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| import torch
import torch.nn as nn
import numpy as np
from typing import Callable, Dict, List
from scipy import stats
class SensitivityMetrics:
"""
论文对比的13种层间量化敏感度指标
分为4类：
1. 权重统计（4种）- 基于权重分布
2. 梯度方法（3种）- 基于反向传播梯度
3. 激活统计（3种）- 基于输出分布
4. 信息论（3种）- 基于信息论度量
"""
@staticmethod
def weight_l2_norm(layer: nn.Module) -> float:
"""1. 权重L2范数"""
return torch.norm(layer.weight).item()
@staticmethod
def weight_max_abs(layer: nn.Module) -> float:
"""2. 权重最大绝对值"""
return layer.weight.abs().max().item()
@staticmethod
def weight_std(layer: nn.Module) -> float:
"""3. 权重标准差"""
return layer.weight.std().item()
@staticmethod
def weight_kurtosis(layer: nn.Module) -> float:
"""4. 权重峰度"""
w = layer.weight.flatten().detach().numpy()
return float(stats.kurtosis(w))
@staticmethod
def gradient_norm(
layer: nn.Module,
loss_fn: Callable,
x: torch.Tensor, y: torch.Tensor
) -> float:
"""5. 梯度范数（需反向传播）"""
layer.weight.requires_grad = True
out = layer(x)
loss = loss_fn(out, y)
loss.backward()
grad_norm = layer.weight.grad.norm().item()
layer.weight.requires_grad = False
return grad_norm
@staticmethod
def gradient_max(
layer: nn.Module,
loss_fn: Callable,
x: torch.Tensor, y: torch.Tensor
) -> float:
"""6. 梯度最大值"""
layer.weight.requires_grad = True
out = layer(x)
loss = loss_fn(out, y)
loss.backward()
grad_max = layer.weight.grad.abs().max().item()
layer.weight.requires_grad = False
return grad_max
@staticmethod
def gradient_mean(
layer: nn.Module,
loss_fn: Callable,
x: torch.Tensor, y: torch.Tensor
) -> float:
"""7. 梯度均值"""
layer.weight.requires_grad = True
out = layer(x)
loss = loss_fn(out, y)
loss.backward()
grad_mean = layer.weight.grad.abs().mean().item()
layer.weight.requires_grad = False
return grad_mean
@staticmethod
def activation_l2(fp32_out: torch.Tensor, int8_out: torch.Tensor) -> float:
"""8. 激活L2距离"""
return torch.norm(fp32_out - int8_out).item()
@staticmethod
def activation_cosine(fp32_out: torch.Tensor, int8_out: torch.Tensor) -> float:
"""9. 激活余弦相似度"""
cos = torch.nn.functional.cosine_similarity(
fp32_out.flatten().unsqueeze(0),
int8_out.flatten().unsqueeze(0)
)
return (1 - cos).item()
@staticmethod
def activation_mse(fp32_out: torch.Tensor, int8_out: torch.Tensor) -> float:
"""10. 激活MSE"""
return torch.nn.functional.mse_loss(fp32_out, int8_out).item()
@staticmethod
def kl_divergence(fp32_out: torch.Tensor, int8_out: torch.Tensor) -> float:
"""11. KL散度"""
p = torch.softmax(fp32_out.flatten(), dim=0)
q = torch.softmax(int8_out.flatten(), dim=0)
kl = (p * (p / (q + 1e-8) + 1e-8).log()).sum().item()
return kl
@staticmethod
def jensen_shannon_divergence(
fp32_out: torch.Tensor,
int8_out: torch.Tensor
) -> float:
"""
12. Jensen-Shannon散度（JSD）⭐
论文核心发现：JSD是唯一在所有4×8=32种配置中
零灾难性失败的指标
"""
p = torch.softmax(fp32_out.flatten().float(), dim=0)
q = torch.softmax(int8_out.flatten().float(), dim=0)
m = 0.5 * (p + q)
def kl(a, b):
return (a * (a / (b + 1e-10) + 1e-10).log()).sum().item()
jsd = 0.5 * kl(p, m) + 0.5 * kl(q, m)
return jsd
@staticmethod
def wasserstein_distance(
fp32_out: torch.Tensor,
int8_out: torch.Tensor
) -> float:
"""13. Wasserstein距离"""
p = torch.softmax(fp32_out.flatten().float(), dim=0)
q = torch.softmax(int8_out.flatten().float(), dim=0)
cdf_p = torch.cumsum(p, dim=0)
cdf_q = torch.cumsum(q, dim=0)
return torch.norm(cdf_p - cdf_q).item()
def compute_all_metrics(
layer: nn.Module,
fp32_out: torch.Tensor,
int8_out: torch.Tensor,
loss_fn=None,
sample_input=None,
sample_target=None
) -> Dict[str, float]:
"""计算13种敏感度指标"""
metrics = SensitivityMetrics()
results = {}
results['weight_l2'] = metrics.weight_l2_norm(layer)
results['weight_max'] = metrics.weight_max_abs(layer)
results['weight_std'] = metrics.weight_std(layer)
results['weight_kurtosis'] = metrics.weight_kurtosis(layer)
if loss_fn is not None and sample_input is not None:
results['grad_norm'] = metrics.gradient_norm(
layer, loss_fn, sample_input, sample_target)
results['grad_max'] = metrics.gradient_max(
layer, loss_fn, sample_input, sample_target)
results['grad_mean'] = metrics.gradient_mean(
layer, loss_fn, sample_input, sample_target)
results['act_l2'] = metrics.activation_l2(fp32_out, int8_out)
results['act_cosine'] = metrics.activation_cosine(fp32_out, int8_out)
results['act_mse'] = metrics.activation_mse(fp32_out, int8_out)
results['kl_div'] = metrics.kl_divergence(fp32_out, int8_out)
results['jsd'] = metrics.jensen_shannon_divergence(fp32_out, int8_out)
results['wasserstein'] = metrics.wasserstein_distance(fp32_out, int8_out)
return results
if __name__ == "__main__":
layer = nn.Linear(256, 128)
x = torch.randn(4, 256)
fp32_out = layer(x)
scale = fp32_out.abs().max() / 127
int8_out = torch.round(fp32_out / scale) * scale
metrics = compute_all_metrics(layer, fp32_out, int8_out)
print("13种敏感度指标:")
print("-" * 40)
for name, value in metrics.items():
print(f" {name:20s}: {value:.6f}")
print(f"\n⭐ JSD (Jensen-Shannon): {metrics['jsd']:.6f}")
print(" → 唯一零灾难性失败指标")
|
