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#!/usr/bin/env python3
"""Deterministic locality and numerical audit for the digital CLLN ladder."""
from __future__ import annotations
import inspect
import json
from pathlib import Path
import sys
import numpy as np
ROOT = Path(__file__).resolve().parents[1]
sys.path.insert(0, str(ROOT))
import sdil.coupled_ladder as ladder # noqa: E402
from sdil.coupled_ladder import ( # noqa: E402
DigitalTrainingConfig,
make_scaled_grid,
solve_linear_grid_state,
tile_figure5_gates,
train_digital_grid,
)
from sdil.physical_grid import ( # noqa: E402
GridCircuit,
GridSquareLawImperfection,
RingClassificationDataset,
edge_voltage_drops,
output_difference,
)
def maximum_unknown_kcl_residual(
circuit: GridCircuit, gates: np.ndarray, voltages: np.ndarray
) -> float:
conductances = circuit.conductance_scale * (
gates - circuit.threshold_voltage)
currents = np.zeros(circuit.node_count)
for conductance, (first, second) in zip(
conductances, circuit.edge_pairs
):
current = conductance * (voltages[first] - voltages[second])
currents[first] += current
currents[second] -= current
fixed = set(circuit.source_nodes)
unknown = [
node for node in range(circuit.node_count) if node not in fixed
]
return float(np.max(np.abs(currents[unknown])))
def main() -> None:
protocol_path = Path(
"results/physical_bias/dillavou_fig5_protocol.json")
protocol = json.loads(protocol_path.read_text())
task = next(
record for record in protocol["experiments"]
if record["method"] == "standard"
)
base_gates = np.asarray(task["initial_gates_v"], dtype=float)
dataset = RingClassificationDataset(
inputs_v=np.asarray(task["inputs_v"], dtype=float).T,
labels_v=(
2.0 * np.asarray(task["classes"], dtype=float) - 1.0
) * 0.018,
)
side4 = make_scaled_grid(4)
layout_exact = bool(
side4.source_nodes == GridCircuit().source_nodes
and side4.target_nodes == GridCircuit().target_nodes
and side4.edge_pairs == GridCircuit().edge_pairs
)
tiling_exact = bool(np.array_equal(
tile_figure5_gates(base_gates, 4), base_gates))
side32 = make_scaled_grid(32)
gates32 = tile_figure5_gates(base_gates, 32)
state32 = solve_linear_grid_state(
side32,
gates32,
side32.source_values(*dataset.inputs_v[0]),
)
kcl_residual = maximum_unknown_kcl_residual(
side32, gates32, state32)
sensitivity_indices = np.unique(np.linspace(
0, side32.edge_count - 1, 128, dtype=int))
sensitivity_step_v = 1e-5
sampled_sensitivities = []
sources32 = side32.source_values(*dataset.inputs_v[0])
for edge in sensitivity_indices:
gates_plus = gates32.copy()
gates_minus = gates32.copy()
gates_plus[edge] += sensitivity_step_v
gates_minus[edge] -= sensitivity_step_v
output_plus = output_difference(
side32,
solve_linear_grid_state(side32, gates_plus, sources32),
)
output_minus = output_difference(
side32,
solve_linear_grid_state(side32, gates_minus, sources32),
)
sampled_sensitivities.append(
(output_plus - output_minus) / (2.0 * sensitivity_step_v))
absolute_sensitivities = np.abs(np.asarray(sampled_sensitivities))
sampled_influence_fraction = float(np.mean(
absolute_sensitivities > 1e-9))
edge_count = side4.edge_count
rng = np.random.default_rng(20260829)
free_drops = rng.normal(0.0, 0.1, edge_count)
clamped_drops = rng.normal(0.0, 0.1, edge_count)
common_offset = rng.normal(0.0, 2.3, edge_count)
common_mode = GridSquareLawImperfection(
free_gain=np.ones(edge_count),
clamped_gain=np.ones(edge_count),
free_input_offset_v=np.zeros(edge_count),
clamped_input_offset_v=np.zeros(edge_count),
multiplier_output_offset_v_per_s=common_offset,
)
ideal_rate = common_mode.ideal_rate(
side4.measured_learning_rate, free_drops, clamped_drops)
observed_rate = common_mode.observed_rate(
side4.measured_learning_rate, free_drops, clamped_drops)
neutral_rate = common_mode.neutral_bias(
side4.measured_learning_rate, free_drops)
common_mode_cancellation_error = float(np.max(np.abs(
observed_rate - neutral_rate - ideal_rate)))
state_dependent = GridSquareLawImperfection.sample_appendix_c(
edge_count, 20260829)
state_one = rng.normal(0.0, 0.05, edge_count)
state_two = rng.normal(0.0, 0.15, edge_count)
bias_one = state_dependent.neutral_bias(
side4.measured_learning_rate, state_one)
bias_two = state_dependent.neutral_bias(
side4.measured_learning_rate, state_two)
state_dependent_bias_rms = float(np.sqrt(np.mean(np.square(
bias_one - bias_two))))
ideal = GridSquareLawImperfection.ideal(edge_count)
config = DigitalTrainingConfig(
epochs=20, record_every=5, learning_time_seconds=0.01)
trajectories = {
method: train_digital_grid(
side4,
base_gates,
dataset,
ideal,
method=method,
config=config,
noise_seed=20260829,
)
for method in ("clean", "matched_noise", "raw", "sdil")
}
reference_gates = np.asarray(trajectories["clean"]["final_gates_v"])
ideal_path_max_gate_difference = float(max(
np.max(np.abs(
np.asarray(trajectories[method]["final_gates_v"])
- reference_gates
))
for method in ("matched_noise", "raw", "sdil")
))
ideal_path_trace_identity = bool(all(
trajectories[method]["trace"] == trajectories["clean"]["trace"]
for method in ("matched_noise", "raw", "sdil")
))
sdil_cost_identity = bool(
trajectories["sdil"]["neutral_scalar_observations"]
== trajectories["sdil"]["local_edge_updates"]
)
source = inspect.getsource(ladder)
forbidden_source_tokens = {
token: token in source
for token in ("import torch", "autograd", ".backward(")
}
no_autodiff_dependency = not any(forbidden_source_tokens.values())
checks = {
"released_side4_layout_exact": layout_exact,
"released_side4_gate_vector_exact": tiling_exact,
"side32_kcl_residual_below_1e_12": kcl_residual < 1e-12,
"side32_sampled_edges_influence_output": (
sampled_influence_fraction == 1.0),
"common_mode_cancellation_below_1e_12": (
common_mode_cancellation_error < 1e-12),
"default_imperfection_is_state_dependent": (
state_dependent_bias_rms > 1e-6),
"ideal_paths_have_identical_gates": (
ideal_path_max_gate_difference == 0.0),
"ideal_paths_have_identical_traces": ideal_path_trace_identity,
"one_neutral_scalar_observation_per_edge_update": (
sdil_cost_identity),
"no_autodiff_dependency": no_autodiff_dependency,
}
report = {
"analysis": "digital_coupled_ladder_locality_audit",
"autodiff_used": False,
"source_protocol": str(protocol_path),
"checks": checks,
"measurements": {
"side32_maximum_unknown_kcl_residual_a": kcl_residual,
"side32_sampled_edge_count": len(sensitivity_indices),
"side32_sampled_output_sensitivity_min_abs": float(
np.min(absolute_sensitivities)),
"side32_sampled_output_sensitivity_median_abs": float(
np.median(absolute_sensitivities)),
"side32_sampled_output_sensitivity_max_abs": float(
np.max(absolute_sensitivities)),
"side32_sampled_influence_fraction_above_1e_9": (
sampled_influence_fraction),
"common_mode_cancellation_max_abs_v_per_s": (
common_mode_cancellation_error),
"state_dependent_neutral_bias_difference_rms_v_per_s": (
state_dependent_bias_rms),
"ideal_path_max_gate_difference_v": (
ideal_path_max_gate_difference),
"sdil_local_edge_updates": (
trajectories["sdil"]["local_edge_updates"]),
"sdil_neutral_scalar_observations": (
trajectories["sdil"]["neutral_scalar_observations"]),
"forbidden_source_tokens": forbidden_source_tokens,
},
"gate": "pass" if all(checks.values()) else "fail",
}
output = Path("results/coupled_ladder/x0_locality_audit.json")
output.parent.mkdir(parents=True, exist_ok=True)
output.write_text(json.dumps(report, indent=2) + "\n")
print(json.dumps(report, indent=2))
print(f"wrote {output}")
if report["gate"] != "pass":
raise SystemExit(1)
if __name__ == "__main__":
main()
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