Bit-weight versus polynomial/MLP spectral comparison

exp_cal10_foreground_bitweights.py compares uncorrected output, bit weights, static/history fifth-degree polynomials and a history MLP on identical test captures. Its two device families answer different questions; do not pool them into one model ranking. All results are behavioral, not measured silicon.

For both smooth nonlinearity and bit-weight mismatch in the same converter path, with standalone versus cascaded correction, see packaged COMBINED_FOREGROUND.md and exp_cal11_combined_foreground.py.

Run

From the copied examples directory, the standalone SAR comparison is:

python 12_foreground/exp_cal10_foreground_bitweights.py --output output/bitweight_spectral

To also compare the previously saved smooth-front-end models:

python 12_foreground/exp_cal10_foreground_bitweights.py --smooth-baseline output/foreground_acceptance --smooth-mixed output/excitation_mlp --output output/bitweight_spectral_all

The smooth mixed run must include --retrain-mlp; see FOREGROUND_WORKFLOWS.md. Nonempty output directories are rejected. Capture manifests, saved models, diagnostics, per-condition metrics, summaries, example spectra, source snapshots and input hashes are saved. Test evaluation reloads the frozen JSON models.

Replay and verify the completed run:

python 12_foreground/audit_foreground_bitweights.py --directory output/bitweight_spectral_all --output output/bitweight_spectral_audit.json

The audit checks hashes, split separation, saved validation selection and frozen test outputs. It independently recalculates spectral ratios using a full complex FFT and recomputes aggregate statistics. For smooth-front-end comparisons, keep the original baseline and mixed-model directories at their original paths: the audit verifies those inputs using the absolute paths saved in configuration.json.

Models and observation contracts

Method	Training observations	Runtime computation
raw	None	Nominal output reconstruction
bits_reference	Binary columns and the same aligned monitor-reference rows as polynomial/MLP	Offset plus weighted sum of current bit columns
bits_sine	One full training sine record; known frequency; no external reference	Frozen offset plus weighted sum of current bit columns
poly5_static	Current scalar output and monitor reference	Six-coefficient polynomial
poly5_history	Current output plus three previous outputs and monitor reference	Full fifth-degree basis, 126 coefficients
mlp_history	Same four scalar features/reference, independent validation	Frozen affine baseline plus 16-unit tanh residual network
known_weights_control	Evaluator-only actual SAR weights	Diagnostic digital reconstruction, never a fitted candidate

The matched-data comparison is bits_reference versus polynomial/MLP. bits_reference is a degree-one fit of the binary feature matrix, with intercept, training standardization and ridge=1e-10. In original bit units it is exactly offset + sum(w_j * b_j[n]); no powers or history of the bits are used. It is mathematically the affine bit-weight model, although a fitted weight is not automatically an independently identifiable physical capacitance.

bits_sine calls the public calibrate_weight_sine, with explicit normalized frequency, force_search=False, harmonic_order=1. It uses the largest-amplitude single-tone record already present in training (chosen by input amplitude, not test performance), at its full sample rate. scale_calibration_output fixes the weight sum to nominal; the fitted DC is removed. This scaling does not affect SNDR/SFDR, but does not establish absolute gain accuracy. It is a practical separate calibration protocol, not a matched training-data/label budget. The solver’s fitted-residual snr_db is never used as test SNDR.

Device families

Signal-generator front end: reuse the original static nonlinearity and coarse-quantized previous-sample feedback from current exp_cal03/05, along with their test records. Polynomial/MLP models are frozen within each replay. The old custom cubic-plus-FIR runs are historical and must not be replayed against the new device. Both input runs must carry the current model identity; rerun them together before using --smooth-baseline / --smooth-mixed. The new supervised bit fit uses exactly the saved mixed training records, stride and monitor reference. Fourteen binary columns are decoded from the observable final midrise code. These do not introduce internal subcodes or identify capacitor mismatch in this model; they are a restricted final-code correction. In particular, current-bit weights cannot generally invert memory.

SAR MSB mismatch: use public sar_convert, with 14 binary weights, or 15 decisions obtained by repeating the third largest weight. Normalize by the sum plus one LSB, then increase the actual MSB weight by 1%. Nominal digital weights remain unchanged. Input range is [-1,1]; sample noise is 1e-5 RMS, with no comparator noise or other analog nonlinearity/memory. Nominal scalar reconstruction includes a half-LSB midpoint. Bit methods receive internal decision columns; polynomial/MLP receive only the nominally reconstructed scalar and its history. Redundant decisions can collapse to the same nominal scalar, so the observation advantage of bit methods is part of this comparison.

Strict binary mismatch can create conversion gaps. Even reconstruction using actual weights cannot generally restore all lost resolution. The known-weight control shows this limit; it is not a universal optimum or noiseless-input result. Repeated-weight redundancy supplies correction margin in this specific model. The same deterministic 1% error is used for all seeds; seed variation is stimulus, noise and training initialization, not a chip-mismatch Monte Carlo.

Default SAR budgets: 64 training and eight validation records, 8192 samples each, stride eight, giving 65,536 training and 8192 validation rows. Half the records are single tones, half two tones. Training/validation/test tone bins are disjoint. Peak budgets span 0.05–0.90, frequency approximately 0.02–0.45 fs. MLP L2=1e-6, 16 hidden units, maximum 1000 L-BFGS-B iterations; independent reference validation MSE selects an observed iterate. Report termination status rather than equating the iteration limit with convergence. The saved smooth MLP retains its original 200-iteration budget. Cross-device scores are not a controlled iteration sweep.

SNDR, SFDR and multi-tone metrics

Each case tests 15 coherent single tones: amplitude 0.1/0.5/0.85 at approximately 0.031/0.113/0.239/0.371/0.467 fs. The last frequency is outside the training range. Two- and three-tone tests are reported separately. All test records have 8192 usable samples at defaults, after warmup and history alignment; no test refitting.

For a single tone, remove DC, use a rectangular window, and calculate:

SNDR = 10 log10(fundamental power / all other non-DC spectral power)
SFDR = 10 log10(fundamental power / largest unwanted spectral-bin power)

Use the full Nyquist band, include all harmonics in SNDR’s denominator, and do not double the Nyquist bin in one-sided power. Coherent tones need no neighboring signal bins. Single-tone values are cross-checked with public analyze_spectrum using win_type='boxcar', side_bin=0. If a failed correction makes a spur larger than the known input fundamental, retain the known-bin result and flag that the automatic peak finder would select another line. Do not silently reinterpret it.

For multi-tone input, spectral_ratio_db uses total desired-tone power over remaining non-DC power. spur_ratio_db uses the strongest desired tone over the largest unwanted bin. sndr_db and sfdr_db are left empty for these rows to avoid confusing this definition with a single-tone test. Intermodulation products outside desired bins remain in noise/distortion; any product coinciding with a desired bin cannot be separated by this FFT measurement.

error_snr_db remains available: it compares output with evaluator-only clean input without gain, phase or DC adjustment. Good spectral ratios alone do not prove absolute accuracy, correct phase, or successful inversion of memory. Summaries first average conditions within each seed, then report mean and sample SD across seeds. Inspect per-amplitude/frequency rows as well as aggregate means.

The mathematical derivation and physical-literature boundaries for polynomial and MLP correction are in packaged FOREGROUND_THEORY.md. SAR decision and reconstruction conventions are defined by adctoolbox.models.sar and the existing 05_debug_digital/exp_d17_sar_msb_error_binary_vs_repeat_calibration.py example.