介绍
深度学习模型越强大,体积也越庞大。GPT-4、Llama 3 405B 这样的大型模型需要数百 GB 的内存,在移动设备或边缘设备上根本无法运行。知识蒸馏(Knowledge Distillation)与模型压缩技术,是在尽可能保留大模型性能的同时让模型变小、变快的核心手段。
本指南涵盖的内容:
- 知识蒸馏的理论背景与完整 PyTorch 实现
- 多种蒸馏方法(Response-based、Feature-based、Relation-based)
- LLM 蒸馏案例(DistilBERT、TinyLLM)
- 结构化 / 非结构化剪枝
- 权重共享与 NAS
1. 知识蒸馏基础
1.1 Teacher-Student 框架
知识蒸馏是 2015 年 Hinton、Vinyals、Dean 提出的技术,核心是将大型 Teacher 模型的"知识"传递给小型 Student 模型。
Teacher Model(大而精确)
│
│ 传递软目标(概率分布)
▼
Student Model(小而快速)
与仅用正确标签(硬目标)训练不同,这里使用的是 Teacher 的软目标(softmax 输出的概率分布)。
举例来说,猫咪图像分类:
- 硬目标:[0, 0, 1, 0, 0](只有正确类别为 1)
- Teacher 软目标:[0.01, 0.05, 0.85, 0.07, 0.02]
软目标中包含"这张图像是猫,但和老虎有几分相似"这样的信息。这种类别间相似性信息,对 Student 的学习有很大帮助。
1.2 温度(Temperature)参数
当 softmax 输出过于自信时(如 [0.001, 0.002, 0.997, ...]),几乎和硬目标一样,信息量很少。温度参数 T 可以让分布变得更平滑:
softmax_T(z_i) = exp(z_i / T) / sum_j(exp(z_j / T))
- T 为 1 时:普通 softmax
- T 大于 1 时:分布更加均匀(传递更多信息)
- T 小于 1 时:分布更加尖锐
import torch
import torch.nn.functional as F
def temperature_softmax(logits, temperature=1.0):
"""经温度调整后的 softmax。"""
return F.softmax(logits / temperature, dim=-1)
# 示例
logits = torch.tensor([2.0, 1.0, 0.1, 0.5])
print("T=1:", temperature_softmax(logits, T=1).numpy().round(3))
# [0.596, 0.219, 0.090, 0.096]
print("T=4:", temperature_softmax(logits, T=4).numpy().round(3))
# [0.345, 0.262, 0.195, 0.216] — 更均匀
1.3 Hinton 的 KD 损失函数
KD 损失是两项的加权和:
KL 散度项(软目标匹配):
L_KD = T^2 * KLDiv(softmax_T(student_logits), softmax_T(teacher_logits))
T^2 缩放:用于让梯度大小与 T 无关。
交叉熵项(硬目标学习):
L_CE = CrossEntropy(student_logits, true_labels)
总损失:
L = alpha * L_CE + (1 - alpha) * L_KD
1.4 完整的 PyTorch 实现
import torch
import torch.nn as nn
import torch.nn.functional as F
import torchvision.models as models
from torch.utils.data import DataLoader
import torchvision.transforms as transforms
import torchvision.datasets as datasets
class KnowledgeDistillationLoss(nn.Module):
"""
Hinton et al. (2015) 的知识蒸馏损失。
L = alpha * CE(student, labels) + (1-alpha) * T^2 * KLDiv(student_soft, teacher_soft)
"""
def __init__(self, temperature=4.0, alpha=0.5):
super().__init__()
self.T = temperature
self.alpha = alpha
self.ce_loss = nn.CrossEntropyLoss()
self.kl_loss = nn.KLDivLoss(reduction='batchmean')
def forward(self, student_logits, teacher_logits, labels):
# 硬目标损失
loss_ce = self.ce_loss(student_logits, labels)
# 软目标损失(KL 散度)
student_soft = F.log_softmax(student_logits / self.T, dim=-1)
teacher_soft = F.softmax(teacher_logits / self.T, dim=-1)
loss_kd = self.kl_loss(student_soft, teacher_soft) * (self.T ** 2)
return self.alpha * loss_ce + (1 - self.alpha) * loss_kd
def train_with_distillation(
teacher, student, train_loader,
num_epochs=10, temperature=4.0, alpha=0.5,
device='cuda'
):
"""Teacher-Student 蒸馏训练循环。"""
teacher = teacher.to(device).eval() # Teacher 冻结
student = student.to(device)
# 冻结 Teacher 参数
for param in teacher.parameters():
param.requires_grad = False
criterion = KnowledgeDistillationLoss(temperature=temperature, alpha=alpha)
optimizer = torch.optim.Adam(student.parameters(), lr=1e-3)
scheduler = torch.optim.lr_scheduler.CosineAnnealingLR(optimizer, T_max=num_epochs)
for epoch in range(num_epochs):
student.train()
total_loss = 0.0
correct = 0
total = 0
for images, labels in train_loader:
images, labels = images.to(device), labels.to(device)
# Teacher 推理(无需梯度)
with torch.no_grad():
teacher_logits = teacher(images)
# Student 推理
student_logits = student(images)
# KD 损失计算
loss = criterion(student_logits, teacher_logits, labels)
optimizer.zero_grad()
loss.backward()
optimizer.step()
total_loss += loss.item() * images.size(0)
correct += (student_logits.argmax(1) == labels).sum().item()
total += images.size(0)
scheduler.step()
print(f"Epoch {epoch+1}/{num_epochs} | "
f"Loss: {total_loss/total:.4f} | "
f"Acc: {correct/total:.4f}")
return student
# 实际使用示例
# Teacher: ResNet50 (25M params), Student: ResNet18 (11M params)
teacher = models.resnet50(weights='DEFAULT')
teacher.fc = nn.Linear(2048, 10)
student = models.resnet18(weights=None)
student.fc = nn.Linear(512, 10)
# 参数量比较
t_params = sum(p.numel() for p in teacher.parameters())
s_params = sum(p.numel() for p in student.parameters())
print(f"Teacher: {t_params:,} params") # ~25.6M
print(f"Student: {s_params:,} params") # ~11.2M
print(f"压缩率: {t_params/s_params:.1f}x")
2. 多种蒸馏方法
2.1 Response-based 蒸馏(logit 匹配)
这是最基本的方法,前面介绍的 Hinton KD 就是典型代表。Student 模仿 Teacher 的最终输出(logit)。
class ResponseBasedDistillation(nn.Module):
"""仅使用最终输出的 Response-based 蒸馏。"""
def __init__(self, temperature=4.0):
super().__init__()
self.T = temperature
def forward(self, student_logits, teacher_logits):
student_soft = F.log_softmax(student_logits / self.T, dim=-1)
teacher_soft = F.softmax(teacher_logits / self.T, dim=-1)
return F.kl_div(student_soft, teacher_soft, reduction='batchmean') * (self.T ** 2)
2.2 Feature-based 蒸馏(中间层)
由 FitNets(Romero et al., 2015)提出,让 Student 学习模仿 Teacher 中间层的 feature map。
由于 Teacher 与 Student 的通道数可能不同,需要用 Regressor 网络来对齐维度。
class FeatureDistillationLoss(nn.Module):
"""匹配中间层 feature 的蒸馏。"""
def __init__(self, teacher_channels, student_channels):
super().__init__()
# 将 Student feature 投影到 Teacher feature 空间
self.regressor = nn.Sequential(
nn.Conv2d(student_channels, teacher_channels, kernel_size=1, bias=False),
nn.BatchNorm2d(teacher_channels),
nn.ReLU(inplace=True),
)
def forward(self, student_feat, teacher_feat):
# 将 Student feature 转换到 Teacher 维度
projected = self.regressor(student_feat)
# 用 MSE 损失匹配 feature
return F.mse_loss(projected, teacher_feat.detach())
class HookBasedDistillation:
"""
用 forward hook 提取中间层 feature。
"""
def __init__(self, model, layer_names):
self.features = {}
self.hooks = []
for name, layer in model.named_modules():
if name in layer_names:
hook = layer.register_forward_hook(
self._make_hook(name)
)
self.hooks.append(hook)
def _make_hook(self, name):
def hook(module, input, output):
self.features[name] = output
return hook
def remove(self):
for hook in self.hooks:
hook.remove()
# 使用示例
teacher = models.resnet50(weights='DEFAULT')
student = models.resnet18(weights=None)
# Teacher: layer3 输出(1024 通道),Student: layer3 输出(256 通道)
teacher_hook = HookBasedDistillation(teacher, ['layer3'])
student_hook = HookBasedDistillation(student, ['layer3'])
feat_distill = FeatureDistillationLoss(
teacher_channels=1024,
student_channels=256
)
# 训练时
x = torch.randn(4, 3, 224, 224)
teacher_out = teacher(x)
student_out = student(x)
teacher_feat = teacher_hook.features['layer3']
student_feat = student_hook.features['layer3']
loss_feat = feat_distill(student_feat, teacher_feat)
2.3 Relation-based 蒸馏(相关关系学习)
RKD(Park et al., 2019)。让 Student 模仿样本之间的关系,学习的不是绝对值,而是相对结构。
class RelationalKnowledgeDistillation(nn.Module):
"""
Relational KD:保留样本对之间的距离关系。
Student 学习 Teacher embedding 空间的结构。
"""
def __init__(self, distance_weight=25.0, angle_weight=50.0):
super().__init__()
self.dist_w = distance_weight
self.angle_w = angle_weight
def pdist(self, e, squared=False, eps=1e-12):
"""成对距离计算。"""
e_sq = (e ** 2).sum(dim=1)
prod = e @ e.t()
res = (e_sq.unsqueeze(1) + e_sq.unsqueeze(0) - 2 * prod).clamp(min=eps)
if not squared:
res = res.sqrt()
return res
def distance_loss(self, teacher_emb, student_emb):
"""保留距离关系的损失。"""
t_d = self.pdist(teacher_emb)
# 归一化
t_d = t_d / (t_d.mean() + 1e-12)
s_d = self.pdist(student_emb)
s_d = s_d / (s_d.mean() + 1e-12)
return F.smooth_l1_loss(s_d, t_d.detach())
def angle_loss(self, teacher_emb, student_emb):
"""保留角度关系的损失。"""
# e_i - e_j 向量之间的角度关系
td = teacher_emb.unsqueeze(0) - teacher_emb.unsqueeze(1) # (N, N, D)
sd = student_emb.unsqueeze(0) - student_emb.unsqueeze(1)
# cosine similarity
td_norm = F.normalize(td.view(-1, td.size(-1)), dim=-1)
sd_norm = F.normalize(sd.view(-1, sd.size(-1)), dim=-1)
t_angle = (td_norm * td_norm.flip(0)).sum(dim=-1)
s_angle = (sd_norm * sd_norm.flip(0)).sum(dim=-1)
return F.smooth_l1_loss(s_angle, t_angle.detach())
def forward(self, teacher_emb, student_emb):
loss = self.dist_w * self.distance_loss(teacher_emb, student_emb)
loss += self.angle_w * self.angle_loss(teacher_emb, student_emb)
return loss
2.4 Attention Transfer
Zagoruyko & Komodakis(2017)。将 Attention map(按通道汇总的 activation)从 Teacher 传递给 Student。
class AttentionTransfer(nn.Module):
"""Attention Transfer:传递 activation map 的空间模式。"""
def attention_map(self, feat):
"""
从 feature map 计算 attention map。
在每个空间位置上,沿通道方向取平方和的开方。
"""
return F.normalize(feat.pow(2).mean(1).view(feat.size(0), -1))
def forward(self, student_feats, teacher_feats):
"""
student_feats, teacher_feats: feature map 列表
对每一对计算 AT 损失。
"""
loss = 0.0
for s_feat, t_feat in zip(student_feats, teacher_feats):
s_attn = self.attention_map(s_feat)
t_attn = self.attention_map(t_feat)
loss += (s_attn - t_attn.detach()).pow(2).mean()
return loss
3. LLM 蒸馏
3.1 DistilBERT
DistilBERT(Sanh et al., 2019)是把 BERT-base(110M 参数)压缩到 66M 的模型。
主要技术:
- 层数减半:12 层 → 6 层
- 移除 Token-type embedding
- 移除 Pooler
- 三重损失:MLM + Distillation + Cosine embedding
from transformers import (
DistilBertModel, BertModel,
DistilBertTokenizer
)
import torch
import torch.nn as nn
import torch.nn.functional as F
class DistilBERTLoss(nn.Module):
"""
DistilBERT 三重损失:
1. MLM CE 损失(语言建模)
2. Soft-target KD 损失(匹配 Teacher logit)
3. Cosine embedding 损失(hidden state 相似度)
"""
def __init__(self, temperature=2.0, alpha=0.5, beta=0.1):
super().__init__()
self.T = temperature
self.alpha = alpha # MLM 权重
self.beta = beta # Cosine 损失权重
def forward(self, student_logits, teacher_logits,
student_hidden, teacher_hidden, mlm_labels):
# 1. MLM 损失
loss_mlm = F.cross_entropy(
student_logits.view(-1, student_logits.size(-1)),
mlm_labels.view(-1),
ignore_index=-100
)
# 2. Soft KD 损失
s_soft = F.log_softmax(student_logits / self.T, dim=-1)
t_soft = F.softmax(teacher_logits / self.T, dim=-1)
loss_kd = F.kl_div(s_soft, t_soft, reduction='batchmean') * (self.T ** 2)
# 3. Cosine embedding 损失(hidden state 相似度)
loss_cos = 1 - F.cosine_similarity(student_hidden, teacher_hidden, dim=-1).mean()
return (self.alpha * loss_mlm
+ (1 - self.alpha) * loss_kd
+ self.beta * loss_cos)
# 推理示例
tokenizer = DistilBertTokenizer.from_pretrained('distilbert-base-uncased')
model = DistilBertModel.from_pretrained('distilbert-base-uncased')
text = "Knowledge distillation is a model compression technique."
inputs = tokenizer(text, return_tensors='pt')
with torch.no_grad():
outputs = model(**inputs)
print(outputs.last_hidden_state.shape)
# torch.Size([1, 11, 768])
DistilBERT 性能:
- 相比 BERT-base 体积缩小 40%
- 推理速度提升 60%
- 保留 GLUE 基准 97% 的性能
3.2 TinyLLaMA 风格蒸馏
在 LLM 蒸馏中,Student 学习 Teacher 的下一个 token 预测分布。
class LLMDistillationTrainer:
"""
LLM 蒸馏训练器。
将 Teacher 的 logit 分布传递给 Student。
"""
def __init__(self, teacher, student, temperature=2.0, alpha=0.5):
self.teacher = teacher
self.student = student
self.T = temperature
self.alpha = alpha
def compute_loss(self, input_ids, attention_mask, labels):
# Teacher 推理(no_grad)
with torch.no_grad():
teacher_out = self.teacher(
input_ids=input_ids,
attention_mask=attention_mask,
)
teacher_logits = teacher_out.logits # (B, seq_len, vocab_size)
# Student 推理
student_out = self.student(
input_ids=input_ids,
attention_mask=attention_mask,
)
student_logits = student_out.logits
# 1. CE 损失(硬目标)
shift_logits = student_logits[..., :-1, :].contiguous()
shift_labels = labels[..., 1:].contiguous()
loss_ce = F.cross_entropy(
shift_logits.view(-1, shift_logits.size(-1)),
shift_labels.view(-1),
ignore_index=-100
)
# 2. KD 损失(软目标)
# 仅对有效 token 计算
mask = (shift_labels != -100).float()
s_log_soft = F.log_softmax(
shift_logits / self.T, dim=-1
)
t_soft = F.softmax(
teacher_logits[..., :-1, :].contiguous() / self.T, dim=-1
)
# 逐 token 的 KL 散度
kl_per_token = F.kl_div(
s_log_soft, t_soft,
reduction='none'
).sum(-1) # (B, seq_len)
loss_kd = (kl_per_token * mask).sum() / mask.sum()
loss_kd = loss_kd * (self.T ** 2)
return self.alpha * loss_ce + (1 - self.alpha) * loss_kd
3.3 Distil Whisper
这是 OpenAI Whisper 语音识别模型的蒸馏版本。
from transformers import (
WhisperProcessor, WhisperForConditionalGeneration
)
# Distil-Whisper: Whisper-large-v2 的蒸馏
# large-v2: 1550M params → distil-large-v2: 756M params (2x faster, same WER)
processor = WhisperProcessor.from_pretrained("distil-whisper/distil-large-v2")
model = WhisperForConditionalGeneration.from_pretrained("distil-whisper/distil-large-v2")
# 仅保留 6 个解码器层(原始 32 个 → 2 个)
# 编码器保持不变
print(f"Encoder layers: {len(model.model.encoder.layers)}")
print(f"Decoder layers: {len(model.model.decoder.layers)}")
4. 结构化剪枝(Structured Pruning)
剪枝是从模型中移除不重要的参数或结构的技术。
结构化剪枝:以过滤器、注意力头、整层为单位移除 → 带来实际速度提升 非结构化剪枝:将单个权重置零 → 稀疏矩阵(需要专用硬件)
4.1 过滤器剪枝
在 CNN 中移除 L1/L2 范数较小的过滤器。
import torch
import torch.nn as nn
import numpy as np
def get_filter_importance(conv_layer, norm='l1'):
"""计算每个过滤器的重要度(norm)。"""
weight = conv_layer.weight.data # (out_ch, in_ch, kH, kW)
if norm == 'l1':
return weight.abs().sum(dim=(1, 2, 3))
elif norm == 'l2':
return weight.pow(2).sum(dim=(1, 2, 3)).sqrt()
elif norm == 'gm':
# 基于 Geometric Median(更 robust)
return weight.view(weight.size(0), -1).norm(p=2, dim=1)
def prune_conv_layer(conv, keep_ratio=0.5):
"""
过滤器剪枝:移除重要度较低的过滤器。
Returns: 新的 Conv2d 层(过滤器数量减少)
"""
importance = get_filter_importance(conv)
n_keep = int(conv.out_channels * keep_ratio)
# 选出重要度排名前 n_keep 的过滤器
_, indices = importance.topk(n_keep)
indices, _ = indices.sort()
# 创建新的 conv 层
new_conv = nn.Conv2d(
conv.in_channels,
n_keep,
kernel_size=conv.kernel_size,
stride=conv.stride,
padding=conv.padding,
bias=conv.bias is not None
)
new_conv.weight.data = conv.weight.data[indices]
if conv.bias is not None:
new_conv.bias.data = conv.bias.data[indices]
return new_conv, indices
class StructuredPruner:
"""ResNet 风格模型的结构化剪枝。"""
def __init__(self, model, prune_ratio=0.5):
self.model = model
self.prune_ratio = prune_ratio
def compute_layer_importance(self):
"""计算每一层过滤器的重要度。"""
importance_dict = {}
for name, module in self.model.named_modules():
if isinstance(module, nn.Conv2d):
importance = get_filter_importance(module)
importance_dict[name] = importance
return importance_dict
def global_threshold_prune(self, sparsity=0.5):
"""
对全部过滤器使用全局阈值进行剪枝。
移除重要度最低的 sparsity 比例的过滤器。
"""
all_importances = []
for name, module in self.model.named_modules():
if isinstance(module, nn.Conv2d):
imp = get_filter_importance(module)
all_importances.append(imp)
# 将所有过滤器的重要度合并为一个
all_imp = torch.cat(all_importances)
threshold = all_imp.kthvalue(int(len(all_imp) * sparsity)).values.item()
# 移除低于阈值的过滤器
masks = {}
for name, module in self.model.named_modules():
if isinstance(module, nn.Conv2d):
imp = get_filter_importance(module)
masks[name] = imp >= threshold
return masks
4.2 注意力头剪枝(Attention Head Pruning)
移除 Transformer 中不重要的 Attention Head。
class AttentionHeadPruner:
"""
Transformer 的 Multi-Head Attention 头剪枝。
Michel et al. (2019): Are Sixteen Heads Really Better than One?
"""
def compute_head_importance(self, model, dataloader, device='cuda'):
"""计算每一层、每个头的重要度。"""
head_importance = {}
model.eval()
for batch in dataloader:
inputs = {k: v.to(device) for k, v in batch.items()}
# 用于保存 Attention 权重的 hook
attention_weights = {}
hooks = []
for name, module in model.named_modules():
if 'attention' in name.lower() and hasattr(module, 'num_heads'):
def hook_fn(m, inp, out, layer_name=name):
if hasattr(out, 'attentions') and out.attentions is not None:
attention_weights[layer_name] = out.attentions
hooks.append(module.register_forward_hook(hook_fn))
with torch.no_grad():
outputs = model(**inputs, output_attentions=True)
# Head importance:attention 权重方差之和
if hasattr(outputs, 'attentions') and outputs.attentions:
for layer_idx, attn in enumerate(outputs.attentions):
# attn: (batch, heads, seq, seq)
head_imp = attn.mean(0).var(-1).mean(-1) # (heads,)
key = f"layer_{layer_idx}"
if key not in head_importance:
head_importance[key] = head_imp
else:
head_importance[key] += head_imp
for hook in hooks:
hook.remove()
return head_importance
def prune_heads(self, model, heads_to_prune):
"""
移除指定的 head。
heads_to_prune: {layer_idx: [head_indices]}
"""
model.prune_heads(heads_to_prune) # HuggingFace 模型内置功能
return model
# 使用 HuggingFace transformers
from transformers import BertForSequenceClassification
model = BertForSequenceClassification.from_pretrained('bert-base-uncased')
# 移除 layer 0 的 head 0、3、5
heads_to_prune = {0: [0, 3, 5], 6: [1, 2]}
model.prune_heads(heads_to_prune)
total_params = sum(p.numel() for p in model.parameters())
print(f"Pruned BERT params: {total_params:,}")
4.3 层剪枝
移除对性能贡献较小的整个 Transformer 层。
class LayerPruner:
"""Transformer 层剪枝。"""
def compute_layer_importance_by_gradient(
self, model, dataloader, device='cuda'
):
"""
基于 gradient 计算每一层的重要度。
重要度 = |gradient * weight| 的平均值
"""
model.train()
layer_importance = {}
for batch in dataloader:
inputs = {k: v.to(device) for k, v in batch.items()}
outputs = model(**inputs)
loss = outputs.loss
loss.backward()
for i, layer in enumerate(model.encoder.layer):
grad_sum = 0.0
param_count = 0
for param in layer.parameters():
if param.grad is not None:
grad_sum += (param.grad * param.data).abs().sum().item()
param_count += param.numel()
key = f"layer_{i}"
imp = grad_sum / max(param_count, 1)
if key not in layer_importance:
layer_importance[key] = 0.0
layer_importance[key] += imp
model.zero_grad()
return layer_importance
def drop_layers(self, model, layers_to_drop):
"""移除指定层,并用剩余层重新组装模型。"""
import copy
new_model = copy.deepcopy(model)
remaining = [
layer for i, layer in enumerate(new_model.encoder.layer)
if i not in layers_to_drop
]
new_model.encoder.layer = nn.ModuleList(remaining)
new_model.config.num_hidden_layers = len(remaining)
return new_model
4.4 PyTorch torch.nn.utils.prune
import torch.nn.utils.prune as prune
model = models.resnet18(weights='DEFAULT')
# 对特定层应用非结构化 L1 剪枝
conv = model.layer1[0].conv1
prune.l1_unstructured(conv, name='weight', amount=0.3)
# 将 weight 的 30% 置零(使用 mask)
# 确认
print(f"Sparsity: {(conv.weight == 0).float().mean():.2f}")
# 结构化剪枝(过滤器单位)
prune.ln_structured(conv, name='weight', amount=0.3, n=2, dim=0)
# 永久应用(移除 mask,实际将 weight 置零)
prune.remove(conv, 'weight')
# 对多个层重复应用
parameters_to_prune = []
for module in model.modules():
if isinstance(module, nn.Conv2d):
parameters_to_prune.append((module, 'weight'))
prune.global_unstructured(
parameters_to_prune,
pruning_method=prune.L1Unstructured,
amount=0.4, # 剪除全部参数的 40%
)
# 确认整体稀疏度
total_zero = sum(
(m.weight == 0).sum().item()
for m in model.modules() if isinstance(m, nn.Conv2d)
)
total_params = sum(
m.weight.numel()
for m in model.modules() if isinstance(m, nn.Conv2d)
)
print(f"Global sparsity: {total_zero/total_params:.2%}")
5. 非结构化剪枝(Unstructured Pruning)
5.1 基于幅值的剪枝
将绝对值较小的权重置零,是最简单的方法。
class MagnitudePruner:
"""基于幅值的非结构化剪枝。"""
def __init__(self, model, sparsity=0.5):
self.model = model
self.sparsity = sparsity
self.masks = {}
def compute_global_threshold(self):
"""计算全部权重的全局阈值。"""
all_weights = []
for name, param in self.model.named_parameters():
if 'weight' in name and param.dim() > 1:
all_weights.append(param.data.abs().view(-1))
all_weights = torch.cat(all_weights)
threshold = all_weights.kthvalue(
int(len(all_weights) * self.sparsity)
).values.item()
return threshold
def apply_pruning(self):
"""用全局阈值生成剪枝 mask。"""
threshold = self.compute_global_threshold()
for name, param in self.model.named_parameters():
if 'weight' in name and param.dim() > 1:
mask = (param.data.abs() >= threshold).float()
self.masks[name] = mask
param.data *= mask # 将低于阈值的权重置零
total_zeros = sum((m == 0).sum().item() for m in self.masks.values())
total_params = sum(m.numel() for m in self.masks.values())
print(f"实际稀疏度: {total_zeros/total_params:.2%}")
def apply_masks(self):
"""反向传播后重新应用 mask(防止已置零的权重被梯度复原)。"""
for name, param in self.model.named_parameters():
if name in self.masks:
param.data *= self.masks[name]
5.2 渐进式剪枝(Gradual Magnitude Pruning)
从一开始就大幅剪枝会导致性能骤降。在训练过程中逐步提高稀疏度的方法更为有效。
class GradualMagnitudePruner:
"""
在训练过程中逐步提高稀疏度的剪枝。
Zhu & Gupta (2017): To Prune, or Not to Prune
"""
def __init__(self, model, initial_sparsity=0.0, final_sparsity=0.8,
begin_step=0, end_step=1000, frequency=100):
self.model = model
self.initial_sparsity = initial_sparsity
self.final_sparsity = final_sparsity
self.begin_step = begin_step
self.end_step = end_step
self.frequency = frequency
self.masks = {}
self._init_masks()
def _init_masks(self):
for name, param in self.model.named_parameters():
if 'weight' in name and param.dim() > 1:
self.masks[name] = torch.ones_like(param.data)
def compute_sparsity(self, step):
"""计算当前步数下的目标稀疏度(cubic schedule)。"""
if step < self.begin_step:
return self.initial_sparsity
if step > self.end_step:
return self.final_sparsity
# Cubic decay schedule
pct_done = (step - self.begin_step) / (self.end_step - self.begin_step)
sparsity = (
self.final_sparsity
+ (self.initial_sparsity - self.final_sparsity)
* (1 - pct_done) ** 3
)
return sparsity
def step(self, global_step):
"""在训练步骤中更新剪枝。"""
if (global_step % self.frequency != 0 or
global_step < self.begin_step or
global_step > self.end_step):
return
target_sparsity = self.compute_sparsity(global_step)
self._update_masks(target_sparsity)
def _update_masks(self, sparsity):
"""按照当前稀疏度目标更新 mask。"""
for name, param in self.model.named_parameters():
if name not in self.masks:
continue
# 只考虑当前存活的权重(排除已被剪枝的部分)
alive = param.data[self.masks[name].bool()]
if len(alive) == 0:
continue
n_prune = int(sparsity * param.data.numel())
if n_prune == 0:
continue
# 找出全体中排名最低的 n_prune 个
threshold = param.data.abs().view(-1).kthvalue(n_prune).values.item()
self.masks[name] = (param.data.abs() > threshold).float()
param.data *= self.masks[name]
6. 权重共享(Weight Sharing)
6.1 跨层参数共享 — ALBERT
ALBERT(Lan et al., 2019)为了大幅减少 BERT 的参数量,在所有 Transformer 层中反复使用相同的参数。
class ALBERTEncoder(nn.Module):
"""
ALBERT 风格权重共享。
将同一个 Transformer 层重复执行 N 次。
"""
def __init__(self, hidden_size=768, num_heads=12,
intermediate_size=3072, num_layers=12):
super().__init__()
# 只定义一个 Transformer 层
self.shared_layer = nn.TransformerEncoderLayer(
d_model=hidden_size,
nhead=num_heads,
dim_feedforward=intermediate_size,
batch_first=True,
norm_first=True,
)
self.num_layers = num_layers
self.norm = nn.LayerNorm(hidden_size)
def forward(self, x, src_key_padding_mask=None):
# 将同一层重复执行 num_layers 次
for _ in range(self.num_layers):
x = self.shared_layer(x, src_key_padding_mask=src_key_padding_mask)
return self.norm(x)
def count_parameters(self):
# 实际参数量(因共享,只统计一次)
return sum(p.numel() for p in self.parameters())
# 参数量比较
bert_encoder = nn.TransformerEncoder(
nn.TransformerEncoderLayer(768, 12, 3072, batch_first=True, norm_first=True),
num_layers=12
)
albert_encoder = ALBERTEncoder(num_layers=12)
bert_params = sum(p.numel() for p in bert_encoder.parameters())
albert_params = albert_encoder.count_parameters()
print(f"BERT encoder: {bert_params:,}") # ~85M
print(f"ALBERT encoder: {albert_params:,}") # ~7M
print(f"压缩率: {bert_params/albert_params:.1f}x") # ~12x
6.2 因式分解(ALBERT 嵌入)
ALBERT 也对嵌入层做了分解:vocab_size x hidden_size → vocab_size x embedding_size + embedding_size x hidden_size。
class FactorizedEmbedding(nn.Module):
"""
ALBERT 的嵌入因式分解。
vocab_size x H → (vocab_size x E) + (E x H)
E << H 以大幅减少参数量。
"""
def __init__(self, vocab_size, embedding_size=128, hidden_size=768):
super().__init__()
self.word_embeddings = nn.Embedding(vocab_size, embedding_size)
# E → H 线性变换
self.embedding_projection = nn.Linear(embedding_size, hidden_size, bias=False)
def forward(self, input_ids):
embed = self.word_embeddings(input_ids) # (B, seq, E)
return self.embedding_projection(embed) # (B, seq, H)
# 参数量比较(vocab_size=30000)
standard_embed = nn.Embedding(30000, 768) # 23.0M params
factorized_embed = FactorizedEmbedding(30000, 128, 768) # 3.97M params
s_params = sum(p.numel() for p in standard_embed.parameters())
f_params = sum(p.numel() for p in factorized_embed.parameters())
print(f"Standard: {s_params:,} → Factorized: {f_params:,}")
print(f"节省: {(s_params - f_params)/s_params:.1%}")
7. 神经网络架构搜索(NAS)
7.1 Manual Design vs AutoML
传统上,CNN 结构由研究者手工设计(VGG、ResNet)。NAS 将这一过程自动化。
NAS 的三个核心要素:
- 搜索空间(Search Space):探索哪些运算 / 结构
- 搜索策略(Search Strategy):强化学习、进化算法、基于梯度等
- 性能评估(Performance Estimation):快速评估候选结构的性能
7.2 DARTS (Differentiable Architecture Search)
Liu et al. (2019)。将结构搜索转化为连续的优化问题。
import torch
import torch.nn as nn
import torch.nn.functional as F
# 候选运算
PRIMITIVES = [
'none', # 无连接
'skip_connect', # 恒等函数
'sep_conv_3x3', # 3x3 Separable Conv
'sep_conv_5x5', # 5x5 Separable Conv
'dil_conv_3x3', # 3x3 Dilated Conv
'dil_conv_5x5', # 5x5 Dilated Conv
'avg_pool_3x3', # 3x3 Average Pool
'max_pool_3x3', # 3x3 Max Pool
]
class MixedOperation(nn.Module):
"""
DARTS:用多种运算的加权和表示一条边。
alpha(架构参数)决定每种运算的权重。
"""
def __init__(self, C, stride, primitives):
super().__init__()
self.ops = nn.ModuleList([
self._build_op(primitive, C, stride)
for primitive in primitives
])
# 可学习的架构参数
self.arch_params = nn.Parameter(
torch.randn(len(primitives)) * 1e-3
)
def _build_op(self, primitive, C, stride):
if primitive == 'none':
return nn.Sequential() # Zero operation
elif primitive == 'skip_connect':
return nn.Identity() if stride == 1 else nn.Sequential(
nn.AvgPool2d(stride, stride, padding=0),
nn.Conv2d(C, C, 1, bias=False),
nn.BatchNorm2d(C)
)
elif primitive == 'sep_conv_3x3':
return nn.Sequential(
nn.Conv2d(C, C, 3, stride=stride, padding=1, groups=C, bias=False),
nn.Conv2d(C, C, 1, bias=False),
nn.BatchNorm2d(C),
nn.ReLU(inplace=True),
)
elif primitive == 'avg_pool_3x3':
return nn.AvgPool2d(3, stride=stride, padding=1)
elif primitive == 'max_pool_3x3':
return nn.MaxPool2d(3, stride=stride, padding=1)
else:
return nn.Identity()
def forward(self, x):
# 用 Softmax 计算权重,再对各运算加权求和
weights = F.softmax(self.arch_params, dim=0)
results = []
for w, op in zip(weights, self.ops):
try:
result = op(x)
if result.shape == x.shape or len(results) == 0:
results.append(w * result)
else:
results.append(w * result)
except Exception:
pass
if results:
# 所有运算结果的加权和
output = results[0]
for r in results[1:]:
if r.shape == output.shape:
output = output + r
return output
return x
class DARTSCell(nn.Module):
"""DARTS 单元:由多个 Mixed Operation 组成的 DAG。"""
def __init__(self, num_nodes, C, stride=1):
super().__init__()
self.num_nodes = num_nodes
self.ops = nn.ModuleList()
# 为每一对节点生成 Mixed Operation
for i in range(num_nodes):
for j in range(i):
self.ops.append(
MixedOperation(C, stride, PRIMITIVES)
)
def forward(self, *inputs):
states = list(inputs)
op_idx = 0
for i in range(self.num_nodes):
# 汇总来自所有先前状态的输入
node_input = sum(
self.ops[op_idx + j](states[j])
for j in range(len(states))
)
op_idx += len(states)
states.append(node_input)
return states[-1]
def get_arch_params(self):
"""返回架构参数。"""
return [op.arch_params for op in self.ops]
def darts_discrete(cell):
"""
将连续架构转换为离散结构。
在每条边上选择权重最高的运算。
"""
for op in cell.ops:
weights = F.softmax(op.arch_params, dim=0)
best_op_idx = weights.argmax().item()
print(f" Selected: {PRIMITIVES[best_op_idx]} "
f"(weight: {weights[best_op_idx]:.3f})")
7.3 EfficientNet 的 NAS 流程
EfficientNet-B0 是通过与 MnasNet 类似的神经网络架构搜索找到的基础结构。
# EfficientNet 的 MBConv 模块(NAS 找到的核心结构)
class MBConvBlock(nn.Module):
"""
Mobile Inverted Bottleneck Convolution.
EfficientNet 的基本构建模块。
"""
def __init__(self, in_channels, out_channels, kernel_size,
stride=1, expand_ratio=6, se_ratio=0.25):
super().__init__()
self.use_residual = (stride == 1 and in_channels == out_channels)
hidden_dim = int(in_channels * expand_ratio)
layers = []
# Expansion phase (1x1 conv)
if expand_ratio != 1:
layers.extend([
nn.Conv2d(in_channels, hidden_dim, 1, bias=False),
nn.BatchNorm2d(hidden_dim),
nn.SiLU(),
])
# Depthwise conv
layers.extend([
nn.Conv2d(hidden_dim, hidden_dim, kernel_size,
stride=stride,
padding=kernel_size // 2,
groups=hidden_dim, bias=False),
nn.BatchNorm2d(hidden_dim),
nn.SiLU(),
])
# Squeeze-and-Excitation(NAS 发现的重要模块)
se_channels = max(1, int(in_channels * se_ratio))
self.se = nn.Sequential(
nn.AdaptiveAvgPool2d(1),
nn.Conv2d(hidden_dim, se_channels, 1),
nn.SiLU(),
nn.Conv2d(se_channels, hidden_dim, 1),
nn.Sigmoid(),
)
# Output phase
layers.extend([
nn.Conv2d(hidden_dim, out_channels, 1, bias=False),
nn.BatchNorm2d(out_channels),
])
self.conv = nn.Sequential(*layers)
def forward(self, x):
out = self.conv[:-2](x) if len(self.conv) > 2 else self.conv(x)
# 应用 SE 模块
out_se = self.se(out)
out = out * out_se
out = self.conv[-2:](out)
if self.use_residual:
return x + out
return out
7.4 Once-for-All 网络
Cai et al. (2020)。训练一个超大型网络后,根据不同的资源限制提取出子网络。
class OFALayer(nn.Module):
"""
Once-for-All:支持多种卷积核大小的弹性层。
训练时:随机选择卷积核大小 → 训练子网络
部署时:只使用特定的卷积核大小
"""
def __init__(self, channels, max_kernel=7):
super().__init__()
# 只训练最大卷积核大小的 conv
self.max_conv = nn.Conv2d(
channels, channels,
kernel_size=max_kernel,
padding=max_kernel // 2,
groups=channels, bias=False
)
self.bn = nn.BatchNorm2d(channels)
self.act = nn.ReLU(inplace=True)
self.active_kernel = max_kernel
def set_active_kernel(self, kernel_size):
"""设置当前激活的卷积核大小。"""
assert kernel_size <= self.max_conv.kernel_size[0]
self.active_kernel = kernel_size
def forward(self, x):
if self.active_kernel == self.max_conv.kernel_size[0]:
weight = self.max_conv.weight
else:
# 从中心裁剪出 active_kernel 大小
center = self.max_conv.kernel_size[0] // 2
half = self.active_kernel // 2
weight = self.max_conv.weight[
:, :,
center - half: center + half + 1,
center - half: center + half + 1
]
padding = self.active_kernel // 2
out = F.conv2d(x, weight, padding=padding, groups=x.size(1))
return self.act(self.bn(out))
# Progressive shrinking 训练(OFA 的核心)
def progressive_shrinking_train(model, dataloader, kernels=[7, 5, 3]):
"""
第 1 阶段:训练最大卷积核(7)
第 2 阶段:在 7、5 卷积核中随机采样训练
第 3 阶段:在 7、5、3 卷积核中随机采样训练
"""
for stage, active_kernels in enumerate(
[kernels[:1], kernels[:2], kernels]
):
optimizer = torch.optim.SGD(model.parameters(), lr=0.1)
print(f"Stage {stage+1}: kernels = {active_kernels}")
for epoch in range(5):
for images, labels in dataloader:
# 随机选择卷积核大小
k = active_kernels[torch.randint(len(active_kernels), (1,)).item()]
# 设置所有层的激活卷积核
for module in model.modules():
if isinstance(module, OFALayer):
module.set_active_kernel(k)
outputs = model(images)
loss = F.cross_entropy(outputs, labels)
optimizer.zero_grad()
loss.backward()
optimizer.step()
8. 集成模型压缩流水线
在实际部署时,会组合使用多种技术:
class ModelCompressionPipeline:
"""
知识蒸馏 → 剪枝 → 量化的集成流水线。
"""
def __init__(self, teacher, student_arch, num_classes):
self.teacher = teacher
self.num_classes = num_classes
# 初始化 Student 模型
self.student = student_arch
def step1_distillation(self, train_loader, val_loader,
epochs=30, device='cuda'):
"""第 1 步:通过知识蒸馏进行基础训练。"""
print("=== Step 1: Knowledge Distillation ===")
self.student = train_with_distillation(
self.teacher, self.student, train_loader,
num_epochs=epochs, temperature=4.0, alpha=0.5,
device=device
)
def step2_pruning(self, train_loader, sparsity=0.5,
finetune_epochs=10, device='cuda'):
"""第 2 步:渐进式剪枝 + 微调。"""
print(f"=== Step 2: Pruning (target sparsity: {sparsity:.0%}) ===")
pruner = GradualMagnitudePruner(
self.student,
initial_sparsity=0.0,
final_sparsity=sparsity,
begin_step=0,
end_step=len(train_loader) * finetune_epochs,
frequency=100
)
optimizer = torch.optim.Adam(
self.student.parameters(), lr=1e-4
)
self.student.to(device)
step = 0
for epoch in range(finetune_epochs):
for images, labels in train_loader:
images, labels = images.to(device), labels.to(device)
outputs = self.student(images)
loss = F.cross_entropy(outputs, labels)
optimizer.zero_grad()
loss.backward()
optimizer.step()
pruner.step(step)
pruner.apply_masks() # 保持剪枝 mask
step += 1
def step3_quantization(self, calibration_loader, device='cpu'):
"""第 3 步:训练后量化(Post-Training Quantization)。"""
print("=== Step 3: Quantization ===")
self.student.eval().to(device)
# 准备静态量化
self.student.qconfig = torch.ao.quantization.get_default_qconfig('fbgemm')
torch.ao.quantization.prepare(self.student, inplace=True)
# 用校准数据确定 scale/zero_point
with torch.no_grad():
for images, _ in calibration_loader:
self.student(images.to(device))
# 应用量化
torch.ao.quantization.convert(self.student, inplace=True)
print("Quantization complete (INT8)")
return self.student
def compare_models(self, val_loader, device='cuda'):
"""比较 Teacher、Student、Pruned、Quantized 模型的性能。"""
def eval_model(model, loader, dev):
model.eval().to(dev)
correct, total = 0, 0
with torch.no_grad():
for images, labels in loader:
images, labels = images.to(dev), labels.to(dev)
preds = model(images).argmax(1)
correct += (preds == labels).sum().item()
total += labels.size(0)
return correct / total
teacher_acc = eval_model(self.teacher, val_loader, device)
student_acc = eval_model(self.student, val_loader, 'cpu')
t_params = sum(p.numel() for p in self.teacher.parameters())
s_params = sum(p.numel() for p in self.student.parameters())
print(f"\n{'='*50}")
print(f"Teacher | Params: {t_params:>10,} | Acc: {teacher_acc:.4f}")
print(f"Student | Params: {s_params:>10,} | Acc: {student_acc:.4f}")
print(f"压缩率: {t_params/s_params:.1f}x | 性能保留率: {student_acc/teacher_acc:.1%}")
结语
知识蒸馏与模型压缩,是让 AI 模型在现实世界中真正可用的核心技术。
要点总结:
- 知识蒸馏:通过 Teacher 的软目标(概率分布)传递类别间的关系信息
- Feature 蒸馏:将中间层的表示传递给 Student
- Relation 蒸馏:保留样本间的关系结构
- LLM 蒸馏:DistilBERT、TinyLLM 等实用的大模型压缩
- 结构化剪枝:以过滤器 / 头 / 层为单位移除,带来实际速度提升
- 非结构化剪枝:通过渐进式稀疏化最小化精度损失
- 权重共享:像 ALBERT 那样反复使用相同参数
- NAS:DARTS、OFA 等自动化的结构搜索
在实际部署时,按蒸馏 → 剪枝 → 量化的顺序依次应用的流水线最为有效。
参考文献
- Hinton et al. (2015). Distilling the Knowledge in a Neural Network. https://arxiv.org/abs/1503.02531
- Romero et al. (2015). FitNets: Hints for Thin Deep Nets.
- Zagoruyko and Komodakis (2017). Paying More Attention to Attention.
- Park et al. (2019). Relational Knowledge Distillation.
- Sanh et al. (2019). DistilBERT. https://arxiv.org/abs/1910.01108
- Lan et al. (2019). ALBERT: A Lite BERT.
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