1 introduction
按照karpathy的教程，一步步的完成transformer的构建，并在这个过程中，加深对transformer设计的理解。
karpathy推荐在进行网络设计的过程中，同时利用jupyter notebook进行快速测试和python进行主要的网络的构建。
2 网络实现
2.1 数据的构建
- 读取text
text = open("input.txt", "r", encoding='utf-8').read()
words = sorted(set(''.join(text)))
vocab_size = len(words)
print(f'vocab_size is: {vocab_size}')
print(''.join(words))
print(text[:1000])
vocab_size is: 65
!$&',-.3:;?ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz
First Citizen:
Before we proceed any further, hear me speak.
All:
Speak, speak.
First Citizen:
You are all resolved rather to die than to famish?
- 将字符转换成数字
stoi = {ch : i for i, ch in enumerate(words)}
itos = {i : ch for i, ch in enumerate(words)}
encode = lambda s: [stoi[ch] for ch in s]
decode = lambda l: ''.join([itos[i] for i in l])
print(encode("hii"))
print(decode(encode("hii")))
[46, 47, 47]
hii
- 制作数据集
import torch
# 生成数据集
data = torch.tensor(encode(text), dtype=torch.long)
print(len(data))
n = int(len(data) * 0.9)
train_data = data[:n]
val_data = data[n:]
print(train_data[:1000])
1115394
tensor([18, 47, 56, 57, 58, 1, 15, 47, 58, 47, 64, 43, 52, 10, 0, 14, 43, 44,
53, 56, 43, 1, 61, 43, 1, 54, 56, 53, 41, 43, 43, 42, 1, 39, 52, 63,
1, 44, 59, 56, 58, 46, 43, 56, 6, 1, 46, 43, 39, 56, 1, 51, 43, 1,
57, 54, 43, 39, 49, 8, 0, 0, 13, 50, 50, 10, 0, 31, 54, 43, 39, 49,
- 构建dataloader
import torch
batch_size = 4
torch.manual_seed(1337)
def get_batch(split):
datasets = {
'train': train_data,
'val': val_data,
}[split]
ix = torch.randint(0, len(datasets) - block_size, (batch_size,))
x = torch.stack([datasets[i:i+block_size] for i in ix])
y = torch.stack([datasets[1+i:i+block_size+1] for i in ix])
return x, y
xb, yb = get_batch('train')
print(f'x shape is: {xb.shape}, y shape is: {yb.shape}')
print(f'x is {xb}')
print(f'y is {yb}')
x shape is: torch.Size([4, 8]), y shape is: torch.Size([4, 8])
x is tensor([[24, 43, 58, 5, 57, 1, 46, 43],
[44, 53, 56, 1, 58, 46, 39, 58],
[52, 58, 1, 58, 46, 39, 58, 1],
[25, 17, 27, 10, 0, 21, 1, 54]])
y is tensor([[43, 58, 5, 57, 1, 46, 43, 39],
[53, 56, 1, 58, 46, 39, 58, 1],
[58, 1, 58, 46, 39, 58, 1, 46],
[17, 27, 10, 0, 21, 1, 54, 39]])
2.2 构建pipeline
- 定义一个最简单的网络
import torch.nn as nn
import torch.nn.functional as F
torch.manual_seed(1337)
class BigramLanguageModel(nn.Module):
def __init__(self, vocab_size):
super().__init__()
self.token_embedding_table = nn.Embedding(vocab_size, vocab_size)
def forward(self, idx, targets=None):
self.out = self.token_embedding_table(idx)
return self.out
xb, yb = get_batch('train')
model = BigramLanguageModel(vocab_size)
out = model(xb)
print(f'x shape is: {xb.shape}')
print(f'out shape is: {out.shape}')
x shape is: torch.Size([4, 8])
out shape is: torch.Size([4, 8, 65])
- 包含输出以后的完整的pipeline是
from typing import Iterator
import torch.nn as nn
import torch.nn.functional as F
torch.manual_seed(1337)
class BigramLanguageModel(nn.Module):
def __init__(self, vocab_size):
super().__init__()
self.token_embedding_table = nn.Embedding(vocab_size, vocab_size)
def forward(self, idx, targets=None):
logits = self.token_embedding_table(idx) # B, T, C
if targets is None:
loss = None
else:
B, T, C = logits.shape
logits = logits.view(B*T, C) # 这是很好理解的
targets = targets.view(B*T) # 但是targets是B，T
loss = F.cross_entropy(logits, targets)
return logits, loss
def generate(self, idx, max_new_tokens):
for _ in range(max_new_tokens):
logits, loss = self(idx)
logits = logits[:, -1, :] # B, C
prob = F.softmax(logits, dim=-1) # 对最后一维进行softmax
ix = torch.multinomial(prob, num_samples=1) # B, C
print(idx)
idx = torch.cat((idx, ix), dim=1) # B,T+1
print(idx)
return idx
# ix = ix.view(B)
xb, yb = get_batch('train')
model = BigramLanguageModel(vocab_size)
out, loss = model(xb)
print(f'x shape is: {xb.shape}')
print(f'out shape is: {out.shape}')
idx = idx = torch.zeros((1, 1), dtype=torch.long)
print(decode(model.generate(idx, max_new_tokens=10)[0].tolist()))
# print(f'idx is {idx}')
x shape is: torch.Size([4, 8])
out shape is: torch.Size([4, 8, 65])
tensor([[0]])
tensor([[ 0, 50]])
tensor([[ 0, 50]])
tensor([[ 0, 50, 7]])
tensor([[ 0, 50, 7]])
tensor([[ 0, 50, 7, 29]])
tensor([[ 0, 50, 7, 29]])
tensor([[ 0, 50, 7, 29, 37]])
tensor([[ 0, 50, 7, 29, 37]])
tensor([[ 0, 50, 7, 29, 37, 48]])
tensor([[ 0, 50, 7, 29, 37, 48]])
tensor([[ 0, 50, 7, 29, 37, 48, 58]])
tensor([[ 0, 50, 7, 29, 37, 48, 58]])
tensor([[ 0, 50, 7, 29, 37, 48, 58, 5]])
tensor([[ 0, 50, 7, 29, 37, 48, 58, 5]])
tensor([[ 0, 50, 7, 29, 37, 48, 58, 5, 15]])
tensor([[ 0, 50, 7, 29, 37, 48, 58, 5, 15]])
tensor([[ 0, 50, 7, 29, 37, 48, 58, 5, 15, 24]])
tensor([[ 0, 50, 7, 29, 37, 48, 58, 5, 15, 24]])
tensor([[ 0, 50, 7, 29, 37, 48, 58, 5, 15, 24, 12]])
l-QYjt’CL?
这里有几个地方需要注意，首先输入输出是：
x is tensor([[24, 43, 58, 5, 57, 1, 46, 43],
[44, 53, 56, 1, 58, 46, 39, 58],
[52, 58, 1, 58, 46, 39, 58, 1],
[25, 17, 27, 10, 0, 21, 1, 54]])
y is tensor([[43, 58, 5, 57, 1, 46, 43, 39],
[53, 56, 1, 58, 46, 39, 58, 1],
[58, 1, 58, 46, 39, 58, 1, 46],
[17, 27, 10, 0, 21, 1, 54, 39]])
并且这个pipeline，网络对输入的长度也没有限制
- 开始训练
这个时候我们需要构建一个完整的训练代码，如果还是用jupyter notebook，每次改变了网络的一个组成部分，需要重新执行很多地方，比较麻烦，所以构建一个.py文件。
import torch
import torch.nn as nn
import torch.nn.functional as F
# hyperparameters
batch_size = 32
block_size = 8
max_iter = 3000
eval_interval = 300
learning_rate = 1e-2
device = 'cuda' if torch.cuda.is_available() else 'cpu'
eval_iters = 200
# ---------------------
torch.manual_seed(1337)
text = open("input.txt", "r", encoding='utf-8').read()
chars = sorted(list(set(text)))
vocab_size = len(chars)
stoi = {ch : i for i, ch in enumerate(chars)}
itos = {i : ch for i, ch in enumerate(chars)}
encode = lambda s: [stoi[ch] for ch in s]
decode = lambda l: ''.join([itos[i] for i in l])
# 生成数据集
data = torch.tensor(encode(text), dtype=torch.long)
n = int(len(data) * 0.9)
train_data = data[:n]
val_data = data[n:]
def get_batch(split):
datasets = {
'train': train_data,
'val': val_data,
}[split]
ix = torch.randint(0, len(datasets) - block_size, (batch_size,))
x = torch.stack([datasets[i:i+block_size] for i in ix])
y = torch.stack([datasets[1+i:i+block_size+1] for i in ix])
x, y = x.to(device), y.to(device)
return x, y
@torch.no_grad()
def estimate_loss():
out = {}
model.eval()
for split in ['train', 'val']:
losses = torch.zeros(eval_iters)
for k in range(eval_iters):
X, Y = get_batch(split)
logits, loss = model(X, Y)
losses[k] = loss.item()
out[split] = losses.mean()
model.train()
return out
class BigramLanguageModel(nn.Module):
def __init__(self, vocab_size):
super().__init__()
self.token_embedding_table = nn.Embedding(vocab_size, vocab_size)
def forward(self, idx, targets=None):
# import pdb; pdb.set_trace()
logits = self.token_embedding_table(idx) # B, T, C
if targets is None:
loss = None
else:
B, T, C = logits.shape
logits = logits.view(B*T, C) # 这是很好理解的
targets = targets.view(B*T) # 但是targets是B，T, C其实并不好理解
loss = F.cross_entropy(logits, targets)
return logits, loss
def generate(self, idx, max_new_tokens):
for _ in range(max_new_tokens):
logits, loss = self(idx)
logits = logits[:, -1, :] # B, C
prob = F.softmax(logits, dim=-1) # 对最后一维进行softmax
ix = torch.multinomial(prob, num_samples=1) # B, 1
# print(idx)
idx = torch.cat((idx, ix), dim=1) # B,T+1
# print(idx)
return idx
model = BigramLanguageModel(vocab_size)
m = model.to(device)
optimizer = torch.optim.AdamW(model.parameters(), lr=learning_rate)
lossi = []
for iter in range(max_iter):
if iter % eval_interval == 0:
losses = estimate_loss()
print(f'step {iter}: train loss {losses["train"]:.4f}, val loss {losses["val"]:.4f}')
xb, yb = get_batch('train')
out, loss = m(xb, yb)
optimizer.zero_grad(set_to_none=True)
loss.backward()
optimizer.step()
# generate from the model
context = torch.zeros((1,1), dtype=torch.long, device=device)
print(decode(m.generate(context, max_new_tokens=500)[0].tolist()))
输出的结果是
step 0: train loss 4.7305, val loss 4.7241
step 300: train loss 2.8110, val loss 2.8249
step 600: train loss 2.5434, val loss 2.5682
step 900: train loss 2.4932, val loss 2.5088
step 1200: train loss 2.4863, val loss 2.5035
step 1500: train loss 2.4665, val loss 2.4921
step 1800: train loss 2.4683, val loss 2.4936
step 2100: train loss 2.4696, val loss 2.4846
step 2400: train loss 2.4638, val loss 2.4879
step 2700: train loss 2.4738, val loss 2.4911
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2.3 self-attention
我们处理当前的字符的时候，需要和历史字符进行通信，历史字符可以看成是某一种特征，使用最简单的均值提取的方式提取历史字符的feature
# 最简单的通信方式，将当前的字符和之前的字符平均进行沟通
# 可以看成是history information的features
a = torch.tril(torch.ones(3, 3))
print(a)
a = torch.tril(a) / torch.sum(a, 1, keepdim=True)
print(a)
tensor([[1., 0., 0.],
[1., 1., 0.],
[1., 1., 1.]])
tensor([[1.0000, 0.0000, 0.0000],
[0.5000, 0.5000, 0.0000],
[0.3333, 0.3333, 0.3333]])
可以采用softmax的方式进行mask
import torch.nn.functional as F
tril = torch.tril(torch.ones(T, T)) # 某种意义上的Q
wei = torch.zeros(T, T) # K
wei = wei.masked_fill(tril == 0, float('-inf'))
print(wei)
wei = F.softmax(wei)
print(wei)
tensor([[0., -inf, -inf, -inf, -inf, -inf, -inf, -inf],
[0., 0., -inf, -inf, -inf, -inf, -inf, -inf],
[0., 0., 0., -inf, -inf, -inf, -inf, -inf],
[0., 0., 0., 0., -inf, -inf, -inf, -inf],
[0., 0., 0., 0., 0., -inf, -inf, -inf],
[0., 0., 0., 0., 0., 0., -inf, -inf],
[0., 0., 0., 0., 0., 0., 0., -inf],
[0., 0., 0., 0., 0., 0., 0., 0.]])
tensor([[1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000],
[0.5000, 0.5000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000],
[0.3333, 0.3333, 0.3333, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000],
[0.2500, 0.2500, 0.2500, 0.2500, 0.0000, 0.0000, 0.0000, 0.0000],
[0.2000, 0.2000, 0.2000, 0.2000, 0.2000, 0.0000, 0.0000, 0.0000],
[0.1667, 0.1667, 0.1667, 0.1667, 0.1667, 0.1667, 0.0000, 0.0000],
[0.1429, 0.1429, 0.1429, 0.1429, 0.1429, 0.1429, 0.1429, 0.0000],
[0.1250, 0.1250, 0.1250, 0.1250, 0.1250, 0.1250, 0.1250, 0.1250]])
特征提取的结果
xbow2 = wei @ x # (T, T) @ (B, T, C) --> (B, T, C) # x对应v
print(xbow2.shape)
torch.Size([4, 8, 2])
加上pos_emb现在的forward版本
def forward(self, idx, targets=None):
# import pdb; pdb.set_trace()
tok_emb = self.token_embedding_table(idx) # B, T, C(n_emb)
pos_emb = self.position_embedding_table(torch.range(T, device=device)) # T,C
# positional encoding
x = tok_emb + pos_emb # (B, T, C) broadcasting
logits = self.lm_head(x) # B, T, C(vocab_size)
if targets is None:
loss = None
else:
B, T, C = logits.shape
logits = logits.view(B*T, C) # 这是很好理解的
targets = targets.view(B*T) # 但是targets是B，T, C其实并不好理解
loss = F.cross_entropy(logits, targets)
return logits, loss
karpathy 给出的一些启示
- Attention is a communication mechanism. Can be seen as nodes in a directed graph looking at each other and aggregating information with a weighted sum from all nodes that point to them, with data-dependent weights.
- There is no notion of space. Attention simply acts over a set of vectors. This is why we need to positionally encode tokens.
- Each example across batch dimension is of course processed completely independently and never “talk” to each other
- In an “encoder” attention block just delete the single line that does masking with tril, allowing all tokens to communicate. This block here is called a “decoder” attention block because it has triangular masking, and is usually used in autoregressive settings, like language modeling.
- “self-attention” just means that the keys and values are produced from the same source as queries. In “cross-attention”, the queries still get produced from x, but the keys and values come from some other, external source (e.g. an encoder module)
- “Scaled” attention additional divides wei by 1/sqrt(head_size). This makes it so when input Q,K are unit variance, wei will be unit variance too and Softmax will stay diffuse and not saturate too much. Illustration below
attention的公式其中scale是为了保证两个分布相乘的时候，方差不变的。
k = torch.randn(B, T, head_size)
q = torch.randn(B, T, head_size)
wei = q @ k.transpose(-2, -1)
wei_scale = wei / head_size**0.5
print(k.var())
print(q.var())
print(wei.var())
print(wei_scale.var())
输出结果
tensor(1.0278)
tensor(0.9802)
tensor(15.9041)
tensor(0.9940)
初始化对结果的影响很大，实际上来说我们还是很希望softmax初始化的结果是一个方差较小的分布，如果不进行scale
torch.softmax(torch.tensor([0.1, -0.2, 0.3, -0.2, 0.5]) * 8, dim=-1)
tensor([0.0326, 0.0030, 0.1615, 0.0030, 0.8000])
对原来的py文件做一些修改：