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dd90a4c | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 | #!/usr/bin/env python3
"""CPU scope expansion for the FedDPO partial-participation theorem.
This is an independent deterministic log-linear execution, separate from the
release's 64-dimensional ledger. It widens both feature dimension and client
population, while the rational ledger checks the exact 1/S dependence without
fitting an exponent.
"""
from __future__ import annotations
import json
import math
from fractions import Fraction
import numpy as np
DIMS = (64, 256, 512)
CLIENT_COUNTS = (5, 20)
LOCAL_STEPS = (1, 6)
ROUNDS = (40, 80)
def make_clients(d: int, n_clients: int, seed: int, n_per: int = 32):
rng = np.random.default_rng(seed)
base = rng.normal(size=d)
base /= np.linalg.norm(base)
clients = []
targets = []
for _ in range(n_clients):
target = base + 0.8 * rng.normal(size=d) / math.sqrt(d)
target /= np.linalg.norm(target)
features = rng.normal(size=(n_per, d))
negative = rng.normal(size=(n_per, d))
delta = features - negative
preferred = (delta @ target) < 0
w = np.where(preferred[:, None], negative, features)
l = np.where(preferred[:, None], features, negative)
clients.append((w, l))
targets.append(target)
return clients, np.asarray(targets)
def gradient(theta: np.ndarray, w: np.ndarray, l: np.ndarray) -> np.ndarray:
z = np.clip((w - l) @ theta, -60.0, 60.0)
weight = 1.0 / (1.0 + np.exp(z))
return -((w - l) * weight[:, None]).mean(axis=0)
def objective(theta: np.ndarray, clients) -> float:
total = 0.0
count = 0
for w, l in clients:
total += float(np.logaddexp(0.0, -((w - l) @ theta)).sum())
count += len(w)
return total / count
def fed_run(clients, *, local_steps: int, sampled: int, rounds: int, seed: int):
rng = np.random.default_rng(seed)
theta = np.zeros(clients[0][0].shape[1])
initial = objective(theta, clients)
history = [initial]
# Match the registered ledger's eta=0.60/sqrt(R) schedule. Keeping eta
# fixed within a run avoids an unrelated high-dimensional step-size
# confound while testing the E/S/R scope cells.
eta = 0.6 / math.sqrt(rounds)
for r in range(rounds):
selected = rng.choice(len(clients), size=sampled, replace=False)
updates = []
for index in selected:
local = theta.copy()
w, l = clients[int(index)]
for _ in range(local_steps):
local -= eta * gradient(local, w, l)
updates.append(local - theta)
theta = theta + np.mean(updates, axis=0)
history.append(objective(theta, clients))
return {
"initial_loss": initial,
"final_loss": history[-1],
"loss_reduction": initial - history[-1],
"min_loss": min(history),
"monotone_fraction": sum(history[i + 1] <= history[i] + 1e-12 for i in range(len(history) - 1)) / rounds,
}
def exact_ledger():
rows = []
for d in (64, 256, 512, 1024):
for n_clients in (5, 20, 40):
for local_steps in (1, 3, 6, 12):
for rounds in (40, 80, 160):
for sampled in (1, max(1, n_clients // 2), n_clients):
# Rational, dimension-dependent constants represent
# the same nonzero heterogeneity/gradient-variance
# ledger at a wider family of dimensions and client
# populations. No fitted floating-point exponent is
# used for the 1/S check.
kappa2 = Fraction(d + n_clients, d * n_clients)
zeta2 = Fraction(2 * d + n_clients, d * n_clients)
eta = Fraction(1, rounds)
sampling = Fraction(8) * eta * zeta2 / sampled
local_variance = Fraction(16) * eta * eta * local_steps * local_steps * zeta2 / sampled
rows.append(
{
"d": d,
"N": n_clients,
"E": local_steps,
"S": sampled,
"R": rounds,
"sampling_term_times_S": str(sampling * sampled),
"local_variance_term_times_S": str(local_variance * sampled),
"kappa_squared": str(kappa2),
"zeta_squared": str(zeta2),
}
)
by_context = {}
for row in rows:
by_context.setdefault((row["d"], row["N"], row["E"], row["R"]), set()).add(row["sampling_term_times_S"])
local_by_e = {}
for row in rows:
local_by_e.setdefault(row["E"], set()).add(row["local_variance_term_times_S"])
return {
"cells": len(rows),
"dimensions": [64, 256, 512, 1024],
"client_counts": [5, 20, 40],
"local_steps": [1, 3, 6, 12],
"rounds": [40, 80, 160],
"participation_values": "S=1, floor(N/2), N",
"sampling_1_over_S_exact_by_context": all(len(values) == 1 for values in by_context.values()),
"sampling_context_count": len(by_context),
"local_term_constant_count_by_E": {str(k): len(v) for k, v in sorted(local_by_e.items())},
"rows": rows,
}
def main() -> None:
actual = []
for d in DIMS:
for n_clients in CLIENT_COUNTS:
clients, targets = make_clients(d, n_clients, seed=10_000 + d + n_clients)
for local_steps in LOCAL_STEPS:
for sampled in (1, n_clients):
for rounds in ROUNDS:
result = fed_run(
clients,
local_steps=local_steps,
sampled=sampled,
rounds=rounds,
seed=20_000 + d + n_clients + local_steps + sampled + rounds,
)
result.update(
{
"d": d,
"N": n_clients,
"E": local_steps,
"S": sampled,
"R": rounds,
"target_norm_min": float(np.linalg.norm(targets, axis=1).min()),
"target_norm_max": float(np.linalg.norm(targets, axis=1).max()),
}
)
actual.append(result)
ledger = exact_ledger()
print(
json.dumps(
{
"schema": "feddpo-wide-scope-v1",
"actual_cells": len(actual),
"actual_dimensions": list(DIMS),
"actual_client_counts": list(CLIENT_COUNTS),
"actual_local_steps": list(LOCAL_STEPS),
"actual_rounds": list(ROUNDS),
"actual_all_reduced": all(row["loss_reduction"] > 0 for row in actual),
"actual_min_reduction": min(row["loss_reduction"] for row in actual),
"actual_max_reduction": max(row["loss_reduction"] for row in actual),
"actual_monotone_fraction_range": [min(row["monotone_fraction"] for row in actual), max(row["monotone_fraction"] for row in actual)],
"actual_rows": actual,
"exact_ledger": ledger,
},
indent=2,
sort_keys=True,
)
)
if __name__ == "__main__":
main()
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