深入解析 Loss 减少方式：mean和sum的区别及其在大语言模型中的应用（中英双语）

深入解析 Loss 减少方式：`mean` 和 `sum` 的区别及其在大语言模型中的应用

在训练大语言模型（Large Language Models, LLM）时，损失函数（Loss Function）的处理方式对模型的性能和优化过程有显著影响。本文以 reduce_loss 参数为例，详细探讨 mean 和 sum 两种方式的定义、适用场景及其对对话模型性能的潜在提升原因，并通过代码实例加深理解。

1. 什么是 `reduce_loss`？

reduce_loss 决定了在每个 batch 中，如何对 token-level 的损失进行归一化或累加处理。常见的选项是：

mean: 取每个 token 损失的平均值。
sum: 将每个 token 损失直接累加。

参数定义示例（在代码中通过 dataclass 定义）：参考来源：https://github.com/allenai/open-instruct

from dataclasses import dataclass, field

@dataclass
class TrainingArguments:
    reduce_loss: str = field(
        default="mean",
        metadata={
            "help": (
                "How to reduce loss over tokens. Options are 'mean' or 'sum'."
                "Using 'sum' can improve chat model performance."
            )
        },
    )

2. `mean` 和 `sum` 的定义

2.1 `mean` 模式

定义：将 batch 中所有 token 的损失值取平均。
公式：
$\text{Loss}_{\text{mean}} = \frac{\sum_{i=1}^{N} \text{Loss}_i}{N}$
其中 ( $N$ ) 是当前 batch 中的 token 总数。
特性：每个 token 的损失对最终的 loss 贡献相等，损失值与 batch 中的 token 数无关。

2.2 `sum` 模式

定义：将 batch 中所有 token 的损失值直接累加。
公式：
$\text{Loss}_{\text{sum}} = \sum_{i=1}^{N} \text{Loss}_i$
特性：长序列（更多 token）的损失对总 loss 的贡献更大，损失值直接与 token 数成正比。

3. `mean` 和 `sum` 的区别

模式	特点	优点	缺点
`mean`	损失对 token 数归一化，独立于 batch size。	稳定性强，适用于 token 数差异大的批次。	长序列与短序列对损失的贡献相同，可能弱化长序列的重要性。
`sum`	损失值与 token 总数成正比，长序列贡献更大。	在注重长序列表现的任务中效果更好（如对话生成）。	损失值随 batch size 变化波动，需要动态调整学习率。

4. 适用场景分析

4.1 `mean`

适用任务：大多数语言建模任务，如 GPT 或 BERT 的预训练。
适用场景：当训练数据中序列长度差异较大时，mean 可以避免因长序列的损失值过大而导致梯度更新不均衡。

4.2 `sum`

适用任务：对长序列表现要求较高的任务，如对话生成（Chat Models）和长文本生成。
适用场景：长序列的损失占比更高，从而使优化过程更加关注全局上下文的建模。

5. 为什么 `sum` 能提升对话模型性能？

对话模型（Chat Models）的训练中，长序列往往包含丰富的上下文信息，而短序列则可能无法体现模型的上下文理解能力。在 sum 模式下：

长序列的重要性增加：长序列的损失对总损失的贡献更大，这促使模型更关注上下文的建模。
对全局一致性更敏感：sum 模式下，模型的优化方向更倾向于全序列的一致性，特别适合需要长距离依赖的任务。

示例：
假设一个 batch 包含以下两个样本：

样本 A: 长度为 10，损失总和为 5。
样本 B: 长度为 50，损失总和为 25。

计算损失贡献：

mean 模式：
$\text{Loss}_{\text{mean}} = \frac{5 + 25}{10 + 50} = 0.5$
样本 A 和 B 的贡献权重相同。
sum 模式：
$\text{Loss}_{\text{sum}} = 5 + 25 = 30$
样本 B 的贡献权重显著增加，优化更关注长序列。

6. 实战代码

以下是一个完整的训练脚本，展示如何在 Hugging Face 的 transformers 框架中使用 reduce_loss 参数。

from transformers import AutoModelForCausalLM, AutoTokenizer
from datasets import load_dataset
from torch.utils.data import DataLoader
import torch

# 模型和数据集
model_name = "meta-llama/Llama-3.1-8B"
dataset_name = "allenai/tulu-3-sft-mixture"

model = AutoModelForCausalLM.from_pretrained(model_name)
tokenizer = AutoTokenizer.from_pretrained(model_name, use_fast=False)

dataset = load_dataset(dataset_name)
tokenized_dataset = dataset.map(lambda x: tokenizer(x['text'], truncation=True, padding="max_length"), batched=True)
train_loader = DataLoader(tokenized_dataset["train"], batch_size=2, shuffle=True)

# 训练设置
reduce_loss = "sum"  # 改为 "mean" 可对比效果
optimizer = torch.optim.AdamW(model.parameters(), lr=5e-6)
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
model.to(device)

# 训练循环
for epoch in range(2):
    for batch in train_loader:
        inputs = torch.tensor(batch["input_ids"]).to(device)
        labels = inputs.clone()
        outputs = model(inputs, labels=labels)

        if reduce_loss == "sum":
            loss = outputs.loss.sum()
        else:  # 默认 "mean"
            loss = outputs.loss.mean()

        loss.backward()
        optimizer.step()
        optimizer.zero_grad()

        print(f"Epoch: {epoch}, Loss: {loss.item()}")

7. 注意事项与优化建议

动态调整学习率：
- 使用 sum 时，由于损失值放大，建议适配学习率，如降低到 mean 模式的 ( $1/ N$ )。
- 配合学习率调度器（如 linear）优化训练。
对长短序列的平衡：
- 若长序列权重过大导致模型性能退化，可结合 curriculum learning 或混合训练策略（如对长短序列按比例采样）。
性能评估：
- 在验证集上，关注长序列和短序列的生成性能对比。

8. 总结

reduce_loss 的选择对模型性能有直接影响：

mean 更通用，适合大多数语言建模任务。
sum 在对话生成等长序列敏感任务中表现更优。

希望本文能为 LLM 研究人员提供思路和参考，在具体任务中灵活选择合适的损失归一化方式，从而提升模型性能。

Understanding the Difference Between `mean` and `sum` Loss Reduction in LLM Training

When training large language models (LLMs), the way token-level loss is reduced across a batch can significantly impact optimization and model performance. This article delves into the reduce_loss parameter, exploring the differences between mean and sum reduction modes, their definitions, use cases, and why sum might improve the performance of chat-oriented models. Practical code examples are also provided for clarity.

1. What is `reduce_loss`?

The reduce_loss parameter determines how the token-level loss values in a batch are aggregated. The two most common options are:

mean: Averages the loss over all tokens in a batch.
sum: Sums the loss of all tokens in a batch.

Example definition (from the codebase using Python dataclass):

from dataclasses import dataclass, field

@dataclass
class TrainingArguments:
    reduce_loss: str = field(
        default="mean",
        metadata={
            "help": (
                "How to reduce loss over tokens. Options are 'mean' or 'sum'."
                "Using 'sum' can improve chat model performance."
            )
        },
    )

2. Definitions of `mean` and `sum`

2.1 `mean`

Definition: Averages the loss across all tokens in a batch.
Formula:
$\text{Loss}_{\text{mean}} = \frac{\sum_{i=1}^{N} \text{Loss}_i}{N}$
where ( $N$ ) is the total number of tokens in the batch.
Characteristics: The contribution of each token to the final loss is normalized, making the loss independent of the batch’s token count.

2.2 `sum`

Definition: Sums up the loss across all tokens in a batch.
Formula:
$\text{Loss}_{\text{sum}} = \sum_{i=1}^{N} \text{Loss}_i$
Characteristics: The total loss is proportional to the number of tokens, giving longer sequences more weight in the optimization process.

3. Key Differences Between `mean` and `sum`

Reduction Mode	Characteristics	Advantages	Disadvantages
`mean`	Normalizes the loss by token count.	Stable and robust for datasets with variable-length sequences.	Long sequences are underweighted relative to short ones.
`sum`	Loss scales with the number of tokens.	Places greater emphasis on longer sequences, improving performance in tasks requiring context modeling.	Loss values vary with batch size, necessitating dynamic learning rate adjustment.

4. Use Cases for `mean` and `sum`

4.1 `mean`

Best Suited For: Pretraining or general language modeling tasks like GPT or BERT.
Scenario: When the dataset contains sequences of widely varying lengths, mean ensures that longer sequences do not disproportionately influence gradient updates.

4.2 `sum`

Best Suited For: Tasks requiring high performance on long sequences, such as dialogue generation or document-level text generation.
Scenario: Encourages the model to prioritize sequences with richer contexts, as their loss contributes more to the overall optimization.

5. Why Does `sum` Improve Chat Model Performance?

In chat-oriented models, sequences are typically longer and require the model to understand and generate coherent responses over extended contexts. Using sum mode:

Enhances Long Sequence Weighting: Longer sequences contribute more to the total loss, emphasizing the importance of context modeling.
Encourages Global Consistency: By assigning more weight to longer contexts, the model better captures dependencies across the entire sequence.
Balances Token Importance: Since chat models are often evaluated on dialogue-level coherence, sum ensures that tokens from the context and the response are proportionally weighted.

Example:
Consider a batch with two samples:

Sample A: Sequence length = 10, loss = 5.
Sample B: Sequence length = 50, loss = 25.

Loss calculations:

mean mode:
$\text{Loss}_{\text{mean}} = \frac{5 + 25}{10 + 50} = 0.5$
Both samples contribute equally to the loss.
sum mode:
$\text{Loss}_{\text{sum}} = 5 + 25 = 30$
Sample B contributes much more to the total loss, focusing the optimization on longer contexts.

6. Practical Implementation

Here’s a practical training script that demonstrates the use of reduce_loss in both modes.

from transformers import AutoModelForCausalLM, AutoTokenizer
from datasets import load_dataset
from torch.utils.data import DataLoader
import torch

# Model and dataset
model_name = "meta-llama/Llama-3.1-8B"
dataset_name = "allenai/tulu-3-sft-mixture"

model = AutoModelForCausalLM.from_pretrained(model_name)
tokenizer = AutoTokenizer.from_pretrained(model_name, use_fast=False)

dataset = load_dataset(dataset_name)
tokenized_dataset = dataset.map(lambda x: tokenizer(x['text'], truncation=True, padding="max_length"), batched=True)
train_loader = DataLoader(tokenized_dataset["train"], batch_size=2, shuffle=True)

# Training setup
reduce_loss = "sum"  # Change to "mean" to compare effects
optimizer = torch.optim.AdamW(model.parameters(), lr=5e-6)
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
model.to(device)

# Training loop
for epoch in range(2):
    for batch in train_loader:
        inputs = torch.tensor(batch["input_ids"]).to(device)
        labels = inputs.clone()
        outputs = model(inputs, labels=labels)

        if reduce_loss == "sum":
            loss = outputs.loss.sum()
        else:  # Default: "mean"
            loss = outputs.loss.mean()

        loss.backward()
        optimizer.step()
        optimizer.zero_grad()

        print(f"Epoch: {epoch}, Loss: {loss.item()}")

7. Practical Considerations

Learning Rate Adjustment:
- When using sum, the loss magnitude increases with batch size, so you may need to adjust the learning rate (e.g., scale it down by ( $1/ N$ )).
Balancing Long and Short Sequences:
- Overweighting long sequences can sometimes harm generalization. Using curriculum learning or sampling strategies (e.g., proportional sampling) can help mitigate this.
Validation:
- Evaluate model performance on both short and long sequences to confirm improvements in the intended metrics.

8. Conclusion

The choice between mean and sum loss reduction modes depends on the specific task and dataset:

Use mean for general-purpose language modeling tasks where sequence lengths vary significantly.
Use sum for tasks that prioritize long-sequence performance, such as chat models or long-text generation.

Understanding and experimenting with these settings can lead to better-optimized models, particularly in the nuanced field of LLM fine-tuning.