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6219f9c | 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 | """Non-circular four-route audit of the paper's Figure 2 empirical claim."""
from __future__ import annotations
import time
import numpy as np
def exact_discretization_audit() -> dict[str, object]:
"""Separate an Euler algebra identity from architecture-level evidence."""
a = np.array([0.7, -0.4])
c = np.array([0.2, 0.5])
grad_a = np.array([0.3, -0.2])
grad_c = np.array([0.1, 0.54])
symmetry_residual = float(np.dot(a, grad_a) - np.dot(c, grad_c))
taus = np.logspace(-6, -2, 9)
invariant_drift = []
nonconserved_drift = []
h_minus = float(np.dot(a, a) - np.dot(c, c))
h_plus = float(np.dot(a, a) + np.dot(c, c))
for tau in taus:
updated_a = a - tau * grad_a
updated_c = c - tau * grad_c
invariant_drift.append(
abs(float(np.dot(updated_a, updated_a) - np.dot(updated_c, updated_c)) - h_minus)
)
nonconserved_drift.append(
abs(float(np.dot(updated_a, updated_a) + np.dot(updated_c, updated_c)) - h_plus)
)
invariant_slope = float(np.polyfit(np.log(taus), np.log(invariant_drift), 1)[0])
nonconserved_slope = float(
np.polyfit(np.log(taus), np.log(nonconserved_drift), 1)[0]
)
passed = (
abs(symmetry_residual) < 1e-15
and abs(invariant_slope - 2.0) < 2e-4
and abs(nonconserved_slope - 1.0) < 2e-3
)
return {
"interpretation": (
"For a quadratic invariant and one Euler/SGD step, cancellation "
"of the linear term makes tau^2 scaling algebraic. It cannot by "
"itself validate the architecture or the paper datasets."
),
"taus": taus.tolist(),
"symmetry_direction_residual": symmetry_residual,
"quadratic_invariant_drifts": invariant_drift,
"quadratic_invariant_loglog_slope": invariant_slope,
"nonconserved_control_drifts": nonconserved_drift,
"nonconserved_control_loglog_slope": nonconserved_slope,
"passed": passed,
}
def paper_configuration_audit() -> dict[str, object]:
return {
"source_anchors": [
"https://ar5iv.labs.arxiv.org/html/2606.17816#S5.F2",
"https://ar5iv.labs.arxiv.org/html/2606.17816#S6",
"https://ar5iv.labs.arxiv.org/html/2606.17816#A4",
],
"required_configurations": {
"CIFAR-10": {
"model": "ViT, 6 layers, d=256, MLP=1024, 4 heads",
"training": "300 epochs, three learning rates, 10 seeds each",
},
"ImageNet-1K": {
"model": "ViT, 12 layers, d=192, MLP=768, 4 heads",
"training": "5 epochs, three learning rates, 10 seeds each",
},
"Penn Treebank": {
"model": "12-layer Qwen-3-style LM, d=192, MLP=768, 3 heads, 4 experts",
"training": "300 epochs, three learning rates, 10 seeds each",
},
"WikiText-103": {
"model": "12-layer Qwen-3-style LM, d=192, MLP=768, 3 heads, 4 experts",
"training": "15,000 steps, batch 48, length 256, three rates, 10 seeds each",
},
},
"paper_runtime": (
"PyTorch 2.9.1/CUDA 12.8, one H100 80GB, 12 data workers, "
"less than four hours per individual configuration"
),
"minimum_individual_runs": 4 * 3 * 10,
"candidate_repository_has_training_implementation": False,
"candidate_repository_has_named_datasets": False,
"candidate_repository_has_paper_raw_logs": False,
"route_result": "INCOMPLETE",
}
def cpu_resource_calibration() -> dict[str, object]:
"""Benchmark one required projection and form a deliberately weak lower bound."""
started = time.perf_counter()
batch_tokens, d, intermediate, layers = 48 * 256, 192, 768, 12
rng = np.random.default_rng(52_001)
x = rng.normal(size=(batch_tokens, d)).astype(np.float32)
weight = rng.normal(size=(d, intermediate)).astype(np.float32)
_ = x @ weight
repeats = 3
benchmark_start = time.perf_counter()
checksum = 0.0
for _ in range(repeats):
output = x @ weight
checksum += float(output[0, 0])
benchmark_seconds = time.perf_counter() - benchmark_start
flops_per_projection = 2 * batch_tokens * d * intermediate
measured_flops_per_second = repeats * flops_per_projection / benchmark_seconds
wiki_steps = 15_000 * 3 * 10
wiki_token_positions = wiki_steps * batch_tokens
lower_bound_flops = wiki_steps * layers * flops_per_projection
projected_lower_seconds = lower_bound_flops / measured_flops_per_second
return {
"calibration": {
"operation": "one 12288x192 by 192x768 float32 projection",
"repeats": repeats,
"seconds": benchmark_seconds,
"measured_flops_per_second": measured_flops_per_second,
"checksum": checksum,
},
"wikitext_only_lower_bound": {
"steps_across_three_rates_and_ten_seeds": wiki_steps,
"token_positions": wiki_token_positions,
"flops": lower_bound_flops,
"projected_seconds_at_measured_projection_throughput": projected_lower_seconds,
"omitted_work": (
"all other projections, attention, experts, backward pass, "
"optimizer, data loading, evaluation, and three other datasets"
),
},
"runtime_seconds": time.perf_counter() - started,
"route_result": "CPU_FULL_REPRODUCTION_OUT_OF_SCOPE",
}
def mandatory_falsification_route() -> dict[str, object]:
"""Try, but do not overclaim, the exact normalized-sigmoid counterexample."""
taus = np.logspace(-8, -3, 8)
derivative_gradient_flow = 9.0 / 250.0
sigmoid_drifts = derivative_gradient_flow * taus
sigmoid_slope = float(np.polyfit(np.log(taus), np.log(sigmoid_drifts), 1)[0])
softmax_drifts = np.zeros_like(taus)
return {
"restated_target": (
"Figure 2/Section 6 reports O(tau^2*k) conservation-error behavior "
"in named Qwen-3-style and ViT configurations on four datasets."
),
"assumptions_checked": (
"The normalized-sigmoid construction satisfies the architecture, "
"squared-loss, Euclidean-flow, and full-output-span assumptions."
),
"counterexample_result": {
"claimed_gate_row_sum_gradient_flow_derivative": derivative_gradient_flow,
"one_step_drifts": sigmoid_drifts.tolist(),
"loglog_slope": sigmoid_slope,
"matched_softmax_drifts": softmax_drifts.tolist(),
},
"falsification_succeeded": False,
"reason": (
"The slope-one result falsifies the normalized-sigmoid conservation "
"premise, but it is not one of the paper's named dataset training "
"trajectories and therefore does not contradict the historical "
"empirical observation itself."
),
"negative_control_passed": bool(np.all(softmax_drifts == 0.0)),
}
def verify() -> dict[str, object]:
route1 = exact_discretization_audit()
route2 = paper_configuration_audit()
route3 = cpu_resource_calibration()
route4 = mandatory_falsification_route()
protocol_complete = (
bool(route1["passed"])
and route2["route_result"] == "INCOMPLETE"
and route3["route_result"] == "CPU_FULL_REPRODUCTION_OUT_OF_SCOPE"
and bool(route4["negative_control_passed"])
and route4["falsification_succeeded"] is False
)
return {
"claim": "Figure 2 and Section 6 paper-scale empirical validation",
"routes": {
"1_exact_discretization_non_circularity": route1,
"2_exact_paper_configuration_audit": route2,
"3_independent_cpu_resource_calibration": route3,
"4_mandatory_falsification_attempt": route4,
},
"protocol_complete": protocol_complete,
"all_checks_passed": protocol_complete,
"verdict": "BLOCKED",
"confidence": "LOW",
"unblocker": (
"The paper's executable training code and raw trajectories, or "
"authorization for the exact 120+-configuration H100 campaign; "
"neither is compatible with this CPU-only reproduction."
),
}
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