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import argparse
import abc
import random
from itertools import permutations
from typing import Set
import os
import json
import numpy as np
from einops import rearrange, repeat
import torch
from torch.utils.data import IterableDataset
from torch import nn, Tensor
class AbstractDataset(abc.ABC):
def __init__(self, group_elements1: Set, group_elements2: Set, frac_train: float):
self.frac_train = frac_train
self.group_elements1 = group_elements1
self.group_elements2 = group_elements2
self.ordered_group_elements1 = list(self.group_elements1)
self.ordered_group_elements2 = list(self.group_elements2)
self.idx2vocab = ["o", "="] + list(group_elements1.union(group_elements2))
self.vocab2idx = {vocab: idx for idx, vocab in enumerate(self.idx2vocab)}
self.n_vocab = len(self.idx2vocab)
self.n_out = len(group_elements1.union(group_elements2))
idxs = list(range(len(self.group_elements1) * len(self.group_elements2)))
random.shuffle(idxs)
self.train_pairs, self.val_pairs = (
idxs[: int(len(idxs) * frac_train)],
idxs[int(len(idxs) * frac_train) :],
)
@abc.abstractmethod
def fetch_output(self, a, b):
pass
def encode(self, sequence):
return [self.vocab2idx[item] for item in sequence]
def decode(self, sequence):
return [self.idx2vocab[item] for item in sequence]
def form_equation(self, a, b, c):
return [a, "o", b, "=", c]
def fetch_example(self, idx):
a = self.ordered_group_elements1[idx // len(self.group_elements2)]
b = self.ordered_group_elements2[idx % len(self.group_elements2)]
c = self.fetch_output(a, b)
equation = self.form_equation(a, b, c)
return self.encode(equation[:-1]), (self.vocab2idx[c] - 2), equation
def fetch_train_example(self):
idx = random.choice(self.train_pairs)
return self.fetch_example(idx)
def fetch_val_example(self):
idx = random.choice(self.val_pairs)
return self.fetch_example(idx)
def reverse_operands(self, a, b):
return b, a
class ModSumDataset(AbstractDataset):
def __init__(self, p, frac_train):
super(ModSumDataset, self).__init__(set(range(p)), set(range(p)), frac_train)
self.p = p
def fetch_output(self, a, b):
return (a + b) % self.p
def fetch_example(self, idx):
a = self.ordered_group_elements1[idx // len(self.group_elements2)]
b = self.ordered_group_elements2[idx % len(self.group_elements2)]
rand = random.random()
if rand < 0.15:
a, b = self.reverse_operands(a, b)
elif rand < 0.3:
a, b = self.negate_operands(a, b)
c = self.fetch_output(a, b)
equation = self.form_equation(a, b, c)
return self.encode(equation[:-1]), (self.vocab2idx[c] - 2), equation
def negate_operands(self, a, b):
return (self.p - a) % self.p, (self.p - b) % self.p
class ModSubtractDataset(AbstractDataset):
def __init__(self, p, frac_train):
super(ModSubtractDataset, self).__init__(
set(range(p)), set(range(p)), frac_train
)
self.p = p
def fetch_output(self, a, b):
return (a - b) % self.p
def fetch_example(self, idx):
a = self.ordered_group_elements1[idx // len(self.group_elements2)]
b = self.ordered_group_elements2[idx % len(self.group_elements2)]
rand = random.random()
if rand < 0.15:
a, b = self.reverse_operands(a, b)
elif rand < 0.3:
a, b = self.negate_operands(a, b)
c = self.fetch_output(a, b)
equation = self.form_equation(a, b, c)
return self.encode(equation[:-1]), (self.vocab2idx[c] - 2), equation
def reverse_operands(self, a, b):
return b, a
def negate_operands(self, a, b):
return (self.p - a) % self.p, (self.p - b) % self.p
class ModDivisonDataset(AbstractDataset):
def __init__(self, p, frac_train):
super(ModDivisonDataset, self).__init__(
set(range(p)), set(range(1, p)), frac_train
)
self.p = p
def fetch_output(self, a, b):
return (a * pow(b, self.p - 2, self.p)) % self.p
def fetch_example(self, idx):
a = self.ordered_group_elements1[idx // len(self.group_elements2)]
b = self.ordered_group_elements2[idx % len(self.group_elements2)]
if random.random() < 0.3:
a, b = self.negate_operands(a, b)
c = self.fetch_output(a, b)
equation = self.form_equation(a, b, c)
return self.encode(equation[:-1]), (self.vocab2idx[c] - 2), equation
def negate_operands(self, a, b):
return (self.p - a) % self.p, b # Only negate the dividend
class PermutationGroup(AbstractDataset):
def __init__(self, k, frac_train):
perms = set(map(tuple, permutations(list(range(k)))))
super(PermutationGroup, self).__init__(perms, perms, frac_train)
self.k = k
def fetch_output(self, a, b):
return tuple([a[b[i]] for i in range(len(b))])
class GroupDataset(IterableDataset):
def __init__(self, dataset: AbstractDataset, split: str):
super(GroupDataset, self).__init__()
assert split in {"train", "val"}
self.dataset = dataset
self.split = split
self.fetch_f = None
if self.split == "train":
self.fetch_f = self.dataset.fetch_train_example
elif self.split == "val":
self.fetch_f = self.dataset.fetch_val_example
else:
raise NotImplementedError
def __iter__(self):
return self
def __next__(self):
x, y, _ = self.fetch_f()
return torch.tensor(x), torch.tensor(y)
def operation_mod_p_data(operation: str, p: int, frac_train: float):
"""
x◦y (mod p) for 0 <= x < p, 1 <= y < p if operation in DIVISION_MODULO_OPERATIONS
x◦y (mod p) for 0 <= x, y < p otherwise
"""
if operation == "x_plus_y":
data = ModSumDataset(p=p, frac_train=frac_train)
elif operation == "x_minus_y":
data = ModSubtractDataset(p=p, frac_train=frac_train)
elif operation == "x_div_y":
data = ModDivisonDataset(p=p, frac_train=frac_train)
elif operation == "permutation":
data = PermutationGroup(k=5, frac_train=frac_train)
return data
def get_data(operation: str, prime: int, training_fraction: float, batch_size: int):
dataset = operation_mod_p_data(operation, prime, training_fraction)
train_dataset = GroupDataset(dataset, "train")
val_dataset = GroupDataset(dataset, "val")
train_loader = torch.utils.data.DataLoader(train_dataset, batch_size=batch_size)
val_loader = torch.utils.data.DataLoader(val_dataset, batch_size=batch_size)
return (
train_loader,
val_loader,
train_dataset.dataset.n_vocab,
train_dataset.dataset.n_out,
)
class DecoderBlock(torch.nn.Module):
def __init__(self, dim_model: int, n_heads: int):
super().__init__()
self.self_attn = nn.MultiheadAttention(dim_model, n_heads)
self.self_attn_norm = nn.LayerNorm(dim_model)
self.ffn = nn.Sequential(
nn.Linear(dim_model, dim_model * 4),
nn.GELU(),
nn.Linear(dim_model * 4, dim_model),
)
self.ffn_norm = nn.LayerNorm(dim_model)
def forward(self, x: Tensor):
attn_mask = torch.full(
(len(x), len(x)), -float("Inf"), device=x.device, dtype=x.dtype
)
attn_mask = torch.triu(attn_mask, diagonal=1)
a1, _ = self.self_attn(x, x, x, attn_mask=attn_mask)
a1 = self.self_attn_norm(x + a1)
a2 = self.ffn(a1)
a2 = self.ffn_norm(a1 + a2)
return a2
class Transformer(torch.nn.Module):
def __init__(
self,
num_layers: int,
dim_model: int,
num_heads: int,
vocab_size: int,
output_size: int,
seq_len: int,
):
super().__init__()
self.token_embeddings = nn.Embedding(vocab_size, dim_model)
self.position_embeddings = nn.Embedding(seq_len, dim_model)
self.model = nn.Sequential(
*[DecoderBlock(dim_model, num_heads) for _ in range(num_layers)],
nn.LayerNorm(dim_model),
nn.Linear(dim_model, output_size),
)
def forward(self, inputs: Tensor):
batch_size, context_len = inputs.shape
token_embedding = self.token_embeddings(inputs)
positions = repeat(
torch.arange(context_len, device=inputs.device), "p -> b p", b=batch_size
)
position_embedding = self.position_embeddings(positions)
embedding = token_embedding + position_embedding
embedding = rearrange(embedding, "b s d -> s b d")
return self.model(embedding)
def train(model, train_loader, val_loader, optimizer, scheduler, device, num_train_batches, num_eval_batches):
# Set model to training mode
model.train()
criterion = torch.nn.CrossEntropyLoss()
loss_total, correct = 0.0, 0.0
total = 0
step_val_acc_95 = None
prev_val_acc = 0
max_acc_increase_rate = 0
# Loop over each batch from the training set
count = 0
for batch in train_loader:
count += 1
# Copy data to device if needed
batch = tuple(t.to(device) for t in batch)
# Unpack the batch from the loader
inputs, labels = batch
# Zero gradient buffers
optimizer.zero_grad()
# Forward pass
output = model(inputs)[-1, :, :]
loss = criterion(output, labels)
correct += (torch.argmax(output, dim=1) == labels).sum()
loss_total += loss * len(labels)
total += len(labels)
# Backward pass
loss.backward()
# Update weights
optimizer.step()
scheduler.step()
# Evaluate on validation set
if count % 100 == 0:
val_metrics = evaluate(model, val_loader, device, num_eval_batches)
val_acc = val_metrics["val_accuracy"]
# Check for 95% validation accuracy
if step_val_acc_95 is None and val_acc >= 0.95:
step_val_acc_95 = count * num_train_batches
# Calculate rate of validation accuracy increase
acc_increase_rate = (val_acc - prev_val_acc) / 100
max_acc_increase_rate = max(max_acc_increase_rate, acc_increase_rate)
prev_val_acc = val_acc
if count >= num_train_batches:
break
acc = correct / total
loss = loss_total / total
metrics = {
"train_accuracy": float(acc),
"train_loss": float(loss),
"step_val_acc_95": step_val_acc_95,
"max_acc_increase_rate": max_acc_increase_rate,
}
return metrics
def evaluate(model, val_loader, device, num_eval_batches):
# Set model to evaluation mode
model.eval()
criterion = torch.nn.CrossEntropyLoss()
correct = 0
loss = 0.0
total = 0
count = 0
# Loop over each batch from the validation set
for batch in val_loader:
# Copy data to device if needed
batch = tuple(t.to(device) for t in batch)
# Unpack the batch from the loader
inputs, labels = batch
# Forward pass
with torch.no_grad():
output = model(inputs)[-1, :, :]
correct += (torch.argmax(output, dim=1) == labels).sum()
loss += criterion(output, labels) * len(labels)
total += labels.shape[0]
count += 1
if count >= num_eval_batches:
break
acc = correct / total
loss = loss / total
metrics = {"val_accuracy": float(acc), "val_loss": float(loss)}
return metrics
def run(out_dir, dataset, seed_offset):
os.makedirs(out_dir, exist_ok=True)
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
torch.manual_seed(1337 + seed_offset)
train_loader, val_loader, n_vocab, n_output = get_data(
operation=dataset,
prime=97,
training_fraction=0.5,
batch_size=512,
)
model = Transformer(
num_layers=2,
dim_model=128,
num_heads=4,
vocab_size=n_vocab,
output_size=n_output,
seq_len=5,
).to(device)
optimizer = torch.optim.AdamW(
model.parameters(),
lr=1e-3,
betas=(0.9, 0.98),
weight_decay=0.5,
)
num_train_batches = 10
num_eval_batches = 8
num_total_updates = 7500
warmup_steps = 50
scheduler = torch.optim.lr_scheduler.LambdaLR(
optimizer, lr_lambda=lambda s: min(s / warmup_steps, 1)
)
final_info, train_log_info, val_log_info = [], [], []
step_val_acc_99 = num_total_updates
for ep in range(num_total_updates // num_train_batches):
train_metrics = train(
model,
train_loader,
val_loader,
optimizer,
scheduler,
device,
num_train_batches,
num_eval_batches,
)
val_metrics = evaluate(
model,
val_loader,
device,
num_eval_batches,
)
train_metrics["step"] = (ep + 1) * num_train_batches
val_metrics["step"] = (ep + 1) * num_train_batches
if step_val_acc_99 == num_total_updates and val_metrics["val_accuracy"] > 0.99:
step_val_acc_99 = val_metrics["step"]
train_log_info.append(train_metrics)
val_log_info.append(val_metrics)
final_info = {
"final_train_loss": train_metrics["train_loss"],
"final_val_loss": val_metrics["val_loss"],
"final_train_acc": train_metrics["train_accuracy"],
"final_val_acc": val_metrics["val_accuracy"],
"step_val_acc_99": step_val_acc_99 if step_val_acc_99 != num_total_updates else None,
"step_val_acc_95": train_metrics["step_val_acc_95"],
"max_acc_increase_rate": train_metrics["max_acc_increase_rate"],
}
print(final_info)
with open(
os.path.join(out_dir, f"final_info_{dataset}_{seed_offset}.json"), "w"
) as f:
json.dump(final_info, f)
return final_info, train_log_info, val_log_info
parser = argparse.ArgumentParser(description="Run experiment")
parser.add_argument("--out_dir", type=str, default="run_0", help="Output directory")
args = parser.parse_args()
if __name__ == "__main__":
num_seeds = {
"x_div_y": 3,
"x_plus_y": 3,
"x_minus_y": 3,
"permutation": 3,
}
out_dir = args.out_dir
all_results = {}
final_infos = {}
for dataset in ["x_div_y", "x_minus_y", "x_plus_y", "permutation"]:
final_info_list = []
for seed_offset in range(num_seeds[dataset]):
print(f"Running {dataset} with seed offset {seed_offset}")
final_info, train_info, val_info = run(args.out_dir, dataset, seed_offset)
all_results[f"{dataset}_{seed_offset}_final_info"] = final_info
all_results[f"{dataset}_{seed_offset}_train_info"] = train_info
all_results[f"{dataset}_{seed_offset}_val_info"] = val_info
final_info_list.append(final_info)
final_info_dict = {
k: [d[k] for d in final_info_list if d[k] is not None] for k in final_info_list[0].keys()
}
means = {f"{k}_mean": np.mean(v) if v else None for k, v in final_info_dict.items()}
stderrs = {
f"{k}_stderr": np.std(v) / np.sqrt(len(v)) if v else None for k, v in final_info_dict.items()
}
final_infos[dataset] = {
"means": means,
"stderrs": stderrs,
"final_info_dict": final_info_dict,
}
with open(os.path.join(out_dir, "final_info.json"), "w") as f:
json.dump(final_infos, f)
with open(os.path.join(out_dir, "all_results.npy"), "wb") as f:
np.save(f, all_results)
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