Reorganizing attention-space geometry with expressive attention

Abstract: Attention regulates information transfer between tokens. For this, query and key vectors are compared, typically in terms of a scalar product, $\mathbf{Q}^T\mathbf{K}$, together with a subsequent softmax normalization. In geometric terms, the standard dot-product attention (DPA) leads to large/small attention weights for parallel/antiparallel queries and keys. Here we study expressive attention (EA), which is based on $(\mathbf{Q}^T\mathbf{K})^2$, the squared dot product. In this case, attention is enhanced when query and key are either parallel or antiparallel, and suppressed for orthogonal configurations. EA can be introduced into any attention-based code without additional compute costs or memory requirements. For a series of autoregressive prediction tasks, we find that expressive attention performs at least as well as vanilla DPA. Increasing task complexity, EA is observed to outperform DPA with increasing margins, which also holds for multi-task settings. For a given model size, EA manages to achieve 100% performance for a range of complexity levels not accessible to DPA. Our results show that it is possible to reorganize the geometry of the matching condition in the space of attention heads without loss of performance.

• The paper introduces Expressive Attention, a novel mechanism employing the squared dot product, which outperforms Dot-Product Attention on complex tasks.
• Experiments show Expressive Attention achieves perfect performance on complex tasks inaccessible to traditional attention, effectively escaping local minima.
• Implications suggest revisiting fundamental attention assumptions and exploring Expressive Attention's potential in large language models and sequence tasks.

Expressive Attention: A Detailed Examination

The paper "Climbing the Complexity Ladder with Expressive Attention" introduces a novel attention mechanism termed Expressive Attention (EA), and evaluates its effectiveness relative to the more traditional Dot-Product Attention (DPA). The work builds on the premise that existing attention mechanisms, while effective, are constrained by their design, which limits expressivity in the high-dimensional space of attention heads. This paper meticulously examines how tweaking a fundamental part of the attention mechanism can lead to improved performance in complex sequence prediction tasks.

Summary of Core Contributions

The proposed Expressive Attention deviates from the conventional method by employing the squared dot product, $(\mathbf{Q}^T\mathbf{K})^2$, to compute attention weights. This subtle yet profound modification allows attention to be enhanced for both parallel and antiparallel vector alignments and suppressed for orthogonal configurations. In contrast, classical DPA accentuates parallel alignments while minimally weighting antiparallel alignments.

The paper substantiates the improved performance of EA over DPA in a variety of tasks, specifically those that increase in complexity. The authors demonstrate this through a series of autoregressive prediction tasks known as NT tasks, where models based on EA consistently outperform those based on DPA, especially as task complexity escalates. Notably, EA achieves 100% performance on a range of complexity levels inaccessible to traditional DPA.

Experimental Insights

Experiments conducted utilize a standardized transformer architecture across various NT tasks of differing bases $N$ and delays $\tau$. A poignant advantage of EA observed across these tasks is its ability to escape local minima in the loss landscape more effectively than DPA. This is attributed to the increased expressive capacity of EA to represent semantic configurations in the attention space.

Moreover, EA's superior performance is particularly highlighted in multitask settings wherein a mix of NT and altered NT tasks (NT-S and NT-R) are presented. EA's resilience and ability to generalize are showcased, enabling the model to adapt and perform efficiently across distinct tasks where DPA often remains trapped in suboptimal heuristics.

Implications and Theoretical Considerations

The implications of this research are substantial for both theoretical and practical applications. By demonstrating that simple modifications to the attention mechanism can significantly boost performance, this work invites further exploration into alternative attention formulations that might better exploit the structure of input data.

From a theoretical standpoint, the findings suggest that local minima in the attention landscape may correlate with heuristic strategies formed under limited expressivity. EA's ability to bypass these minima indicates a potential avenue for disentangling and understanding the emergent properties of neural networks, particularly in handling intricate dependencies within data.

Speculations on Future Research

The promising results observed with EA propose several directions for future research. These include a deeper investigation into the conditions under which EA outperforms DPA, an exploration of EA's potential in natural language processing tasks, and integration within larger LLMs where nuanced data dependencies are prevalent. Furthermore, the relationship between expressivity and architectural depth could yield insights into optimal network designs in sequence-based models.

In conclusion, this paper provides a compelling argument for revisiting and reengineering the fundamental assumptions underlying attention mechanisms. By climbing the complexity ladder with expressive attention, researchers are afforded a novel tool that not only enriches the representation capacity of neural networks but also challenges existing paradigms in sequence processing models.