File size: 11,671 Bytes
581227b |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 |
from dataclasses import dataclass
from typing import Optional
import math
import torch
import torch.nn as nn
import torch.nn.functional as F
@dataclass
class ModelArgs:
dim: int = 4096
n_layers: int = 32
n_heads: int = 32
n_kv_heads: Optional[int] = None
vocab_size: int = -1 # Later set in the build method
multiple_of: int = 256
ffn_dim_multiplier: Optional[float] = None
norm_eps: float = 1e-5
# Needed for KV cache
max_batch_size: int = 32
max_seq_len: int = 2048
device: str = None
class RMSNorm(nn.Module):
def __init__(self, dim: int, eps: float = 1e-6):
super().__init__()
self.eps = eps
# The gamma parameter
self.weight = nn.Parameter(torch.ones(dim))
def _norm(self, x: torch.Tensor):
# (B, Seq_Len, Dim) * (B, Seq_Len, 1) = (B, Seq_Len, Dim)
# rsqrt: 1 / sqrt(x)
return x * torch.rsqrt(x.pow(2).mean(-1, keepdim=True) + self.eps)
def forward(self, x: torch.Tensor):
# (Dim) * (B, Seq_Len, Dim) = (B, Seq_Len, Dim)
return self.weight * self._norm(x.float()).type_as(x)
def precompute_theta_pos_frequencies(head_dim: int, seq_len: int, device: str, theta: float = 10000.0):
# As written in the paragraph 3.2.2 of the paper
# >> In order to generalize our results in 2D to any xi ∈ Rd where **d is even**, [...]
assert head_dim % 2 == 0, "Dimension must be divisible by 2"
# Build the theta parameter
# According to the formula theta_i = 10000^(-2(i-1)/dim) for i = [1, 2, ... dim/2]
# Shape: (Head_Dim / 2)
theta_numerator = torch.arange(0, head_dim, 2).float()
# Shape: (Head_Dim / 2)
theta = 1.0 / (theta ** (theta_numerator / head_dim)).to(device) # (Dim / 2)
# Construct the positions (the "m" parameter)
# Shape: (Seq_Len)
m = torch.arange(seq_len, device=device)
# Multiply each theta by each position using the outer product.
# Shape: (Seq_Len) outer_product* (Head_Dim / 2) -> (Seq_Len, Head_Dim / 2)
freqs = torch.outer(m, theta).float()
# We can compute complex numbers in the polar form c = R * exp(m * theta), where R = 1 as follows:
# (Seq_Len, Head_Dim / 2) -> (Seq_Len, Head_Dim / 2)
freqs_complex = torch.polar(torch.ones_like(freqs), freqs)
return freqs_complex
def apply_rotary_embeddings(x: torch.Tensor, freqs_complex: torch.Tensor, device: str):
# Separate the last dimension pairs of two values, representing the real and imaginary parts of the complex number
# Two consecutive values will become a single complex number
# (B, Seq_Len, H, Head_Dim) -> (B, Seq_Len, H, Head_Dim/2)
x_complex = torch.view_as_complex(x.float().reshape(*x.shape[:-1], -1, 2))
# Reshape the freqs_complex tensor to match the shape of the x_complex tensor. So we need to add the batch dimension and the head dimension
# (Seq_Len, Head_Dim/2) --> (1, Seq_Len, 1, Head_Dim/2)
freqs_complex = freqs_complex.unsqueeze(0).unsqueeze(2)
# Multiply each complex number in the x_complex tensor by the corresponding complex number in the freqs_complex tensor
# Which results in the rotation of the complex number as shown in the Figure 1 of the paper
# (B, Seq_Len, H, Head_Dim/2) * (1, Seq_Len, 1, Head_Dim/2) = (B, Seq_Len, H, Head_Dim/2)
x_rotated = x_complex * freqs_complex
# Convert the complex number back to the real number
# (B, Seq_Len, H, Head_Dim/2) -> (B, Seq_Len, H, Head_Dim/2, 2)
x_out = torch.view_as_real(x_rotated)
# (B, Seq_Len, H, Head_Dim/2, 2) -> (B, Seq_Len, H, Head_Dim)
x_out = x_out.reshape(*x.shape)
return x_out.type_as(x).to(device)
def repeat_kv(x: torch.Tensor, n_rep: int) -> torch.Tensor:
batch_size, seq_len, n_kv_heads, head_dim = x.shape
if n_rep == 1:
return x
return (
# (B, Seq_Len, N_KV_Heads, 1, Head_Dim)
x[:, :, :, None, :]
# (B, Seq_Len, N_KV_Heads, N_Rep, Head_Dim)
.expand(batch_size, seq_len, n_kv_heads, n_rep, head_dim)
# (B, Seq_Len, N_KV_Heads * N_Rep, Head_Dim)
.reshape(batch_size, seq_len, n_kv_heads * n_rep, head_dim)
)
class SelfAttention(nn.Module):
def __init__(self, args: ModelArgs):
super().__init__()
# Indicates the number of heads for the Keys and Values
self.n_kv_heads = args.n_heads if args.n_kv_heads is None else args.n_kv_heads
# Indicates the number of heads for the Queries
self.n_heads_q = args.n_heads
# Indicates how many times the Keys and Values should be repeated
self.n_rep = self.n_heads_q // self.n_kv_heads
# Indicates the dimension of each head, that is, the part of the embedding that each head will be responsible for
self.head_dim = args.dim // args.n_heads
self.wq = nn.Linear(args.dim, args.n_heads * self.head_dim, bias=False)
self.wk = nn.Linear(args.dim, self.n_kv_heads * self.head_dim, bias=False)
self.wv = nn.Linear(args.dim, self.n_kv_heads * self.head_dim, bias=False)
self.wo = nn.Linear(args.n_heads * self.head_dim, args.dim, bias=False)
self.cache_k = torch.zeros((args.max_batch_size, args.max_seq_len, self.n_kv_heads, self.head_dim))
self.cache_v = torch.zeros((args.max_batch_size, args.max_seq_len, self.n_kv_heads, self.head_dim))
def forward(
self,
x: torch.Tensor,
start_pos: int,
freqs_complex: torch.Tensor
):
batch_size, seq_len, _ = x.shape # (B, 1, Dim)
# (B, 1, Dim) -> (B, 1, H_Q * Head_Dim)
xq = self.wq(x)
# (B, 1, Dim) -> (B, 1, H_KV * Head_Dim)
xk = self.wk(x)
# (B, 1, Dim) -> (B, 1, H_KV * Head_Dim)
xv = self.wv(x)
# (B, 1, H_Q * Head_Dim) -> (B, 1, H_Q, Head_Dim)
xq = xq.view(batch_size, seq_len, self.n_heads_q, self.head_dim)
# (B, 1, H_KV * Head_Dim) -> (B, 1, H_KV, Head_Dim)
xk = xk.view(batch_size, seq_len, self.n_kv_heads, self.head_dim)
# (B, 1, H_KV * Head_Dim) -> (B, 1, H_KV, Head_Dim)
xv = xv.view(batch_size, seq_len, self.n_kv_heads, self.head_dim)
# (B, 1, H_Q, Head_Dim) --> (B, 1, H_Q, Head_Dim)
xq = apply_rotary_embeddings(xq, freqs_complex, device=x.device)
# (B, 1, H_KV, Head_Dim) --> (B, 1, H_KV, Head_Dim)
xk = apply_rotary_embeddings(xk, freqs_complex, device=x.device)
# Replace the entry in the cache
self.cache_k[:batch_size, start_pos : start_pos + seq_len] = xk
self.cache_v[:batch_size, start_pos : start_pos + seq_len] = xv
# (B, Seq_Len_KV, H_KV, Head_Dim)
keys = self.cache_k[:batch_size, : start_pos + seq_len]
# (B, Seq_Len_KV, H_KV, Head_Dim)
values = self.cache_v[:batch_size, : start_pos + seq_len]
# Since every group of Q shares the same K and V heads, just repeat the K and V heads for every Q in the same group.
# (B, Seq_Len_KV, H_KV, Head_Dim) --> (B, Seq_Len_KV, H_Q, Head_Dim)
keys = repeat_kv(keys, self.n_rep)
# (B, Seq_Len_KV, H_KV, Head_Dim) --> (B, Seq_Len_KV, H_Q, Head_Dim)
values = repeat_kv(values, self.n_rep)
# (B, 1, H_Q, Head_Dim) -> (B, H_Q, 1, Head_Dim)
xq = xq.transpose(1, 2)
# (B, Seq_Len_KV, H_Q, Head_Dim) -> (B, H_Q, Seq_Len_KV, Head_Dim)
keys = keys.transpose(1, 2)
# (B, Seq_Len_KV, H_Q, Head_Dim) -> (B, H_Q, Seq_Len_KV, Head_Dim)
values = values.transpose(1, 2)
# (B, H_Q, 1, Head_Dim) @ (B, H_Q, Head_Dim, Seq_Len_KV) -> (B, H_Q, 1, Seq_Len_KV)
scores = torch.matmul(xq, keys.transpose(2, 3)) / math.sqrt(self.head_dim)
# (B, H_Q, 1, Seq_Len_KV) -> (B, H_Q, 1, Seq_Len_KV)
scores = F.softmax(scores.float(), dim=-1).type_as(xq)
# (B, H_Q, 1, Seq_Len) @ (B, H_Q, Seq_Len_KV, Head_Dim) -> (B, H_Q, 1, Head_Dim)
output = torch.matmul(scores, values)
# (B, H_Q, 1, Head_Dim) -> (B, 1, H_Q, Head_Dim) -> (B, 1, Dim)
output = (output.transpose(1, 2).contiguous().view(batch_size, seq_len, -1))
return self.wo(output) # (B, 1, Dim) -> (B, 1, Dim)
class FeedForward(nn.Module):
def __init__(
self,
args: ModelArgs
):
super().__init__()
hidden_dim = 4 * args.dim
hidden_dim = int(2 * hidden_dim / 3)
if args.ffn_dim_multiplier is not None:
hidden_dim = int(args.ffn_dim_multiplier * hidden_dim)
# Round the hidden_dim to the nearest multiple of the multiple_of parameter
hidden_dim = args.multiple_of * ((hidden_dim + args.multiple_of - 1) // args.multiple_of)
self.w1 = nn.Linear(args.dim, hidden_dim, bias=False)
self.w2 = nn.Linear(hidden_dim, args.dim, bias=False)
self.w3 = nn.Linear(args.dim, hidden_dim, bias=False)
def forward(self, x: torch.Tensor):
# (B, Seq_Len, Dim) --> (B, Seq_Len, Hidden_Dim)
swish = F.silu(self.w1(x))
# (B, Seq_Len, Dim) --> (B, Seq_Len, Hidden_Dim)
x_V = self.w3(x)
# (B, Seq_Len, Hidden_Dim) * (B, Seq_Len, Hidden_Dim) --> (B, Seq_Len, Hidden_Dim)
x = swish * x_V
# (B, Seq_Len, Hidden_Dim) --> (B, Seq_Len, Dim)
x = self.w2(x)
return x
class EncoderBlock(nn.Module):
def __init__(self, args: ModelArgs):
super().__init__()
self.n_heads = args.n_heads
self.dim = args.dim
self.head_dim = args.dim // args.n_heads
self.attention = SelfAttention(args)
self.feed_forward = FeedForward(args)
# Normalization BEFORE the attention block
self.attention_norm = RMSNorm(args.dim, eps=args.norm_eps)
# Normalization BEFORE the feed forward block
self.ffn_norm = RMSNorm(args.dim, eps=args.norm_eps)
def forward(self, x: torch.Tensor, start_pos: int, freqs_complex: torch.Tensor):
# (B, Seq_Len, Dim) + (B, Seq_Len, Dim) --> (B, Seq_Len, Dim)
h = x + self.attention.forward(
self.attention_norm(x), start_pos, freqs_complex
)
# (B, Seq_Len, Dim) + (B, Seq_Len, Dim) --> (B, Seq_Len, Dim)
out = h + self.feed_forward.forward(self.ffn_norm(h))
return out
class Transformer(nn.Module):
def __init__(self, args: ModelArgs):
super().__init__()
assert args.vocab_size != -1, "Vocab size must be set"
self.args = args
self.vocab_size = args.vocab_size
self.n_layers = args.n_layers
self.tok_embeddings = nn.Embedding(self.vocab_size, args.dim)
self.layers = nn.ModuleList()
for layer_id in range(args.n_layers):
self.layers.append(EncoderBlock(args))
self.norm = RMSNorm(args.dim, eps=args.norm_eps)
self.output = nn.Linear(args.dim, self.vocab_size, bias=False)
self.freqs_complex = precompute_theta_pos_frequencies(self.args.dim // self.args.n_heads, self.args.max_seq_len * 2, device=self.args.device)
def forward(self, tokens: torch.Tensor, start_pos: int):
# (B, Seq_Len)
batch_size, seq_len = tokens.shape
assert seq_len == 1, "Only one token at a time can be processed"
# (B, Seq_Len) -> (B, Seq_Len, Dim)
h = self.tok_embeddings(tokens)
# Retrieve the pairs (m, theta) corresponding to the positions [start_pos, start_pos + seq_len]
freqs_complex = self.freqs_complex[start_pos:start_pos + seq_len]
# Consecutively apply all the encoder layers
for layer in self.layers:
h = layer(h, start_pos, freqs_complex)
h = self.norm(h)
output = self.output(h).float()
return output |