Bidirectional attention $\unicode{x2013}$ composed of self-attention with
positional encodings and the masked language model (MLM) objective
$\unicode{x2013}$ has emerged as a key component of modern large language
models (LLMs). Despite its empirical success, few studies have examined its
statistical underpinnings: What statistical model is bidirectional attention
implicitly fitting? What sets it apart from its non-attention predecessors? We
explore these questions in this paper. The key observation is that fitting a
single-layer single-head bidirectional attention, upon reparameterization, is
equivalent to fitting a continuous bag of words (CBOW) model with
mixture-of-experts (MoE) weights. Further, bidirectional attention with
multiple heads and multiple layers is equivalent to stacked MoEs and a mixture
of MoEs, respectively. This statistical viewpoint reveals the distinct use of
MoE in bidirectional attention, which aligns with its practical effectiveness
in handling heterogeneous data. It also suggests an immediate extension to
categorical tabular data, if we view each word location in a sentence as a
tabular feature. Across empirical studies, we find that this extension
outperforms existing tabular extensions of transformers in out-of-distribution
(OOD) generalization. Finally, this statistical perspective of bidirectional
attention enables us to theoretically characterize when linear word analogies
are present in its word embeddings. These analyses show that bidirectional
attention can require much stronger assumptions to exhibit linear word
analogies than its non-attention predecessors.

通过重新参数化，将多层多头的双向注意力视为堆叠的 MoE 和混合的 MoE，从而揭示了双向注意力中使用 MoE 的独特之处，并说明了其在处理异构数据方面的实际有效性。此外，统计视角还揭示了双向注意力的词嵌入中线性类比的限制条件。

双向关注作为连续单词专家的混合

Bidirectional Attention as a Mixture of Continuous Word Experts

Continuous Bag of Words (CBOW) is a powerful text embedding method. Due to
its strong capabilities to encode word content, CBOW embeddings perform well on
a wide range of downstream tasks while being efficient to compute. However,
CBOW is not capable of capturing the word order. The reason is that the
computation of CBOW's word embeddings is commutative, i.e., embeddings of XYZ
and ZYX are the same. In order to address this shortcoming, we propose a
learning algorithm for the Continuous Matrix Space Model, which we call
Continual Multiplication of Words (CMOW). Our algorithm is an adaptation of
word2vec, so that it can be trained on large quantities of unlabeled text. We
empirically show that CMOW better captures linguistic properties, but it is
inferior to CBOW in memorizing word content. Motivated by these findings, we
propose a hybrid model that combines the strengths of CBOW and CMOW. Our
results show that the hybrid CBOW-CMOW-model retains CBOW's strong ability to
memorize word content while at the same time substantially improving its
ability to encode other linguistic information by 8%. As a result, the hybrid
also performs better on 8 out of 11 supervised downstream tasks with an average
improvement of 1.2%.

通过提出核心技术 —— 连续矩阵空间模型的学习算法 ——CMOW，结合 CBOW（连续词袋模型）和 CMOW 的优点，实现更好地标注文本信息，具有广泛的应用前景。