Understanding the Expressive Power and Mechanisms of Transformer for Sequence Modeling

Understanding the Expressive Power and Mechanisms of Transformer for Sequence Modeling

3 Jul 2024 | Mingze Wang, Weinan E
This paper investigates the expressive power and underlying mechanisms of the Transformer for sequence modeling, focusing on long, sparse, and complex memories. The authors systematically study the approximation properties of different components of the Transformer, including dot-product self-attention, positional encoding, and feed-forward layers, and establish explicit approximation rates. Key findings include: 1. **Role of Hyperparameters**: The number of layers, attention heads, and the width of feed-forward layers significantly affect the Transformer's ability to handle intricate interrelationships in memories. Deeper Transformers can handle more complex memories, while simpler models with fewer layers and attention heads can suffice for less complex tasks. 2. **Different Roles of Layers**: The feed-forward layers are responsible for approximating nonlinear memory functions and the readout function, while attention layers extract tokens from memory locations. This separation highlights the distinct roles of each component in the overall performance. 3. **Necessity of Dot-Product Attention**: For simpler tasks, dot-product attention is not necessary and can be omitted. However, for more complex tasks involving adaptive memories, the cooperation between dot-product attention and relative positional encoding (RPE) is crucial for effective memory extraction. 4. **Efficiency of RPE**: RPE primarily approximates memory kernels and can handle heavy-tailed memories, overcoming the curse of dimensionality faced by recurrent neural networks. 5. **Theoretical Insights and Experiments**: Theoretical results are validated through experiments, providing practical suggestions for alternative architectures and highlighting the importance of understanding the underlying mechanisms of Transformer components. The paper contributes to a deeper understanding of how the Transformer handles various sequence modeling tasks, offering insights into its expressive power and the roles of its key components.This paper investigates the expressive power and underlying mechanisms of the Transformer for sequence modeling, focusing on long, sparse, and complex memories. The authors systematically study the approximation properties of different components of the Transformer, including dot-product self-attention, positional encoding, and feed-forward layers, and establish explicit approximation rates. Key findings include: 1. **Role of Hyperparameters**: The number of layers, attention heads, and the width of feed-forward layers significantly affect the Transformer's ability to handle intricate interrelationships in memories. Deeper Transformers can handle more complex memories, while simpler models with fewer layers and attention heads can suffice for less complex tasks. 2. **Different Roles of Layers**: The feed-forward layers are responsible for approximating nonlinear memory functions and the readout function, while attention layers extract tokens from memory locations. This separation highlights the distinct roles of each component in the overall performance. 3. **Necessity of Dot-Product Attention**: For simpler tasks, dot-product attention is not necessary and can be omitted. However, for more complex tasks involving adaptive memories, the cooperation between dot-product attention and relative positional encoding (RPE) is crucial for effective memory extraction. 4. **Efficiency of RPE**: RPE primarily approximates memory kernels and can handle heavy-tailed memories, overcoming the curse of dimensionality faced by recurrent neural networks. 5. **Theoretical Insights and Experiments**: Theoretical results are validated through experiments, providing practical suggestions for alternative architectures and highlighting the importance of understanding the underlying mechanisms of Transformer components. The paper contributes to a deeper understanding of how the Transformer handles various sequence modeling tasks, offering insights into its expressive power and the roles of its key components.
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