08 — Hyper-Optimization

The reference crate first shipped a hand-picked shield config (112 Givens passes, 7-bit feedback). This file records how the optimize module replaces that guess with a derived, robustness-verified optimum, and what it found. All numbers are SYNTHETIC / L0, reproduced by cargo test -p wifi-densepose-privshield.

1. What is being optimized, and against what

Two knobs, two objectives, one hard constraint:

Knob	Costs	Does it trade against privacy?
`feedback_bits` (angle resolution)	Throughput: residual falls with bits, feedback airtime rises with bits	No — the keyed rotation is applied regardless of resolution
`givens_passes` (rotation mixing)	Compute only	Yes — more mixing ⇒ lower re-ID

Constraint: re-ID must collapse into the chance band 1/N · 2 + 0.03 — and it must do so robustly: for both attacker metrics (Euclidean and Cosine) and both identity counts (N = 16 and N = 32, the harder, lower-chance case).

The key structural fact: rotation mixing is throughput-free. The per-session rotation is derived from the shared link secret on both ends (like MIMOCrypt) — it is never transmitted — so extra Givens passes cost compute, not airtime. That means privacy margin is essentially free; the only throughput tradeoff lives in feedback_bits.

2. Throughput is a 1-D problem with an interior optimum

Because the residual falls with bits while feedback airtime rises, throughput has a genuine interior optimum in feedback_bits (LinkModel, default SNR 20 dB, feedback_overhead_per_bit = 0.0008):

bits	throughput ratio
1	0.9681
2	0.9757
3	0.9769 ← unconstrained optimum
4	0.9766
5	0.9760 ← shipped (spec-allowed)
7	0.9744 (the old hand-picked value)
9	0.9728
12	0.9704

The unconstrained optimum is 3 bits — which coincides with the DySPAN-2026 MEASURED finding that ~3-bit feedback is the privacy–utility sweet spot, because the receiver compensates the keyed rotation and extra bits mostly buy airtime. 802.11 compressed beamforming quantizes ψ/φ to roughly 5–9 bits, so the shipped shield uses the throughput-best spec-allowed value, 5 bits (0.9760), rather than the out-of-spec 3-bit optimum. Either way it beats the old 7-bit choice.

3. Mixing: the minimum robust budget, and a free margin

Worst-case shield-on re-ID vs. givens_passes (bits = 5; worst over Euclidean and Cosine):

passes	re-ID @ N=16	re-ID @ N=32	robust collapse?
16	0.75	0.62	no
24	0.50	0.35	no
32	0.20	0.14	no (N=32 band is 0.0925)
48	0.12	0.057	yes ← proven minimum
64	0.078	0.044	yes
96	0.047	0.018	yes ← shipped (2× margin)
112	0.078	0.042	yes (the old default — no better than 96)

The proven minimum for robust collapse is 48 passes — the hand-picked 112 was 2.3× over-provisioned. Since mixing is throughput-free, the shield ships 96 passes (PRIVACY_MARGIN_FACTOR = 2 × 48, rounded up to a candidate): it drives re-ID below chance at N=16 (0.047 < 0.0625) at zero throughput cost, and is still cheaper compute than the original 112.

4. The adopted config, and why it beats the original

	Old (hand-picked)	Hyper-optimized (shipped)
Givens passes	112	96 (from proven-min 48 × 2)
Feedback bits	7	5 (spec-optimal)
Shield-on re-ID (N=16)	0.078	0.047
Throughput ratio	0.9744	0.9760
Robust across metrics & N	not checked	verified

The optimum is strictly better on privacy and throughput at once, and is now verified rather than assumed. ShieldConfig::default() is exactly the optimizer's output; the test optimize::shipped_default_equals_optimizer_output fails if they ever drift apart.

5. The Pareto frontier (and an honest note)

optimize::pareto_frontier enumerates non-dominated (worst-case re-ID, throughput) points over a pass × bits grid. In this model the frontier collapses toward the max-mixing, 5-bit point, because mixing is throughput-free — so beyond the throughput knob (bits) there is no privacy– throughput tradeoff to trace. That degeneracy is itself the finding: the only thing privacy costs here is feedback resolution, and even that is cheap. On real hardware, where comm/identity subspaces are only approximately separable and where more aggressive mixing may touch the data-carrying beam, this frontier is expected to open up — a hardware study (roadmap P5) will re-measure it.

6. Per-deployment adaptivity

The optimum is not one number — optimize derives it per deployment:

SNR → feedback resolution. optimal_bits_across_snr shows the unconstrained throughput-optimal resolution shifting with SNR: 4 bits at 5–10 dB, 3 bits at 20–40 dB (low SNR values fine resolution more because the Shannon capacity is near-linear there, so the residual costs more). Within the spec-allowed {5,7,9} set the choice is 5 bits across this whole range — the residual is already negligible at 5 bits — which is why the shipped shield is SNR-stable.
Identity count → mixing. adaptive_shield(base, n) derives the config for a room with n expected occupants. A notable finding: in this model the collapse budget is N-independent (min 48 passes collapses N∈{8,64} alike), because a well-mixed Haar-like rotation destroys per-identity structure regardless of how many identities there are — the budget is set by the fine-subspace dimension, not the candidate count. So adaptive_shield returns the same 96/5 across that range: the default is robust, not a point tuning.

Both are surfaced through the harness guidance --topic optimization.

7. Robustness caveats (unchanged from the threat model)

The collapse is verified against two classifiers and two N; a learned attacker on real captures must still be checked (P2/P5).
feedback_bits affects only throughput in this model, not re-ID; on hardware, coarse quantization also adds obfuscation, which would help privacy — the model conservatively ignores that.
All optimization results are SYNTHETIC until a hardware witness exists.

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