学会数数，才能理解语言：揭秘大型语言模型中的上下文位置编码

大型语言模型（LLM）在处理文本、音频、代码等序列数据时，往往需要理解其中的顺序信息。例如，在理解一段文字时，我们需要知道每个词语的位置，才能准确地理解其含义。然而，传统的注意力机制无法直接捕捉到序列中的顺序信息，因此需要引入位置编码（PE）来解决这个问题。

传统的 PE 方法通常将每个词语的位置信息直接编码成一个向量，并将其添加到词语的表示中。这种方法虽然简单有效，但存在一个问题：它无法根据上下文来灵活地调整位置信息。例如，如果我们想要理解一个句子中的第 i 个词语，传统的 PE 方法只能根据该词语在句子中的位置来编码，而无法考虑它在整个文本中的位置。

为了解决这个问题，本文介绍了一种新的位置编码方法：上下文位置编码（CoPE）。CoPE 的核心思想是将位置信息与上下文信息结合起来，根据上下文来动态地调整位置编码。

为什么需要上下文位置编码？

想象一下，你正在阅读一篇长篇小说。你想要知道某一个人物在小说中出现的次数，你会怎么做？你可能会逐字逐句地阅读，并记录下该人物出现的次数。然而，如果你想要知道该人物在每一章中出现的次数，你可能需要先找到每章的开头和结尾，然后才能进行统计。

传统的 PE 方法就相当于逐字逐句地阅读，它只能根据每个词语在句子中的位置来进行编码。而 CoPE 则相当于先找到每章的开头和结尾，然后根据上下文来动态地调整位置编码。

CoPE 的工作原理

CoPE 的工作原理可以概括为以下几个步骤：

计算门控值： 对于每个词语，CoPE 会根据其上下文信息计算一个门控值。门控值是一个介于 0 到 1 之间的数值，表示该词语是否应该被计入位置编码。
计算位置值： CoPE 会根据门控值来计算每个词语的位置值。如果门控值为 1，则该词语会被计入位置编码；如果门控值为 0，则该词语不会被计入位置编码。
插值位置嵌入： 由于位置值可以是分数，因此 CoPE 使用插值方法来计算位置嵌入。

CoPE 的优势

CoPE 具有以下几个优势：

上下文感知： CoPE 可以根据上下文信息来动态地调整位置编码，从而更准确地反映词语在序列中的位置信息。
多层级抽象： CoPE 可以同时表示不同层级的抽象信息，例如词语、句子、段落等。
灵活可控： CoPE 的门控值可以根据不同的任务需求进行调整，从而实现不同的位置编码策略。

实验结果

本文对 CoPE 在多个任务上的表现进行了评估，包括：

Flip-Flop 任务： 该任务要求模型能够记住一个序列中的最后一次写入操作。CoPE 在该任务上取得了显著的提升，尤其是在泛化能力方面。
选择性复制任务： 该任务要求模型能够从一个序列中选择性地复制一些词语。CoPE 在该任务上也取得了显著的提升，尤其是在处理包含大量空白词语的序列方面。
计数任务： 该任务要求模型能够统计一个序列中特定类型词语的个数。CoPE 在该任务上取得了显著的提升，尤其是在处理包含多个变量的序列方面。
语言模型任务： CoPE 在 Wikitext-103 数据集上取得了更好的语言建模效果。
代码模型任务： CoPE 在代码数据集上取得了更好的代码建模效果。

总结

CoPE 是一种新的位置编码方法，它可以根据上下文信息来动态地调整位置编码，从而更准确地反映词语在序列中的位置信息。CoPE 在多个任务上取得了显著的提升，表明它具有很强的实用价值。

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https://arxiv.org/pdf/2405.18719

Here's a breakdown of the paper's key points:

Problem:

Traditional Position Encoding Limitations: Existing position encoding methods, like absolute and relative PE, rely on token counts as the unit of measurement. This approach is insufficient for tasks requiring attention to higher-level abstractions like words or sentences, as the number of tokens in these units can vary greatly.
Inability to Generalize: Standard PE methods struggle to generalize to out-of-distribution scenarios where the token distribution differs from the training data.

Proposed Solution: CoPE

CoPE addresses these limitations by making position encoding context-dependent. Here's how it works:

Gate Calculation: For each query token, CoPE computes a gate value for every preceding token in the sequence. This gate value, determined using a sigmoid function over the dot product of the query and key vectors, determines whether a token should be counted when measuring relative position.

A gate value close to 1 indicates the token should be counted.
A gate value close to 0 indicates the token should be ignored.

Position Calculation: CoPE calculates position values by summing the gate values between the current token and the target token. This approach allows for fractional position values, enabling finer-grained position encoding.
Position Embedding Interpolation: As fractional position values don't have direct embeddings, CoPE interpolates between embeddings of the two nearest integer positions.
Attention Calculation: Finally, CoPE incorporates the interpolated position embeddings into the attention mechanism, allowing for context-aware position-based attention.

Advantages of CoPE:

Contextualized Position Encoding: CoPE enables the model to learn different position encodings based on the context, allowing it to attend to various levels of abstraction (e.g., words, sentences).
Improved Generalization: CoPE demonstrates superior generalization capabilities compared to traditional methods, especially in out-of-distribution scenarios.

Experimental Results:

The paper showcases CoPE's effectiveness on various tasks:

Flip-Flop Task: CoPE achieves near-perfect accuracy on both in-distribution and out-of-distribution settings, outperforming existing PE methods.
Selective Copy Task: CoPE successfully learns to copy relevant tokens while ignoring blanks, demonstrating its ability to handle variable-length units.
Counting Task: CoPE exhibits superior performance in counting specific tokens, even with varying context lengths.
Language Modeling: CoPE shows improved perplexity on the WikiText-103 benchmark compared to absolute PE.

Conclusion:

CoPE presents a significant advancement in position encoding for attention mechanisms. By making position encoding context-dependent, CoPE allows models to learn more nuanced and generalizable representations of positions within sequences, leading to improved performance on a variety of tasks.