Bidirectional Attention as a Mixture of Continuous Word Experts
This work provides a foundational statistical interpretation for a key component in modern AI, with implications for model design and analysis, though it is incremental in building on existing attention mechanisms.
The paper tackles the problem of understanding the statistical model underlying bidirectional attention in LLMs, revealing it as equivalent to a mixture-of-experts CBOW model, and shows that this perspective leads to improved OOD generalization in tabular data and theoretical insights on linear word analogies.
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.