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Depth Comparison Benchmark - ThinkingDial 核心验证实验
目标:验证 ThinkingDial 的不同 depth 在数学推理任务上的表现差异。
这是证明 ThinkingDial 机制有效性的关键实验。
实验设计:
1. 扩大模型配置到 ~10M 参数(hidden=512, layers=8, heads=8)
2. 用合成数学数据(四则运算)预训练所有 depth
3. 用 GRPO + GSM8K 奖励函数分别在不同 depth 下微调
4. 输出 depth 准确率对比表
Usage: python experiments/depth_benchmark.py
"""
import sys
import math
import random
import time
import torch
import torch.nn.functional as F
from pathlib import Path
from typing import Dict, List, Tuple
sys.path.insert(0, str(Path(__file__).parent.parent))
from models.fusion_model import FusionModel, FusionConfig
from models.thinking_dial import (
ThinkingDialModel, ThinkingConfig, GRPOTrainer, GRPOConfig
)
from evaluation.gsm8k_reward import GSM8KEvaluator, extract_answer, normalize_answer
DEVICE = "cuda" if torch.cuda.is_available() else "cpu"
print(f"[Benchmark] Device: {DEVICE}")
print()
# ─── 实验配置 ───────────────────────────────────────────────────────────────
EXP_CONFIG = {
# ~5M 参数模型配置(CPU 可在合理时间内完成)
"hidden_size": 256,
"num_hidden_layers": 6,
"num_attention_heads": 8,
"intermediate_size": 512,
"vocab_size": 1000,
"max_position_embeddings": 128,
"block_size": 32,
"latent_dim": 16,
# 训练参数
"pretrain_epochs": 100,
"pretrain_batch_size": 8,
"pretrain_lr": 1e-3,
"grpo_epochs": 30,
"grpo_batch_size": 4,
"grpo_lr": 1e-4,
"grpo_num_samples": 3,
"num_thinking_depths": 4,
"test_batch_size": 50,
"seed": 42,
}
def estimate_params(config: FusionConfig) -> int:
"""粗略估计模型参数量"""
emb = config.vocab_size * config.hidden_size
per_layer = (
# attention: Q, K, V, O projections
4 * config.hidden_size * config.hidden_size +
# FFN: gate, up, down
3 * config.hidden_size * config.intermediate_size +
# SBLA latent projections (approx)
2 * config.hidden_size * config.latent_dim +
# norms
2 * config.hidden_size
)
return emb + config.num_hidden_layers * per_layer + config.hidden_size * config.vocab_size
# ─── 合成数学数据 ──────────────────────────────────────────────────────────
def generate_math_data(n: int = 2000, ops: List[str] = None, max_val: int = 100,
seed: int = 42) -> List[Tuple[str, int, int, int]]:
"""
生成合成数学运算数据。
格式: (x, op_code, y, result)
op_code: 0=+, 1=-, 2=*, 3=/
"""
if ops is None:
ops = ["+", "-"] # 先只做加减法(乘除需要更大模型)
op_map = {"+": 0, "-": 1, "*": 2, "/": 3}
rng = random.Random(seed)
data = []
for _ in range(n):
op = rng.choice(ops)
code = op_map[op]
if op == "+":
x = rng.randint(1, max_val)
y = rng.randint(1, max_val)
result = x + y
elif op == "-":
x = rng.randint(1, max_val * 2)
y = rng.randint(1, x) # 保证结果 >= 0
result = x - y
elif op == "*":
x = rng.randint(2, 20)
y = rng.randint(2, 20)
result = x * y
elif op == "/":
y = rng.randint(2, 20)
result = rng.randint(1, 20)
x = y * result # 保证整除
# 结果 clamp 到 vocab 范围
result = max(0, min(result, EXP_CONFIG["vocab_size"] - 2))
data.append((x, code, y, result))
return data
def encode_example(x: int, op: int, y: int, result: int) -> Tuple[List[int], List[int]]:
"""
编码数学题:
input: [2, x, op, y, 0, 0, 0] (7 tokens, padded)
labels: [-100, x, op, y, 99, result, 1] (7 tokens, same length)
Loss 计算: predict y->99, 99->result, result->1
"""
input_ids = [2, x, op, y, 0, 0, 0]
labels = [-100, x, op, y, 99, result, 1]
return input_ids, labels
# ─── 梯度化奖励函数 ────────────────────────────────────────────────────────
def gradient_reward_fn(prompt: str, response: str) -> float:
"""
梯度化奖励函数(用于合成数学任务):
- 能提取到数字 → +0.1
- 数值接近正确值(误差 < 10%)→ +0.3
- 完全正确 → +1.0
"""
extracted = extract_answer(response)
if extracted is None:
return 0.0
# 查找 ground truth
gold = None
try:
# 从 prompt 中提取数字: CLS x OP y
tokens = prompt.strip().split()
if len(tokens) >= 3:
x, op_code, y = int(tokens[0]), int(tokens[1]), int(tokens[2])
if op_code == 0:
gold = x + y
elif op_code == 1:
gold = x - y
elif op_code == 2:
gold = x * y
elif op_code == 3:
gold = x // y if y != 0 else 0
except (ValueError, IndexError):
pass
if gold is None:
return 0.1 # 至少输出了数字
extracted_norm = normalize_answer(extracted)
gold_norm = normalize_answer(gold)
if extracted_norm == gold_norm:
return 1.0
# 检查是否接近(误差 < 10%)
if gold != 0:
rel_error = abs(extracted_norm - gold_norm) / abs(gold_norm)
if rel_error < 0.1:
return 0.3
# 输出了数字但答案错误
return 0.1
# ─── 实验核心 ───────────────────────────────────────────────────────────────
def pretrain_model(config: FusionConfig, data: list) -> ThinkingDialModel:
"""阶段 1:用合成数学数据预训练"""
model = FusionModel(config)
thinking_config = ThinkingConfig(
num_thinking_depths=EXP_CONFIG["num_thinking_depths"]
)
td_model = ThinkingDialModel(model, thinking_config)
td_model.train().to(DEVICE)
optimizer = torch.optim.AdamW(td_model.parameters(), lr=EXP_CONFIG["pretrain_lr"])
losses = []
for epoch in range(EXP_CONFIG["pretrain_epochs"]):
batch = random.sample(data, min(EXP_CONFIG["pretrain_batch_size"], len(data)))
input_batch = []
target_batch = []
for x, op, y, result in batch:
inp, tgt = encode_example(x, op, y, result)
input_batch.append(inp)
target_batch.append(tgt)
input_ids = torch.tensor(input_batch, device=DEVICE, dtype=torch.long)
labels = torch.tensor(target_batch, device=DEVICE, dtype=torch.long)
optimizer.zero_grad()
outputs = td_model(input_ids, labels=labels)
loss = outputs.loss
loss.backward()
torch.nn.utils.clip_grad_norm_(td_model.parameters(), 1.0)
optimizer.step()
losses.append(loss.item())
if (epoch + 1) % 10 == 0:
avg = sum(losses[-10:]) / 10
print(f" Pretrain Epoch {epoch+1}/{EXP_CONFIG['pretrain_epochs']}: "
f"Loss = {avg:.4f}")
final_loss = sum(losses[-10:]) / 10
print(f" Pretrain complete. Final loss: {final_loss:.4f}")
return td_model
def grpo_finetune(td_model: ThinkingDialModel, data: list,
depth: int, gsm8k_eval: GSM8KEvaluator = None) -> Dict:
"""
阶段 2:GRPO 微调(使用合成数学数据 + 可选 GSM8K 奖励)
Returns:
{losses, rewards, depth}
"""
grpo_config = GRPOConfig(
grpo_sample_size=EXP_CONFIG["grpo_num_samples"],
kl_coef=0.05,
)
# 设置奖励函数
def reward_fn(prompt, response):
if gsm8k_eval is not None:
return gsm8k_eval.reward(prompt, response)
return gradient_reward_fn(prompt, response)
td_model.train()
optimizer = torch.optim.AdamW(
[p for p in td_model.parameters() if p.requires_grad],
lr=EXP_CONFIG["grpo_lr"]
)
epoch_losses = []
epoch_rewards = []
for epoch in range(EXP_CONFIG["grpo_epochs"]):
batch = random.sample(data, min(EXP_CONFIG["grpo_batch_size"], len(data)))
batch_losses = []
batch_rewards = []
for x, op, y, result in batch:
inp, _ = encode_example(x, op, y, result)
input_ids = torch.tensor([inp], device=DEVICE, dtype=torch.long)
# 用指定 depth 生成多个样本
gen_ids = []
for _ in range(EXP_CONFIG["grpo_num_samples"]):
with torch.no_grad():
out = td_model.generate(
input_ids,
max_new_tokens=8,
thinking_depth=depth,
do_sample=True,
temperature=1.0,
pad_token_id=0,
)
gen_ids.append(out[0].tolist())
# 计算奖励
rewards = []
for gen in gen_ids:
new_tokens = gen[len(inp):]
# Extract result: expected format [99, result, 1, ...]
if len(new_tokens) >= 2 and new_tokens[0] == 99:
predicted = new_tokens[1]
else:
predicted = None
# Compute reward
if predicted is not None and predicted == result:
r = 1.0
elif predicted is not None:
# Gradient reward: check proximity
if result != 0 and abs(predicted - result) / abs(result) < 0.1:
r = 0.3
else:
r = 0.1
else:
r = 0.0
rewards.append(r)
# GRPO: 基于奖励计算 loss
if len(rewards) > 1 and sum(rewards) > 0:
# 归一化奖励
rewards_t = torch.tensor(rewards, device=DEVICE, dtype=torch.float)
mean_r = rewards_t.mean()
std_r = rewards_t.std() + 1e-8
advantages = (rewards_t - mean_r) / std_r
# 对每个样本计算 policy gradient loss
total_loss = torch.tensor(0.0, device=DEVICE)
for i, gen in enumerate(gen_ids):
gen_t = torch.tensor([gen], device=DEVICE, dtype=torch.long)
# Mask labels: only compute loss on generated tokens
gen_labels = gen_t[:, 1:].clone()
gen_labels[:, :len(inp)-1] = -100 # ignore input portion
# Forward to get log probs
outputs = td_model(gen_t[:, :-1], labels=gen_labels)
neg_log_prob = outputs.loss
# Policy gradient: -advantage * log_prob
total_loss += advantages[i] * neg_log_prob
loss = total_loss / len(gen_ids)
optimizer.zero_grad()
loss.backward()
torch.nn.utils.clip_grad_norm_(td_model.parameters(), 1.0)
optimizer.step()
batch_losses.append(loss.item())
batch_rewards.append(mean_r.item())
else:
batch_losses.append(0.0)
batch_rewards.append(0.0)
epoch_losses.append(sum(batch_losses) / len(batch_losses))
epoch_rewards.append(sum(batch_rewards) / len(batch_rewards))
if (epoch + 1) % 10 == 0:
print(f" GRPO Epoch {epoch+1}/{EXP_CONFIG['grpo_epochs']}: "
f"Loss = {epoch_losses[-1]:.4f}, "
f"Mean Reward = {epoch_rewards[-1]:.4f}")
print(f" GRPO complete. Final reward: {epoch_rewards[-1]:.4f}")
return {
"losses": epoch_losses,
"rewards": epoch_rewards,
"depth": depth,
}
def evaluate_accuracy(td_model: ThinkingDialModel, data: list,
depth: int, n_samples: int = None) -> Dict:
"""
在测试集上评估指定 depth 的准确率。
期望生成格式: [..., 99, result, 1, ...] -> 取 position 5 的 token 作为结果
"""
if n_samples is None:
n_samples = EXP_CONFIG["test_batch_size"]
test_data = random.sample(data, min(n_samples, len(data)))
correct = 0
total = len(test_data)
results_by_op = {"+": {"correct": 0, "total": 0},
"-": {"correct": 0, "total": 0},
"*": {"correct": 0, "total": 0},
"/": {"correct": 0, "total": 0}}
td_model.eval()
op_names = {0: "+", 1: "-", 2: "*", 3: "/"}
for x, op, y, result in test_data:
inp, _ = encode_example(x, op, y, result)
input_ids = torch.tensor([inp], device=DEVICE, dtype=torch.long)
with torch.no_grad():
out = td_model.generate(
input_ids,
max_new_tokens=8,
thinking_depth=depth,
do_sample=False,
pad_token_id=0,
)
gen_tokens = out[0, len(inp):].tolist()
# Expected: model generates [99, result, 1, ...]
gen_result = None
if len(gen_tokens) >= 2 and gen_tokens[0] == 99:
gen_result = gen_tokens[1]
elif gen_tokens:
gen_result = gen_tokens[0]
op_name = op_names.get(op, "?")
results_by_op[op_name]["total"] += 1
if gen_result is not None:
if normalize_answer(gen_result) == normalize_answer(result):
correct += 1
results_by_op[op_name]["correct"] += 1
accuracy = correct / total if total > 0 else 0.0
return {
"depth": depth,
"accuracy": accuracy,
"correct": correct,
"total": total,
"by_op": results_by_op,
}
# ─── 消融实验 ───────────────────────────────────────────────────────────────
def create_vanilla_model(config: FusionConfig):
"""
创建无 ThinkingDial 的 vanilla Transformer 对照组。
直接用 FusionModel(无 thinking depth 偏置)。
"""
model = FusionModel(config)
model.train().to(DEVICE)
return model
def pretrain_vanilla(model: FusionModel, data: list) -> Dict:
"""Vanilla Transformer 预训练(无 ThinkingDial)"""
optimizer = torch.optim.AdamW(model.parameters(), lr=EXP_CONFIG["pretrain_lr"])
losses = []
for epoch in range(EXP_CONFIG["pretrain_epochs"]):
batch = random.sample(data, min(EXP_CONFIG["pretrain_batch_size"], len(data)))
input_batch = []
target_batch = []
for x, op, y, result in batch:
inp, tgt = encode_example(x, op, y, result)
input_batch.append(inp)
target_batch.append(tgt)
input_ids = torch.tensor(input_batch, device=DEVICE, dtype=torch.long)
labels = torch.tensor(target_batch, device=DEVICE, dtype=torch.long)
optimizer.zero_grad()
outputs = model(input_ids, labels=labels)
loss = outputs.loss
loss.backward()
torch.nn.utils.clip_grad_norm_(model.parameters(), 1.0)
optimizer.step()
losses.append(loss.item())
final_loss = sum(losses[-10:]) / 10
return {"losses": losses, "final_loss": final_loss}
def evaluate_vanilla(model: FusionModel, data: list, n_samples: int = None) -> Dict:
"""评估 vanilla Transformer 准确率"""
if n_samples is None:
n_samples = EXP_CONFIG["test_batch_size"]
test_data = random.sample(data, min(n_samples, len(data)))
correct = 0
total = len(test_data)
model.eval()
for x, op, y, result in test_data:
inp, _ = encode_example(x, op, y, result)
input_ids = torch.tensor([inp], device=DEVICE, dtype=torch.long)
with torch.no_grad():
out = model.generate(
input_ids,
max_new_tokens=8,
do_sample=False,
pad_token_id=0,
)
gen_tokens = out[0, len(inp):].tolist()
gen_result = None
if len(gen_tokens) >= 2 and gen_tokens[0] == 99:
gen_result = gen_tokens[1]
else:
gen_result = extract_answer(" ".join(str(t) for t in gen_tokens))
if gen_result is not None:
if normalize_answer(gen_result) == normalize_answer(result):
correct += 1
accuracy = correct / total if total > 0 else 0.0
return {"accuracy": accuracy, "correct": correct, "total": total}
# ─── 主实验流程 ──────────────────────────────────────────────────────────────
def run_benchmark():
print("=" * 70)
print("ThinkingDial Depth Comparison Benchmark")
print("=" * 70)
print()
random.seed(EXP_CONFIG["seed"])
torch.manual_seed(EXP_CONFIG["seed"])
# 配置模型
config = FusionConfig(
vocab_size=EXP_CONFIG["vocab_size"],
hidden_size=EXP_CONFIG["hidden_size"],
num_hidden_layers=EXP_CONFIG["num_hidden_layers"],
num_attention_heads=EXP_CONFIG["num_attention_heads"],
intermediate_size=EXP_CONFIG["intermediate_size"],
max_position_embeddings=EXP_CONFIG["max_position_embeddings"],
block_size=EXP_CONFIG["block_size"],
latent_dim=EXP_CONFIG["latent_dim"],
)
n_params = estimate_params(config)
print(f"Model config: {EXP_CONFIG['hidden_size']}d x {EXP_CONFIG['num_hidden_layers']}L x {EXP_CONFIG['num_attention_heads']}H")
print(f"Estimated parameters: ~{n_params:,}")
print()
# 生成训练数据
train_data = generate_math_data(n=500, ops=["+"], max_val=20, seed=42)
test_data = generate_math_data(n=100, ops=["+"], max_val=20, seed=999)
print(f"Training set: {len(train_data)} examples")
print(f"Test set: {len(test_data)} examples")
print()
# ─── 实验 1: Depth 对比(相同模型,不同 depth) ─────────────────────
print("=" * 60)
print("EXPERIMENT 1: Depth Comparison (Same Model, Different Depths)")
print("=" * 60)
print()
t0 = time.time()
print("[1/4] Pretraining ThinkingDial model...")
td_model = pretrain_model(config, train_data)
print(f" Time: {time.time() - t0:.1f}s")
print()
# 在预训练后立即评估所有 depth(零样本)
print("[2/4] Zero-shot accuracy by depth (before GRPO)...")
zero_shot_results = {}
for depth in range(EXP_CONFIG["num_thinking_depths"]):
result = evaluate_accuracy(td_model, test_data, depth)
zero_shot_results[depth] = result
print(f" Depth {depth}: {result['accuracy']*100:.1f}% "
f"({result['correct']}/{result['total']})")
print()
# 对每个 depth 进行 GRPO 微调(共享预训练权重)
print("[3/4] GRPO fine-tuning per depth...")
grpo_results = {}
for depth in range(EXP_CONFIG["num_thinking_depths"]):
print(f" --- Depth {depth} ---")
# 每次从预训练检查点开始
td_model_copy = pretrain_model(config, train_data) # 重新预训练保证公平
grpo_res = grpo_finetune(td_model_copy, train_data, depth)
grpo_results[depth] = grpo_res
# 评估
result = evaluate_accuracy(td_model_copy, test_data, depth)
grpo_results[depth]["eval"] = result
print(f" Post-GRPO Accuracy: {result['accuracy']*100:.1f}%")
print()
# 清理
del td_model_copy
if DEVICE == "cuda":
torch.cuda.empty_cache()
print("[4/4] Post-GRPO accuracy by depth...")
post_grpo_results = {}
for depth in range(EXP_CONFIG["num_thinking_depths"]):
result = grpo_results[depth]["eval"]
post_grpo_results[depth] = result
print(f" Depth {depth}: {result['accuracy']*100:.1f}% "
f"({result['correct']}/{result['total']})")
print()
# ─── 实验 2: 消融实验(Vanilla vs ThinkingDial) ──────────────────
print("=" * 60)
print("EXPERIMENT 2: Ablation (Vanilla Transformer vs ThinkingDial)")
print("=" * 60)
print()
print("[1/2] Pretraining vanilla Transformer...")
t1 = time.time()
vanilla_model = create_vanilla_model(config)
vanilla_train = pretrain_vanilla(vanilla_model, train_data)
print(f" Pretrain loss: {vanilla_train['final_loss']:.4f}")
print(f" Time: {time.time() - t1:.1f}s")
print()
print("[2/2] Evaluating vanilla Transformer...")
vanilla_result = evaluate_vanilla(vanilla_model, test_data)
print(f" Vanilla accuracy: {vanilla_result['accuracy']*100:.1f}% "
f"({vanilla_result['correct']}/{vanilla_result['total']})")
print()
# ─── 结果汇总 ──────────────────────────────────────────────────────
print()
print("=" * 70)
print("RESULTS SUMMARY")
print("=" * 70)
print()
print("Table 1: Zero-shot Accuracy by Thinking Depth")
print("-" * 50)
print(f"{'Depth':<10} {'Accuracy':<12} {'Correct/Total':<15}")
print("-" * 50)
for depth in range(EXP_CONFIG["num_thinking_depths"]):
r = zero_shot_results[depth]
print(f"{depth:<10} {r['accuracy']*100:>6.1f}% {r['correct']}/{r['total']}")
print()
print("Table 2: Post-GRPO Accuracy by Thinking Depth")
print("-" * 50)
print(f"{'Depth':<10} {'Accuracy':<12} {'Correct/Total':<15} {'Final Reward':<15}")
print("-" * 50)
for depth in range(EXP_CONFIG["num_thinking_depths"]):
r = grpo_results[depth]["eval"]
reward = grpo_results[depth]["rewards"][-1]
print(f"{depth:<10} {r['accuracy']*100:>6.1f}% "
f"{r['correct']}/{r['total']:<10} {reward:>8.4f}")
print()
print("Table 3: Ablation Comparison")
print("-" * 50)
print(f"{'Model':<25} {'Accuracy':<12} {'Correct/Total':<15}")
print("-" * 50)
# ThinkingDial best depth
best_depth = max(range(EXP_CONFIG["num_thinking_depths"]),
key=lambda d: post_grpo_results[d]["accuracy"])
td_acc = post_grpo_results[best_depth]
print(f"ThinkingDial (depth={best_depth}) {td_acc['accuracy']*100:>6.1f}% "
f"{td_acc['correct']}/{td_acc['total']}")
print(f"Vanilla Transformer {vanilla_result['accuracy']*100:>6.1f}% "
f"{vanilla_result['correct']}/{vanilla_result['total']}")
print()
# 分析
td_best_acc = post_grpo_results[best_depth]["accuracy"]
vanilla_acc = vanilla_result["accuracy"]
print("Analysis:")
if td_best_acc > vanilla_acc:
improvement = (td_best_acc - vanilla_acc) / vanilla_acc * 100
print(f" ThinkingDial (depth={best_depth}) outperforms vanilla by +{improvement:.1f}%")
elif td_best_acc == vanilla_acc:
print(f" ThinkingDial matches vanilla performance")
else:
degradation = (vanilla_acc - td_best_acc) / vanilla_acc * 100
print(f" ThinkingDial underperforms vanilla by -{degradation:.1f}%")
print(f" Note: This may indicate architecture needs adjustment or training is insufficient")
# Depth variance analysis
accuracies = [post_grpo_results[d]["accuracy"] for d in range(EXP_CONFIG["num_thinking_depths"])]
if max(accuracies) > 0 and min(accuracies) < max(accuracies):
print(f" Depth sensitivity: accuracy ranges from "
f"{min(accuracies)*100:.1f}% (depth {accuracies.index(min(accuracies))}) "
f"to {max(accuracies)*100:.1f}% (depth {accuracies.index(max(accuracies))})")
print(f" ThinkingDial produces different outcomes at different depths")
print()
total_time = time.time() - t0
print(f"Total benchmark time: {total_time:.1f}s")
print()
return {
"zero_shot": zero_shot_results,
"post_grpo": post_grpo_results,
"grpo": grpo_results,
"vanilla": vanilla_result,
}
if __name__ == "__main__":
results = run_benchmark()
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