26-EFT.WP.STG.Lensing v1.0 | Appendix D — Metrics & Drift Measures (Lens-Specific)

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Appendix D — Metrics & Drift Measures (Lens-Specific)

One-sentence goal: Define a unified family of metrics and drift measures for lenses (spectral / geometric / physical / learning / runtime), including conventions, thresholds, and windowing rules, and close the loop with the manifest and contract systems.

I. Scope & Objects

• Objects: K (single-layer kernel), K_eff (composed lens), graph, visibility, y_spec / y_var (dual-form outputs), RefCond, runtime SLI / SLO.
• Inputs: training & evaluation data, spectral responses, physical-consistency measures, dashboard telemetry, historical reference ref@ts0.
• Outputs: metrics.lens.* metric sets, drift.* decomposition, labeled C71-* contract decisions with evidence URIs.

II. Terms & Variables

• G(k): kernel gain in the spectral domain, k ∈ spec(graph); unit(G) = "-", dim(G) = "1".
• T_trans: transmittance; boundary_residual = || B y ||_2; conservation_residual.
• delta_form = ( || y_spec - y_var ||_2 / || y_spec ||_2 ); tol_form.
• vis_score ∈ [0,1]; los_ratio; mask.
• err_rec (inversion/de-lensing error), ece (calibration error), latency (ms), drift_score ∈ [0,1].
• Time & windows: tau_mono is the compute timebase; sliding window W = [ ts − Δt, ts ].

III. Postulates P71D-*

• P71D-1: Every persisted metric must include unit(field) and dim(field), and pass check_dim( y − f(x) ).
• P71D-2: Dual-form and physical metrics must be replayable; data dependencies are referenced by URI and not duplicated in the manifest.
• P71D-3: Drift must be decomposable and attributable to spectral / visibility / physical / data / topology categories.

IV. Minimal Equations S71D-*

1. Dual-form consistency
   • S71D-01: delta_form = ( || y_spec - y_var ||_2 / || y_spec ||_2 ); delta_form_p{q} denotes quantiles.
   • S71D-02: latency_gap = | latency_spec - latency_var |.
2. Spectral domain & kernel stability
   • S71D-11: gain_sup = sup_k | G(k) |; passband_ripple = sup_{k∈P} | G(k) - G0(k) |.
   • S71D-12: leakage = ∫_{k∈S} | G(k) | d k / ∫_{k∈all} | G(k) | d k (declare the measure over k).
   • S71D-13: rho_bound = spectral_radius( K_eff ).
3. Physical consistency & boundaries
   • S71D-21: T_trans = ( E(y; M) / E(x; M) ); conservation_residual = | T_trans - T_ref |.
   • S71D-22: boundary_residual = || B y ||_2.
4. Visibility & occlusion
   • S71D-31: vis_score = mean( mask ); los_ratio = |LOS| / ( |LOS| + |NLOS| ).
   • S71D-32: vis_dice = ( 2 ⟨mask, mask_ref⟩ / ( ||mask||_1 + ||mask_ref||_1 ) ).
5. Inversion & reconstruction quality
   • S71D-41: err_rec = ( || x_hat - x ||_2 / || x ||_2 ); err_rec_p{q} for quantiles.
   • S71D-42: sparsity = ( || Φ x_hat ||_0 / N ) (with sparsifying transform Φ).
6. Reliability & calibration (learned lenses)
   • S71D-51: ece = ∑_b ( | acc_b - conf_b | * w_b ).
   • S71D-52: reliability_gap = sup_p | F_pred(p) - F_emp(p) |.
7. Runtime SLIs
   S71D-61: latency_p{q}; cpu_pct, mem_pct, err_rate; cache_hit.
8. Drift decomposition & aggregation
   • S71D-71 (spectral drift): drift_spec = ( ∫ | G_t(k) - G_ref(k) | d k / ∫ | G_ref(k) | d k ).
   • S71D-72 (visibility drift): drift_vis = | vis_score_t - vis_score_ref |.
   • S71D-73 (physical drift): drift_phys = w1 * | T_trans_t - T_ref | + w2 * boundary_residual_t.
   • S71D-74 (data drift): drift_data = MMD( x_t, x_ref ) or KS( feat_t, feat_ref ) (declare the statistical measure).
   • S71D-75 (topology drift): drift_graph = ( || L_t - L_ref ||_F / || L_ref ||_F ) (graph Laplacian L).
   • S71D-79 (aggregation):
     drift_score = α*drift_spec + β*drift_vis + γ*drift_phys + δ*drift_data + ζ*drift_graph,
     with normalized coefficients α…ζ persisted.

V. Metrology Pipeline M71-D*

• Ready: fix reference ref@ts0, window Δt, sampling strategy & measures; load RefCond.
• Compute: in parallel, produce spectral, physical, visibility, inversion, and runtime metric families; compute delta_form for dual forms.
• Aggregate: within window W, compute quantiles and sliding statistics (p50 / p90 / p99, EWMA); produce drift_* and drift_score.
• Check: apply C71-* contracts; attach evidence URIs and annotations for violations.
• Persist: write to manifest.lens.metrics.* and panel snapshot hashes; sign and publish.

VI. Contract & Threshold Suggestions C71D-*

• C71D-01 TwoFormDelta: delta_form_p99 ≤ tol_form (default tol_form ∈ [0.01, 0.05], business-dependent).
• C71D-11 SpectralGainBound: gain_sup ≤ 1.2; passband_ripple ≤ 0.05; leakage ≤ 0.02.
• C71D-21 TransmissionBalance: | T_trans - T_ref | ≤ 0.02; boundary_residual ≤ 0.01.
• C71D-31 VisibilityHealth: vis_score ≥ 0.6; | los_ratio - los_ratio_ref | ≤ 0.1.
• C71D-41 InversionQuality: err_rec_p90 ≤ 0.15; sparsity ≤ s_max (task-specific).
• C71D-51 Reliability: ece ≤ 0.03; reliability_gap ≤ 0.05.
• C71D-61 RuntimeSLO: latency_p99 ≤ L_max; err_rate ≤ 1e−3; cache_hit ≥ 0.8.
• C71D-71 DriftGuard: drift_score ≤ τ_drift; if any component exceeds its sub-threshold, enter the degradation strategy.

VII. Implementation Bindings I71- (Metrics & Drift)*

• compute_lens_metrics(x, y_spec, y_var, K_eff, graph, RefCond) -> metrics
• estimate_spectral_response(K_eff, graph) -> { G(k), gain_sup, ripple, leakage }
• measure_physical_consistency(x, y, B, M) -> { T_trans, boundary_residual, conservation_residual }
• calc_visibility(mask, los_sets) -> { vis_score, los_ratio, vis_dice }
• infer_inversion_quality(x_hat, x, Phi) -> { err_rec, sparsity }
• aggregate_runtime_sli(stream) -> { latency_p{q}, cpu_pct, mem_pct, err_rate, cache_hit }
• compute_drift(metrics_t, metrics_ref, graph_t, graph_ref, policy) -> { drift_*, drift_score }
  Invariants: check_dim(*) == true; rho_bound < 1 (stability); non_decreasing(ts); evidence URIs resolvable with verifiable hashes.

VIII. Cross-References

• Lens kernels & spectral domain: Chapter 5.
• Visibility & occlusion: Chapter 4.
• De-lensing / inversion: Chapter 7.
• Multi-layer composition & stability: Chapter 8.
• Learning & reliability: Chapter 9.
• Physical consistency: Chapter 10.
• Runtime panels & SLOs: Chapter 11.
• Manifest persistence: Chapter 15 & Appendix C.
• Contract library: Appendix B (C71-*).

IX. Quality & Risk Control

1. Example SLOs: delta_form_p99 ≤ 0.02, latency_p99 ≤ 50 ms, drift_score ≤ 0.3.
2. Drift response tiers:
   • 0.3 < drift_score ≤ 0.5: trigger recalibration candidates; increase EWMA decay.
   • 0.5 < drift_score ≤ 0.7: enable conservative kernels (reduced gain); locally revert to K_baseline.
   • drift_score > 0.7: hard rollback + human audit; freeze learning updates.
3. Audit: log every threshold change with strategy-card version & evidence; verify panel snapshot ↔ manifest signature consistency.

Summary

• This appendix specifies lens metrics and drift conventions, thresholds, and workflows, enabling an end-to-end measurement loop from spectral → physical → visibility → learning → runtime.
• Aligned with manifest.lens, C71-* contracts, and I71-* interfaces, it ensures traceability, replayability, and rollbackability.