held to sub-symbol accuracy (which the closed-loop timing advance provides). - **Artifacts.** `experiments/e4_async.py` -> `experiments/data/e4_async.json`; `fig/fig_async.pdf`. ## E5 — Nonlinear inter-user semantic structure - **Question.** Does the mechanism survive when no scalar or linear description of the inter-user dependence exists? - **Setup.** Embeddings e_u = normalize(g_u([s; p_u])) with fixed random two-layer tanh view networks g_u per user (seed 7): users share the scene s only through independent nonlinear transformations. Cases: shared scene vs independent scenes (control). Schemes: trained UWCA, OFDMA, NOMA-SIC, and the scalar-parameterized genie LMMSE fed the *measured* mean pairwise cosine. - **Key results.** The linear correlation is destroyed (mean cosine 0.006), so the genie LMMSE collapses onto the ceiling (0.515 vs OFDMA 0.518 @10 dB) — no scalar or linear receiver can represent the shared structure. UWCA still attains 0.363 @10 dB / 0.220 @20 dB. The independent-scene control (UWCA 0.441) isolates the manifold-prior share, so the further reduction to 0.363 is pure nonlinear cross-user structure. - **Artifacts.** `experiments/e5_nonlinear.py` -> `experiments/data/e5_nonlinear.json`. ## E6 — Residual orthogonality vs content preservation - **Question.** What exactly decorrelates at the decoder output: the delivered content, or the errors? - **Setup.** E1's trained HIGH decoder; per-sample Pearson correlation across the 64 dimensions, averaged over user pairs and 100x64 samples per SNR, for: input embeddings, decoded embeddings, and decoding residuals r_u = e_hat_u - e_u; OFDMA decoded correlation as reference. - **Key results.** The decoded-embedding correlation rises with SNR from 0.31 toward the 0.39 input level (the shared content is delivered, not stripped), while the residual correlation falls 0.23 -> 0.14 (2.8x below the input level) — the emergent residual orthogonality. OFDMA's decoded correlation is 0.00 at every SNR: orthogonal access erases the inter-user semantic structure from the delivered embeddings. - **Artifacts.** `experiments/e6_residual_orth.py` -> `experiments/data/e6_residual_orth.json` -> `fig/fig_resorth.pdf` (manuscript Fig. 4). ## E7 — Adaptation across fading families - **Question.** Does the meta-trained initialization cover a multi-dimensional space of operating conditions that a one-dimensional per-SNR model bank cannot, and is the sharpness scalar stable? - **Setup.** Task family = 6 SNRs x {Rayleigh, Rician K=5 dB, K=10 dB} x phase residual {0,10} deg (36 tasks). Systems: one initialization meta-trained over the full family (300 epochs, eta and outer-gradient norm logged every epoch); a per-SNR specialist bank trained on Rayleigh/no-phase and indexed by nearest SNR. Held-out tests: Rician K=20 dB + 15 deg (10/18 dB), Nakagami m=3 + 5 deg (a fading law in no training task), Rayleigh + 20 deg @6 dB, plus an in-distribution check; zero-shot and after S in {1,5,10,20} inner steps (SGD 0.02, one 64-sample support batch). - **Key results.** The family initialization transfers zero-shot with 9-46% lower SER than the specialist bank on every held-out condition (e.g. 0.114 vs 0.158 Rician-K20-15deg @10 dB; 0.139 vs 0.190 under the unseen Nakagami law); inner-loop adaptation is stable (within 0.005 over 20 steps). eta converges to 0.94 (max 1.00) and the outer gradient norm stays below 0.024 against a clipping bound of 5 — no softmax saturation or divergence. - **Artifacts.** `experiments/e7_meta.py` -> `experiments/data/e7_meta.json` (includes eta/gradient trajectories). ## E8 — End-to-end training with anti-collapse regularization - **Question.** Can the encoder be trained jointly with the decoder without representation collapse, and what causes the collapse when it occurs? - **Setup.** Four configurations on HIGH: frozen encoder (reference); naive end-to-end with the distortion measured against the encoder's own output (a moving target); source-anchored end-to-end (distortion vs normalize(x)); moving target + a VICReg-style variance-covariance regularizer (hinge at 1/sqrt(d) per-dim std, 25x variance + 100/d covariance weights). Collapse-proof metric: batch nearest-neighbor retrieval accuracy over the *encoded* gallery, plus the effective rank of the encoder-output covariance. - **Key results.** The naive configuration collapses (retrieval falls to chance, 0.005 vs 0.536 frozen @10 dB), locating the pathology in the moving-target objective rather than the cross-attention. Source anchoring keeps effective rank 59.6 of 64 and lands within 0.04 SER of the frozen reference; the variance-covariance regularizer restores retrieval to 0.509 with a learned task-specific code. The frozen encoder in the main experiments is therefore a controlled-isolation choice. - **Artifacts.** `experiments/e8_e2e.py` -> `experiments/data/e8_e2e.json`. ## E9 — Online top-k relevance acquisition and measured overhead - **Question.** How does sparse top-k attention obtain the relevance ranking it needs, starting from no knowledge, and what does the acquisition cost? - **Setup.** U=32, eight relevance clusters of four, k=4, briefly trained full-attention model. Protocol: frames 1-3 run full attention (which needs no relevance knowledge) while the BS accumulates beta_hat by EWMA (zeta=0.5) of decoded-embedding cosines; from frame 4, per-row top-k via argpartition on beta_hat. References: an oracle whose peers are selected from the true clusters, and permanent full attention. Timing: decoder forward vs EWMA-update-plus-selection wall-clock for U in {8,16,32,64,128} (256-sample frames, GPU, 20-run averages). - **Key results.** From the first post-warm-up frame the online selection matches the oracle exactly and slightly exceeds full attention (discarding irrelevant peers discards their noise); ranking needs far less accuracy than estimation because intra-cluster (~0.42) and inter-cluster (~0) cosines are well separated. Estimation plus selection cost 0.02-0.04 ms against the 0.3-5.4 ms decoder pass, incurred once per relevance coherence interval. - **Artifacts.** `experiments/e9_topk_online.py` -> `experiments/data/e9_topk_online.json` (trajectory + timing). --- ## Simulation studies (`simulation/`) - **Three-scenario SER study** (manuscript Fig. 2): analytical simulation `simulation/semantic_correlation_sim.py` with the trained decoder-only overlay from `simulation/maml_semantic.py --decoder_only`; threshold sweep tau in [0.30,0.50] and the mean-cosine comparison in `simulation/threshold_phase_study.py`. - **beta sweep** (monotone gain law): `simulation/betasweep.py` (figure `fig/fig4_beta_sweep.pdf`). - **Attention heatmaps**: `simulation/plot_figures.py` (figure `fig/fig6_hlm.pdf`). - **Hyperparameter studies** (S, lambda, d, H, K): `simulation/ablation_hks.py`, `simulation/dsweep.py`, `simulation/e2e_check.py`. - **Real-data study** (manuscript Fig. 5): UCI optical-recognition digits (8x8=64 dimensions), `simulation/realdata_train.py` + `simulation/realdata_plot.py`.