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#!/usr/bin/env python3
"""Deterministic audits for Transformer BP/FA/KP/SDIL feedback transport."""
import json
import os
import sys
import torch
sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
from sdil.transformer import ( # noqa: E402
FeedbackLinear,
LocalDecoderTransformer,
LocalTransformerConfig,
)
def _named_forward_gradients(model):
feedback_ids = {
id(module.feedback)
for module in model.feedback_linears()
if isinstance(module.feedback, torch.nn.Parameter)}
return {
name: parameter.grad.detach().clone()
for name, parameter in model.named_parameters()
if id(parameter) not in feedback_ids}
def _relative_error(actual, expected):
return float(
torch.linalg.vector_norm(actual - expected)
/ torch.linalg.vector_norm(expected).clamp_min(1e-30))
def audit_matched_forward_and_symmetric_limit():
config = LocalTransformerConfig(
vocab_size=11, context_length=7, depth=2, width=8, heads=2,
mlp_ratio=2, seed=101)
bp = LocalDecoderTransformer(config, "bp", dtype=torch.float64)
fa = LocalDecoderTransformer(config, "fa", dtype=torch.float64)
fa.set_feedback_equal_to_forward()
generator = torch.Generator().manual_seed(102)
tokens = torch.randint(0, 11, (3, 7), generator=generator)
targets = torch.randint(0, 11, (3, 7), generator=generator)
bp_output = bp(tokens, targets)
fa_output = fa(tokens, targets)
forward_error = float(torch.max(torch.abs(
bp_output["logits"] - fa_output["logits"])).detach())
bp_output["loss"].backward()
fa_output["loss"].backward()
bp_gradients = _named_forward_gradients(bp)
fa_gradients = _named_forward_gradients(fa)
if bp_gradients.keys() != fa_gradients.keys():
raise AssertionError("forward parameter names differ")
errors = {
name: _relative_error(fa_gradients[name], bp_gradients[name])
for name in bp_gradients}
if forward_error >= 1e-12 or max(errors.values()) >= 2e-12:
raise AssertionError({
"forward_error": forward_error,
"gradient_errors": errors,
})
return {
"matched_forward_max_absolute_error": forward_error,
"symmetric_limit_max_relative_error": max(errors.values()),
"audited_forward_parameter_tensors": len(errors),
"matched_forward_parameter_count": bp.n_forward_parameters,
"matched_feedback_tensor_count": len(list(fa.feedback_linears())),
}
def audit_fa_independence_and_kp_locality():
forward_generator = torch.Generator().manual_seed(111)
feedback_generator = torch.Generator().manual_seed(112)
fa = FeedbackLinear(
5, 3, "fa", forward_generator, feedback_generator,
dtype=torch.float64)
feedback_before = fa.feedback.detach().clone()
with torch.no_grad():
fa.weight.add_(torch.randn(
fa.weight.shape, generator=forward_generator,
dtype=fa.weight.dtype))
fa_independence_error = float(torch.max(torch.abs(
fa.feedback - feedback_before)))
forward_generator = torch.Generator().manual_seed(113)
feedback_generator = torch.Generator().manual_seed(114)
kp = FeedbackLinear(
5, 3, "clean_kp", forward_generator, feedback_generator,
dtype=torch.float64)
x = torch.randn(
2, 4, 5, generator=forward_generator, dtype=torch.float64,
requires_grad=True)
upstream = torch.randn(
2, 4, 3, generator=forward_generator, dtype=torch.float64)
output = kp(x)
(output * upstream).sum().backward()
expected = upstream.reshape(-1, 3).t() @ x.detach().reshape(-1, 5)
forward_error = _relative_error(kp.weight.grad, expected)
feedback_error = _relative_error(kp.feedback.grad, expected)
if max(fa_independence_error, forward_error, feedback_error) >= 1e-12:
raise AssertionError({
"fa_independence_error": fa_independence_error,
"forward_local_error": forward_error,
"feedback_local_error": feedback_error,
})
return {
"fa_feedback_change_after_forward_weight_mutation":
fa_independence_error,
"kp_forward_local_correlation_relative_error": forward_error,
"kp_feedback_local_correlation_relative_error": feedback_error,
"kp_feedback_gradient_recomputed_locally": True,
}
def audit_sdil_innovation_identity():
config = LocalTransformerConfig(
vocab_size=13, context_length=6, depth=2, width=8, heads=2,
mlp_ratio=2, traffic_ratio=4.0, seed=121)
kp = LocalDecoderTransformer(config, "clean_kp", dtype=torch.float64)
sdil = LocalDecoderTransformer(config, "sdil", dtype=torch.float64)
generator = torch.Generator().manual_seed(122)
tokens = torch.randint(0, 13, (3, 6), generator=generator)
targets = torch.randint(0, 13, (3, 6), generator=generator)
kp(tokens, targets)["loss"].backward()
sdil(tokens, targets)["loss"].backward()
kp_gradients = {
name: parameter.grad.detach()
for name, parameter in kp.named_parameters()}
sdil_gradients = {
name: parameter.grad.detach()
for name, parameter in sdil.named_parameters()}
errors = {
name: _relative_error(sdil_gradients[name], kp_gradients[name])
for name in kp_gradients}
statistics = sdil.teaching_statistics()
traffic_ratio = (
statistics["traffic_rms"]
/ max(statistics["innovation_rms"], 1e-30))
raw_is_contaminated = (
statistics["raw_rms"] > statistics["innovation_rms"])
if max(errors.values()) >= 2e-12 or not raw_is_contaminated:
raise AssertionError({
"gradient_errors": errors,
"statistics": statistics,
"observed_traffic_ratio": traffic_ratio,
})
return {
"kp_sdil_max_gradient_relative_error": max(errors.values()),
"mean_raw_rms": statistics["raw_rms"],
"mean_innovation_rms": statistics["innovation_rms"],
"mean_traffic_rms": statistics["traffic_rms"],
"raw_signal_contaminated": raw_is_contaminated,
"paired_neutral_subtraction": True,
}
def main():
torch.set_num_threads(1)
result = {
"matched_forward_and_symmetric_limit":
audit_matched_forward_and_symmetric_limit(),
"fa_independence_and_kp_locality":
audit_fa_independence_and_kp_locality(),
"sdil_innovation_identity": audit_sdil_innovation_identity(),
}
print(json.dumps(result, indent=2, sort_keys=True))
if __name__ == "__main__":
main()
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