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---
schema_version: 1
baseline: xl_mimo_beam_training
reference:
doi: 10.1109/TMC.2024.3462960
evidence_level: educational-surrogate
paper_figure_parity: false
model: >-
Compact encoder-decoder CNN mapping synthetic estimated near-field CSI to
constant-modulus phases, trained with a Hermitian coherent-rate loss.
assumptions:
- Synthetic spherical-wave channels replace the unavailable paper dataset.
- Beam coefficients have unit element magnitude and norm square Nt.
- The rate normalization is SNR divided by the actual antenna count.
- The full-digital channel direction is a reference, not an analog optimum.
- External finite phase coordinates wrap with period 2 under exp(j*pi*v).
parameters:
seed: 20260717
certificate_antenna_count: 64
low_snr_antenna_count: 256
coherent_test_snr_linear: 1.0
tiny_channel_element_magnitude: 1.0e-6
dynamic_range_channel_magnitudes:
- 1.0e-30
- 1.0e20
maximum_checked_geometry_distance_meter: 1.0e308
exact_cancellation_large_term: 1.0e280
exact_cancellation_residual: 1.0e-60
pre_rounding_product_cancellation_component: 1.7e308
final_gradient_cancellation_residual: 1.0e-300
final_gradient_snr_linear: 1.0e300
oracle:
type: closed-form-coherent-gain-and-seeded-repeatability
expected:
coherent_rate_64_antennas_bit_per_second_per_hz: 6.022367813028454
tiny_rate_bit_per_second_per_hz: 3.6932993042030045e-10
complex128_cancellation_rate_bit_per_second_per_hz: 7.213475204444818e-21
complex64_1e-30_rate_is_positive: true
complex64_1e20_rate_is_finite: true
huge_cancellation_tail_rate_bit_per_second_per_hz: 0.41503749927884376
subrange_cancellation_tail_rate_bit_per_second_per_hz: 4.808983469629878e-21
overflowing_individual_products_cancel_to_zero: true
extreme_cancellation_gradient_rate_bit_per_second_per_hz: 4.808983469629878e-301
extreme_cancellation_phase_gradient:
- 3.021573427884796e280
- -3.021573427884796e280
- 0.0
nonrepresentable_final_gradient_is_explicit: true
upstream_scaled_phase_gradient:
- 3.021573427884796e307
- -3.021573427884796e307
- 0.0
original_dtype_gradient_overflow_is_explicit: true
roundable_float32_subnormal_phase_gradient:
- -1.401298464324817e-45
- 1.401298464324817e-45
roundable_float32_upper_edge_phase_gradient:
- -3.4028234663852886e38
- 3.4028234663852886e38
seeded_synthetic_data_repeatability: bitwise
extreme_finite_geometry_is_supported: true
tolerances:
coherent_rate_absolute: 1.0e-6
tiny_rate_absolute: 3.0e-15
dynamic_range_relative: 2.0e-7
subrange_cancellation_relative: 2.0e-13
final_gradient_relative: 3.0e-13
evidence:
command: >-
python scripts/verify_simulation_baseline.py
xl_mimo_beam_training --json
certificate_checks:
- complex128_cancellation_residual_preserved
- complex64_large_channel_rate_is_finite
- complex64_tiny_channel_rate_is_positive
- final_gradient_scaling_precedes_range_check
- final_rate_autograd_is_finite_after_extreme_cancellation
- nondefault_array_normalization
- overflowing_exact_products_cancel_before_rounding
- roundable_float32_subnormal_gradient_is_preserved
- roundable_float32_upper_edge_gradient_is_preserved
- seeded_channel_data_is_repeatable
- subrange_tail_survives_1e280_exact_cancellation
- tiny_positive_rate_preserved
- target_dtype_gradient_overflow_is_explicit
- unit_tail_survives_1e200_exact_cancellation
- unrepresentable_final_gradient_is_explicit
checks:
- Hermitian coherent combining with a nondefault array size
- log1p preservation of a tiny positive float32 rate
- seeded perfect and estimated synthetic CSI repeatability
- scale-safe rates for cancellation, tiny, and large channel counterexamples
- compensated permutation-invariant sum for a unit tail between 1e200 terms
- exact binary64 superaccumulation for a 1e-60 tail between 1e280 terms
- exact pre-rounding complex products whose individually overflowing terms cancel
- final-rate autograd scaling for a 1e-300 tail between complex 1e280 terms
- upstream scaling before the final binary64 gradient range decision
- round-to-nearest preservation of a 0.75-minsub float32 phase gradient
- round-to-nearest preservation just above the finite float32 maximum
- explicit rejection when a requested final gradient exceeds binary64 or
the original complex64/float32 input dtype
- explicit float32 feature conversion domain
- overflow-safe exact spherical distance and reduced phase at 1e308 meters
limitations:
- The official paper dataset and trained checkpoint are not redistributed.
- No paper curve, learned-model quality, or optimality claim is certified.
- The certificate does not train a production model.
- SNR is a fixed condition; gradients are defined for channels and phases only.
- The exact loss synchronizes through CPU binary-integer arithmetic and is a
reference training primitive, not a high-throughput production kernel.
- Requested final gradients outside binary64 or the original input dtype
raise an explicit range error during backward propagation.