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model.py
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| 1 |
+
"""
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| 2 |
+
Small transformer model for modular arithmetic experiments.
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| 3 |
+
============================================================
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| 4 |
+
A minimal GPT-style decoder-only transformer designed to:
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| 5 |
+
1. Train from scratch in minutes on a single GPU
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| 6 |
+
2. Expose all internal activations (hidden states, attention patterns)
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| 7 |
+
3. Support checkpoint saving/loading for representation tracking
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| 8 |
+
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| 9 |
+
Architecture matches Nanda et al. 2023 (grokking) configuration
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| 10 |
+
with adjustments for our two-task experiment.
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| 11 |
+
"""
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| 12 |
+
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| 13 |
+
import torch
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| 14 |
+
import torch.nn as nn
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| 15 |
+
import torch.nn.functional as F
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| 16 |
+
import math
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| 17 |
+
from typing import Dict, Optional, Tuple, List
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| 18 |
+
from dataclasses import dataclass
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| 19 |
+
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| 20 |
+
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| 21 |
+
@dataclass
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| 22 |
+
class TransformerConfig:
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| 23 |
+
"""Configuration for the small transformer."""
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| 24 |
+
vocab_size: int = 101 # p + NUM_SPECIAL (97 + 4)
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| 25 |
+
n_layers: int = 2
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| 26 |
+
d_model: int = 128
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| 27 |
+
n_heads: int = 4
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| 28 |
+
d_mlp: int = 512
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| 29 |
+
max_seq_len: int = 5 # [a, op, b, =, c]
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| 30 |
+
dropout: float = 0.0
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| 31 |
+
layer_norm: bool = True
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| 32 |
+
|
| 33 |
+
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| 34 |
+
class MultiHeadAttention(nn.Module):
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| 35 |
+
def __init__(self, config: TransformerConfig):
|
| 36 |
+
super().__init__()
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| 37 |
+
self.n_heads = config.n_heads
|
| 38 |
+
self.d_head = config.d_model // config.n_heads
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| 39 |
+
self.d_model = config.d_model
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| 40 |
+
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| 41 |
+
self.W_Q = nn.Linear(config.d_model, config.d_model, bias=False)
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| 42 |
+
self.W_K = nn.Linear(config.d_model, config.d_model, bias=False)
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| 43 |
+
self.W_V = nn.Linear(config.d_model, config.d_model, bias=False)
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| 44 |
+
self.W_O = nn.Linear(config.d_model, config.d_model, bias=False)
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| 45 |
+
self.dropout = nn.Dropout(config.dropout)
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| 46 |
+
|
| 47 |
+
def forward(self, x: torch.Tensor,
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| 48 |
+
return_attn: bool = False) -> Tuple[torch.Tensor, Optional[torch.Tensor]]:
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| 49 |
+
B, T, D = x.shape
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| 50 |
+
|
| 51 |
+
Q = self.W_Q(x).view(B, T, self.n_heads, self.d_head).transpose(1, 2)
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| 52 |
+
K = self.W_K(x).view(B, T, self.n_heads, self.d_head).transpose(1, 2)
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| 53 |
+
V = self.W_V(x).view(B, T, self.n_heads, self.d_head).transpose(1, 2)
|
| 54 |
+
|
| 55 |
+
# Scaled dot-product attention with causal mask
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| 56 |
+
scores = (Q @ K.transpose(-2, -1)) / math.sqrt(self.d_head)
|
| 57 |
+
causal_mask = torch.triu(torch.ones(T, T, device=x.device), diagonal=1).bool()
|
| 58 |
+
scores.masked_fill_(causal_mask.unsqueeze(0).unsqueeze(0), float('-inf'))
|
| 59 |
+
attn_weights = F.softmax(scores, dim=-1)
|
| 60 |
+
attn_weights = self.dropout(attn_weights)
|
| 61 |
+
|
| 62 |
+
out = (attn_weights @ V).transpose(1, 2).reshape(B, T, D)
|
| 63 |
+
out = self.W_O(out)
|
| 64 |
+
|
| 65 |
+
if return_attn:
|
| 66 |
+
return out, attn_weights # [B, H, T, T]
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| 67 |
+
return out, None
|
| 68 |
+
|
| 69 |
+
|
| 70 |
+
class MLP(nn.Module):
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| 71 |
+
def __init__(self, config: TransformerConfig):
|
| 72 |
+
super().__init__()
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| 73 |
+
self.W_in = nn.Linear(config.d_model, config.d_mlp)
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| 74 |
+
self.W_out = nn.Linear(config.d_mlp, config.d_model)
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| 75 |
+
self.dropout = nn.Dropout(config.dropout)
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| 76 |
+
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| 77 |
+
def forward(self, x: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
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| 78 |
+
hidden = F.gelu(self.W_in(x))
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| 79 |
+
out = self.dropout(self.W_out(hidden))
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| 80 |
+
return out, hidden # return pre-projection activations for probing
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| 81 |
+
|
| 82 |
+
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| 83 |
+
class TransformerBlock(nn.Module):
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| 84 |
+
def __init__(self, config: TransformerConfig):
|
| 85 |
+
super().__init__()
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| 86 |
+
self.attn = MultiHeadAttention(config)
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| 87 |
+
self.mlp = MLP(config)
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| 88 |
+
self.ln1 = nn.LayerNorm(config.d_model) if config.layer_norm else nn.Identity()
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| 89 |
+
self.ln2 = nn.LayerNorm(config.d_model) if config.layer_norm else nn.Identity()
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| 90 |
+
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| 91 |
+
def forward(self, x: torch.Tensor,
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| 92 |
+
return_internals: bool = False) -> Dict[str, torch.Tensor]:
|
| 93 |
+
# Pre-norm residual architecture
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| 94 |
+
attn_out, attn_weights = self.attn(self.ln1(x), return_attn=return_internals)
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| 95 |
+
x_post_attn = x + attn_out
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| 96 |
+
|
| 97 |
+
mlp_out, mlp_hidden = self.mlp(self.ln2(x_post_attn))
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| 98 |
+
x_post_mlp = x_post_attn + mlp_out
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| 99 |
+
|
| 100 |
+
result = {'hidden_state': x_post_mlp}
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| 101 |
+
if return_internals:
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| 102 |
+
result['attn_weights'] = attn_weights
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| 103 |
+
result['mlp_hidden'] = mlp_hidden
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| 104 |
+
result['residual_post_attn'] = x_post_attn
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| 105 |
+
return result
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| 106 |
+
|
| 107 |
+
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| 108 |
+
class SmallTransformer(nn.Module):
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| 109 |
+
"""
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| 110 |
+
Minimal GPT for modular arithmetic with full activation access.
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| 111 |
+
"""
|
| 112 |
+
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| 113 |
+
def __init__(self, config: TransformerConfig):
|
| 114 |
+
super().__init__()
|
| 115 |
+
self.config = config
|
| 116 |
+
self.tok_embed = nn.Embedding(config.vocab_size, config.d_model)
|
| 117 |
+
self.pos_embed = nn.Embedding(config.max_seq_len, config.d_model)
|
| 118 |
+
self.blocks = nn.ModuleList([TransformerBlock(config) for _ in range(config.n_layers)])
|
| 119 |
+
self.ln_final = nn.LayerNorm(config.d_model) if config.layer_norm else nn.Identity()
|
| 120 |
+
self.lm_head = nn.Linear(config.d_model, config.vocab_size, bias=False)
|
| 121 |
+
|
| 122 |
+
# Weight tying (embedding ↔ output)
|
| 123 |
+
self.lm_head.weight = self.tok_embed.weight
|
| 124 |
+
|
| 125 |
+
self.apply(self._init_weights)
|
| 126 |
+
|
| 127 |
+
def _init_weights(self, module):
|
| 128 |
+
if isinstance(module, nn.Linear):
|
| 129 |
+
nn.init.normal_(module.weight, std=0.02)
|
| 130 |
+
if module.bias is not None:
|
| 131 |
+
nn.init.zeros_(module.bias)
|
| 132 |
+
elif isinstance(module, nn.Embedding):
|
| 133 |
+
nn.init.normal_(module.weight, std=0.02)
|
| 134 |
+
|
| 135 |
+
def forward(self, input_ids: torch.Tensor,
|
| 136 |
+
labels: Optional[torch.Tensor] = None,
|
| 137 |
+
return_internals: bool = False) -> Dict[str, torch.Tensor]:
|
| 138 |
+
B, T = input_ids.shape
|
| 139 |
+
device = input_ids.device
|
| 140 |
+
|
| 141 |
+
tok_emb = self.tok_embed(input_ids)
|
| 142 |
+
pos_emb = self.pos_embed(torch.arange(T, device=device))
|
| 143 |
+
x = tok_emb + pos_emb
|
| 144 |
+
|
| 145 |
+
# Collect internals
|
| 146 |
+
all_hidden_states = [x.detach()]
|
| 147 |
+
all_attn_weights = []
|
| 148 |
+
all_mlp_hidden = []
|
| 149 |
+
|
| 150 |
+
for block in self.blocks:
|
| 151 |
+
block_out = block(x, return_internals=return_internals)
|
| 152 |
+
x = block_out['hidden_state']
|
| 153 |
+
all_hidden_states.append(x.detach())
|
| 154 |
+
if return_internals:
|
| 155 |
+
all_attn_weights.append(block_out['attn_weights'].detach())
|
| 156 |
+
all_mlp_hidden.append(block_out['mlp_hidden'].detach())
|
| 157 |
+
|
| 158 |
+
x = self.ln_final(x)
|
| 159 |
+
logits = self.lm_head(x)
|
| 160 |
+
|
| 161 |
+
result = {'logits': logits}
|
| 162 |
+
|
| 163 |
+
if labels is not None:
|
| 164 |
+
loss = F.cross_entropy(logits.view(-1, logits.size(-1)),
|
| 165 |
+
labels.view(-1), ignore_index=-100)
|
| 166 |
+
result['loss'] = loss
|
| 167 |
+
|
| 168 |
+
if return_internals:
|
| 169 |
+
result['hidden_states'] = all_hidden_states # List of [B, T, D]
|
| 170 |
+
result['attn_weights'] = all_attn_weights # List of [B, H, T, T]
|
| 171 |
+
result['mlp_hidden'] = all_mlp_hidden # List of [B, T, D_mlp]
|
| 172 |
+
|
| 173 |
+
return result
|
| 174 |
+
|
| 175 |
+
def get_representations(self, input_ids: torch.Tensor,
|
| 176 |
+
token_position: int = -1) -> List[torch.Tensor]:
|
| 177 |
+
"""
|
| 178 |
+
Get hidden state at each layer for a specific token position.
|
| 179 |
+
Returns list of [batch_size, d_model] tensors.
|
| 180 |
+
"""
|
| 181 |
+
with torch.no_grad():
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| 182 |
+
out = self.forward(input_ids, return_internals=True)
|
| 183 |
+
return [hs[:, token_position, :] for hs in out['hidden_states']]
|
| 184 |
+
|
| 185 |
+
def count_parameters(self) -> int:
|
| 186 |
+
return sum(p.numel() for p in self.parameters())
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