wehub-resource-sync
275 lines
9.6 KiB
Python
275 lines
9.6 KiB
Python
"""Token and positional embeddings.
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Builds three modules:
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- TokenEmbedding: vocab_size x d_model lookup
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- LearnedPositionalEmbedding: max_context_length x d_model lookup
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- SinusoidalPositionalEmbedding: parameter-free sin/cos table
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Composes them via EmbeddingComposer for the transformer input.
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Run: python3 code/main.py
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"""
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from __future__ import annotations
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import math
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from dataclasses import dataclass
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import torch
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import torch.nn as nn
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DEFAULT_INIT_STD = 0.02
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def _init_normal(weight: torch.Tensor, std: float = DEFAULT_INIT_STD) -> None:
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"""Init a parameter tensor in place from a small Gaussian."""
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with torch.no_grad():
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weight.normal_(mean=0.0, std=std)
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class TokenEmbedding(nn.Module):
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"""Vocabulary-id to vector lookup."""
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def __init__(self, vocab_size: int, d_model: int, init_std: float = DEFAULT_INIT_STD) -> None:
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super().__init__()
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if vocab_size < 1:
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raise ValueError(f"vocab_size must be >= 1, got {vocab_size}")
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if d_model < 1:
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raise ValueError(f"d_model must be >= 1, got {d_model}")
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self.vocab_size = vocab_size
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self.d_model = d_model
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self.embedding = nn.Embedding(vocab_size, d_model)
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_init_normal(self.embedding.weight, std=init_std)
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def forward(self, ids: torch.Tensor) -> torch.Tensor:
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if ids.dtype != torch.long:
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raise TypeError(f"ids must be long tensor, got {ids.dtype}")
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if ids.dim() != 2:
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raise ValueError(f"ids must be (B, T), got shape {tuple(ids.shape)}")
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return self.embedding(ids)
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class LearnedPositionalEmbedding(nn.Module):
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"""Position-id to vector lookup with learned parameters."""
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def __init__(
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self,
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max_context_length: int,
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d_model: int,
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init_std: float = DEFAULT_INIT_STD,
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) -> None:
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super().__init__()
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if max_context_length < 1:
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raise ValueError(f"max_context_length must be >= 1, got {max_context_length}")
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if d_model < 1:
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raise ValueError(f"d_model must be >= 1, got {d_model}")
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self.max_context_length = max_context_length
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self.d_model = d_model
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self.embedding = nn.Embedding(max_context_length, d_model)
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_init_normal(self.embedding.weight, std=init_std)
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def forward(self, seq_len: int) -> torch.Tensor:
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if seq_len < 1:
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raise ValueError(f"seq_len must be >= 1, got {seq_len}")
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if seq_len > self.max_context_length:
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raise ValueError(
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f"seq_len {seq_len} exceeds max_context_length {self.max_context_length}"
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)
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positions = torch.arange(seq_len, device=self.embedding.weight.device)
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return self.embedding(positions)
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class SinusoidalPositionalEmbedding(nn.Module):
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"""Parameter-free position-to-vector mapping.
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pe[p, 2k] = sin(p / 10000^(2k/d_model))
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pe[p, 2k+1] = cos(p / 10000^(2k/d_model))
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"""
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def __init__(self, max_context_length: int, d_model: int, base: float = 10000.0) -> None:
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super().__init__()
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if max_context_length < 1:
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raise ValueError(f"max_context_length must be >= 1, got {max_context_length}")
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if d_model < 1:
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raise ValueError(f"d_model must be >= 1, got {d_model}")
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if d_model % 2 != 0:
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raise ValueError(f"d_model must be even for sinusoidal, got {d_model}")
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self.max_context_length = max_context_length
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self.d_model = d_model
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self.base = base
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pe = self._build_table(max_context_length, d_model, base)
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self.register_buffer("pe", pe, persistent=False)
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@staticmethod
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def _build_table(max_context_length: int, d_model: int, base: float) -> torch.Tensor:
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pos = torch.arange(max_context_length, dtype=torch.float32).unsqueeze(1)
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i = torch.arange(d_model // 2, dtype=torch.float32)
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denom = base ** (2 * i / d_model)
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angle = pos / denom
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pe = torch.zeros(max_context_length, d_model, dtype=torch.float32)
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pe[:, 0::2] = torch.sin(angle)
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pe[:, 1::2] = torch.cos(angle)
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return pe
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def forward(self, seq_len: int) -> torch.Tensor:
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if seq_len < 1:
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raise ValueError(f"seq_len must be >= 1, got {seq_len}")
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if seq_len > self.max_context_length:
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raise ValueError(
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f"seq_len {seq_len} exceeds max_context_length {self.max_context_length}"
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)
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return self.pe[:seq_len]
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class EmbeddingComposer(nn.Module):
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"""Sums a token embedding with a positional embedding.
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The positional embedding may be learned or sinusoidal.
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"""
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def __init__(
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self,
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token_embedding: TokenEmbedding,
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positional_embedding: nn.Module,
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) -> None:
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super().__init__()
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if not isinstance(token_embedding, TokenEmbedding):
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raise TypeError("token_embedding must be a TokenEmbedding")
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if not isinstance(
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positional_embedding,
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(LearnedPositionalEmbedding, SinusoidalPositionalEmbedding),
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):
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raise TypeError(
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"positional_embedding must be Learned or Sinusoidal Positional Embedding"
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)
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if token_embedding.d_model != getattr(positional_embedding, "d_model", None):
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raise ValueError("token and positional embeddings must share d_model")
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self.token_embedding = token_embedding
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self.positional_embedding = positional_embedding
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@property
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def d_model(self) -> int:
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return self.token_embedding.d_model
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def forward(self, ids: torch.Tensor) -> torch.Tensor:
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if ids.dim() != 2:
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raise ValueError(f"ids must be (B, T), got shape {tuple(ids.shape)}")
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seq_len = ids.shape[1]
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tok = self.token_embedding(ids)
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pos = self.positional_embedding(seq_len)
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return tok + pos.unsqueeze(0)
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def count_parameters(module: nn.Module) -> int:
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return sum(p.numel() for p in module.parameters() if p.requires_grad)
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def neighbour_cosine_curve(table: torch.Tensor, max_offset: int = 8) -> list[float]:
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"""Average cosine similarity between row p and row p+k for k in 1..max_offset.
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Returns a list of length max_offset.
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"""
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if table.dim() != 2:
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raise ValueError("table must be (L, D)")
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if max_offset < 1:
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raise ValueError(f"max_offset must be >= 1, got {max_offset}")
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if max_offset >= table.shape[0]:
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raise ValueError(
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f"max_offset {max_offset} must be < number of rows {table.shape[0]}"
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)
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rows = table.detach().to(torch.float32)
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norms = rows.norm(dim=1, keepdim=True).clamp(min=1e-8)
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unit = rows / norms
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result: list[float] = []
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for k in range(1, max_offset + 1):
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a = unit[:-k]
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b = unit[k:]
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dot = (a * b).sum(dim=1).mean().item()
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result.append(dot)
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return result
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@dataclass
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class DemoConfig:
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vocab_size: int = 320
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d_model: int = 64
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max_context_length: int = 128
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batch_size: int = 4
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seq_len: int = 32
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seed: int = 11
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def _print_section(title: str) -> None:
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bar = "-" * len(title)
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print(f"\n{title}\n{bar}")
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def main() -> int:
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cfg = DemoConfig()
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torch.manual_seed(cfg.seed)
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token_emb = TokenEmbedding(cfg.vocab_size, cfg.d_model)
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learned_pos = LearnedPositionalEmbedding(cfg.max_context_length, cfg.d_model)
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sinusoidal_pos = SinusoidalPositionalEmbedding(cfg.max_context_length, cfg.d_model)
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learned_composer = EmbeddingComposer(token_emb, learned_pos)
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sinusoidal_composer = EmbeddingComposer(token_emb, sinusoidal_pos)
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ids = torch.randint(0, cfg.vocab_size, (cfg.batch_size, cfg.seq_len), dtype=torch.long)
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_print_section("Shapes")
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out_learned = learned_composer(ids)
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out_sinusoidal = sinusoidal_composer(ids)
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print(f"token_emb output : {tuple(token_emb(ids).shape)}")
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print(f"learned composer : {tuple(out_learned.shape)}")
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print(f"sinusoidal cmp. : {tuple(out_sinusoidal.shape)}")
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assert out_learned.shape == (cfg.batch_size, cfg.seq_len, cfg.d_model)
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assert out_sinusoidal.shape == (cfg.batch_size, cfg.seq_len, cfg.d_model)
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_print_section("Parameter counts")
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token_params = count_parameters(token_emb)
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learned_params = count_parameters(learned_pos)
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sinusoidal_params = count_parameters(sinusoidal_pos)
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print(f"token embedding : {token_params:>7}")
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print(f"learned positional : {learned_params:>7}")
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print(f"sinusoidal positional : {sinusoidal_params:>7} (parameter-free)")
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assert sinusoidal_params == 0
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_print_section("Neighbour cosine similarity")
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learned_curve = neighbour_cosine_curve(learned_pos.embedding.weight, max_offset=6)
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sinusoidal_curve = neighbour_cosine_curve(sinusoidal_pos.pe, max_offset=6)
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print("offset k | learned cos | sinusoidal cos")
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for k, (a, b) in enumerate(zip(learned_curve, sinusoidal_curve), start=1):
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print(f" {k:>4} | {a:>+7.4f} | {b:>+7.4f}")
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_print_section("Sinusoidal property: smooth decay")
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monotone_count = sum(
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sinusoidal_curve[i] >= sinusoidal_curve[i + 1] - 1e-3
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for i in range(len(sinusoidal_curve) - 1)
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)
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print(
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f"sinusoidal curve monotone steps: {monotone_count}/{len(sinusoidal_curve) - 1}"
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)
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_print_section("Length extrapolation")
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short = cfg.max_context_length // 2
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long = cfg.max_context_length
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print(f"sinusoidal at len {short:>3} : ok")
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_ = sinusoidal_pos(short)
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print(f"sinusoidal at len {long:>3} : ok")
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_ = sinusoidal_pos(long)
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print("learned bounded by max_context_length: must error past max")
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try:
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_ = learned_pos(long + 1)
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except ValueError as e:
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print(f" caught: {e}")
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print("\nDemo OK.")
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return 0
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if __name__ == "__main__":
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raise SystemExit(main())
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