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# MIT license
import math
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
class L0Module(nn.Module):
limit_a, limit_b, epsilon = -.1, 1.1, 1e-6
all_types = ["hidden_z", "heads_z", "mha_z", "intermediate_z", "ffn_z"]
def __init__(self, config,
start_sparsity=0.0,
target_sparsity=0.0,
lagrangian_warmup=0,
init_loga=0.5,
temperature=2. / 3.,
pruning_type=["hidden", "heads", "intermediate", "layer"],
magical_number=0.8, # from Wang et al. 2020
):
super(L0Module, self).__init__()
self.magical_number = magical_number
self.lagrangian_warmup = lagrangian_warmup
self.pruning_type = pruning_type
self.start_sparsity = start_sparsity
self.target_sparsity = target_sparsity
self.temperature = temperature
self.hidden_size = config.hidden_size
self.intermediate_size = config.intermediate_size
self.num_attention_heads = config.num_attention_heads
self.dim_per_head = self.hidden_size // self.num_attention_heads
self.num_hidden_layers = config.num_hidden_layers
self.params_per_head_layer = self.hidden_size * \
self.hidden_size * 4 + self.hidden_size * 4
self.params_per_head = self.params_per_head_layer // self.num_attention_heads
self.params_per_mlp_layer = self.hidden_size * self.intermediate_size * \
2 + self.hidden_size + self.intermediate_size
self.params_per_intermediate_dim = self.params_per_mlp_layer // self.intermediate_size
# we ignore the parameters in normalization layers (it takes a very small amount)
self.full_model_size = (
self.params_per_head_layer + self.params_per_mlp_layer) * self.num_hidden_layers
self.prunable_model_size = 0
init_loga = init_loga if isinstance(init_loga, float) else 0.5
self.loga_mean = math.log(
1.0 - self.epsilon - init_loga) - math.log(init_loga + self.epsilon)
self.types = []
self.z_logas = {}
self.parameters_per_dim = {}
self.sizes = {}
self.shapes = {}
self.hidden_loga = None
self.hidden_type = None
for t in pruning_type:
self.initialize_one_module(t)
self.lambda_1 = nn.Parameter(torch.tensor(10.00))
self.lambda_2 = nn.Parameter(torch.tensor(10.00))
def initialize_parameters(self, size, num_layer=None, mean=None):
if num_layer is not None:
loga = nn.Parameter(torch.Tensor(num_layer, size))
else:
loga = nn.Parameter(torch.Tensor(size))
mean = mean or self.loga_mean
# loga.data.normal_(mean, 1e-2)
loga.data.normal_(mean, 0)
return loga
def initialize_one_module(self, module_name):
default_mean = 10
if module_name == "intermediate":
self.intermediate_loga = self.initialize_parameters(
self.intermediate_size, self.num_hidden_layers, mean=default_mean)
self.add_one_module(
self.intermediate_loga, type_name="intermediate",
parameter_per_dim=self.params_per_intermediate_dim, size=self.intermediate_size,
shape=[self.num_hidden_layers, 1, 1, self.intermediate_size]
)
self.prunable_model_size += self.params_per_mlp_layer * self.num_hidden_layers
elif module_name == "heads":
self.heads_loga = self.initialize_parameters(
self.num_attention_heads, self.num_hidden_layers, mean=default_mean)
self.add_one_module(
self.heads_loga, type_name="heads",
parameter_per_dim=self.params_per_head, size=self.num_attention_heads,
shape=[self.num_hidden_layers, 1,
self.num_attention_heads, 1, 1]
)
self.prunable_model_size += self.params_per_head * \
self.num_hidden_layers * self.num_attention_heads
elif module_name == "hidden":
self.hidden_loga = self.initialize_parameters(
self.hidden_size, mean=default_mean)
self.add_one_module(
self.hidden_loga, type_name="hidden",
parameter_per_dim=self.hidden_size * 4 + self.hidden_size * 4 * 2,
size=self.hidden_size, shape=[self.hidden_size]
)
elif module_name == "layer":
self.ffn_loga = self.initialize_parameters(
self.num_hidden_layers, mean=default_mean)
self.add_one_module(
self.ffn_loga, type_name="ffn",
parameter_per_dim=self.params_per_mlp_layer, size=1,
shape=[self.num_hidden_layers]
)
self.mha_loga = self.initialize_parameters(
self.num_hidden_layers, mean=default_mean)
self.add_one_module(
self.mha_loga, type_name="mha",
parameter_per_dim=self.params_per_head * self.num_attention_heads, size=1,
shape=[self.num_hidden_layers]
)
# ! init the z_logas
def add_one_module(self, z_loga, type_name, parameter_per_dim, size, shape):
self.types.append(type_name)
self.z_logas[type_name] = z_loga
self.parameters_per_dim[type_name] = parameter_per_dim
self.sizes[type_name] = size
self.shapes[type_name] = shape
def constrain_parameters(self):
for key in self.z_logas:
self.z_logas[key].data.clamp_(
min=math.log(1e-2), max=math.log(1e2))
def cdf_qz(self, x, loga):
"""Implements the CDF of the 'stretched' concrete distribution"""
xn = (x - self.limit_a) / (self.limit_b - self.limit_a)
logits = math.log(xn) - math.log(1.0 - xn)
return torch.sigmoid(logits * self.temperature - loga).clamp(min=self.epsilon, max=1 - self.epsilon)
def score_loga(self, loga):
return 1.0 - self.cdf_qz(0.0, loga)
def get_num_parameters_and_constraint(self, hidden=False):
num_parameters = 0
layers = self.num_hidden_layers
hidden_size = self.hidden_size
heads = self.num_attention_heads
device = self.z_logas[self.types[0]].device
# 12 * 1 * 1
mha_score = self.score_loga(self.mha_loga).view(
-1, 1, 1) if "mha" in self.types else torch.ones([layers, 1, 1]).to(device)
# 12 * 12 * 1
heads_score = self.score_loga(self.heads_loga).unsqueeze(
dim=-1) if "heads" in self.types else torch.ones([layers, heads, 1]).to(device)
if "heads" not in self.parameters_per_dim:
self.parameters_per_dim["heads"] = self.params_per_head
if "intermediate" not in self.parameters_per_dim:
self.parameters_per_dim["intermediate"] = self.params_per_intermediate_dim
if hidden:
hidden_score = self.score_loga(
self.hidden_loga) if "hidden" in self.types else torch.ones([hidden_size]).to(device)
heads_score = (
heads_score * mha_score) if mha_score is not None else heads_score # 38+106
heads_score = heads_score.reshape(-1)
num_parameters += torch.outer(hidden_score, heads_score).sum(
) * self.parameters_per_dim["heads"] / self.hidden_size
else:
heads_score = heads_score * mha_score
num_parameters += heads_score.sum() * \
self.parameters_per_dim["heads"]
# 12 * 1
if 'ffn' in self.types:
ffn_score = self.score_loga(self.ffn_loga).unsqueeze(
dim=-1) if "ffn" in self.types else torch.ones([layers, 1]).to(device)
else:
ffn_score = 1
# 12 * 3072
intermediate_score = self.score_loga(self.intermediate_loga) if "intermediate" in self.types else torch.ones([
layers, hidden_size * 4]).to(device)
intermediate_score = intermediate_score * ffn_score
if hidden:
intermediate_score = intermediate_score.reshape(-1) # 13893+22971
num_parameters += torch.sum(torch.outer(hidden_score,
intermediate_score)) * 2
else:
num_parameters += intermediate_score.sum() * \
self.parameters_per_dim["intermediate"]
return num_parameters
def get_target_sparsity(self, pruned_steps):
target_sparsity = (self.target_sparsity - self.start_sparsity) * \
min(1, pruned_steps / self.lagrangian_warmup) + self.start_sparsity
return target_sparsity
def lagrangian_regularization(self, pruned_steps):
target_sparsity = self.get_target_sparsity(
pruned_steps) if self.lagrangian_warmup > 0 else self.target_sparsity
expect_sparsity = 1 - self.get_num_parameters_and_constraint(
"hidden" in self.types) / self.prunable_model_size
# lagrangian_loss = (
# self.lambda_1 * (expect_sparsity - target_sparsity).abs() +
# self.lambda_2 * (expect_sparsity - target_sparsity).square()
# )
zero = torch.tensor(0.0, device=expect_sparsity.device)
lagrangian_loss = (
self.lambda_1 * torch.maximum(target_sparsity - expect_sparsity, zero) +
self.lambda_2 *
torch.maximum(target_sparsity - expect_sparsity, zero).square()
)
return lagrangian_loss, expect_sparsity.detach().item(), target_sparsity
# during training
def _sample_z(self, loga):
# Uniform random numbers for the concrete distribution
u = torch.zeros_like(loga).uniform_(self.epsilon, 1.0 - self.epsilon)
# quantile concrete
z = torch.sigmoid(
(torch.log(u) - torch.log(1 - u) + loga) / self.temperature)
z = z * (self.limit_b - self.limit_a) + self.limit_a
z = F.hardtanh(z, min_val=0.0, max_val=1.0)
return z
# during inference
def _deterministic_z(self, size, loga, soft=True):
soft_mask = torch.sigmoid(
loga / self.temperature * self.magical_number)
if not soft:
return soft_mask
expected_num_zeros = size - self.score_loga(loga).sum().item()
num_zeros = round(expected_num_zeros)
if num_zeros > 0:
if soft_mask.ndim == 0:
soft_mask = torch.tensor(0).to(loga.device)
else:
_, indices = torch.topk(soft_mask, k=num_zeros, largest=False)
soft_mask[indices] = 0.
return soft_mask
def get_z_from_zs(self, zs):
numpified_zs = {}
# for t in self.all_types:
# name = t[:-2]
for t in self.types:
name = t
numpified_zs[name] = (zs[t].squeeze().detach().cpu(
).numpy() > 0) if t in zs else np.ones(self.shapes[name])
return numpified_zs
def calculate_model_size(self, zs):
if zs is None:
return {"pruned_sparsity": 0.0}
layers = self.num_hidden_layers
hidden_size = self.hidden_size
heads = self.num_attention_heads
device = self.z_logas[self.types[0]].device
numpified_zs = self.get_z_from_zs(zs)
hidden_z = numpified_zs["hidden"] if "hidden" in numpified_zs.keys() else np.ones([
hidden_size])
heads_z = numpified_zs["heads"] if "heads" in numpified_zs.keys() else np.ones([
layers, 1, heads, 1, 1])
mha_z = numpified_zs["mha"].reshape(-1, 1, 1, 1, 1) if "mha" in numpified_zs.keys(
) else np.ones([heads_z.shape[0], 1, 1, 1, 1])
intermediate_z = numpified_zs["intermediate"] if "intermediate" in numpified_zs.keys(
) else np.ones([layers, 1, 1, hidden_size * 4])
ffn_z = numpified_zs["ffn"].reshape(-1, 1, 1, 1) if "ffn" in numpified_zs.keys(
) else np.ones([heads_z.shape[0], 1, 1, 1])
remain_hidden = hidden_z.sum().item()
remain_intermediate = intermediate_z.reshape(
self.num_hidden_layers, self.intermediate_size).sum(-1).tolist()
remain_heads = heads_z.reshape(
self.num_hidden_layers, self.num_attention_heads).sum(-1).tolist()
heads = np.outer((heads_z * mha_z).reshape(-1), hidden_z).sum().item()
intermediate = np.outer(
(intermediate_z * ffn_z).reshape(-1), hidden_z).sum().item()
remain_model_size = heads * self.dim_per_head * 4 + intermediate * 2
pruned_model_size = self.prunable_model_size - remain_model_size
results = {
'mha': mha_z.reshape(-1).astype(int).tolist(),
'ffn': ffn_z.reshape(-1).astype(int).tolist(),
'remain_hidden': remain_hidden,
'remain_intermediate': remain_intermediate,
'remain_heads': remain_heads,
'pruned_params': pruned_model_size,
'remain_params': remain_model_size,
'pruned_sparsity': pruned_model_size / self.prunable_model_size
}
return results
def forward(self, soft=True):
zs = {f"{t}_z": [] for t in self.types}
if self.training:
for i, t in enumerate(self.types):
loga = self.z_logas[t]
z = self._sample_z(loga)
zs[f"{t}_z"] = z.reshape(self.shapes[t])
else:
for i, t in enumerate(self.types):
if t != "hidden": # hidden is not a per layer sample
tmp = []
for loga in self.z_logas[t]:
z = self._deterministic_z(
self.sizes[t], loga.detach(), soft=soft)
tmp.append(z.reshape(self.shapes[t][1:]))
zs[f"{t}_z"] = torch.stack(tmp)
else:
zs[f"{t}_z"] = self._deterministic_z(
self.sizes[t], self.hidden_loga.detach(), soft=soft)
return zs
@torch.no_grad()
def l0_mask(self):
zs = {f"{t}_z": [] for t in self.types}
# self.magical_number = 1.0
def get_mask(loga): return torch.sigmoid(
loga / self.temperature * self.magical_number)
for t in self.types:
if t == "hidden":
zs[f"{t}_z"] = get_mask(self.hidden_loga)
else:
tmp = []
loga_all_layers = self.z_logas[t]
for layer in range(len(loga_all_layers)):
loga = loga_all_layers[layer]
z = get_mask(loga)
tmp.append(z.reshape(self.shapes[t][1:]))
zs[f"{t}_z"] = torch.stack(tmp)
return zs
if __name__ == '__main__':
from collections import namedtuple
Config = namedtuple('Config', [
'hidden_size', 'intermediate_size', 'num_attention_heads', 'num_hidden_layers'])
config = Config(hidden_size=768, intermediate_size=4 * 768,
num_attention_heads=12, num_hidden_layers=12)
l0_module = L0Module(config, lagrangian_warmup=200, target_sparsity=0.5)
l0_module.train()
zs = l0_module()
l0_module.eval()
zs = l0_module()
result = l0_module.calculate_model_size(zs)
print(result)
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