Can Mamba Always Enjoy the "Free Lunch"?

Transformers have been the cornerstone of current Large Language Models (LLMs); however, its linear growth in overhead during inference with respect to sequence length poses challenges for modeling long sequences. In this context, Mamba has gradually attracted attention due to its constant-level size during inference and existing empirical results have shown that it can perform comparably to Transformers in sequence modeling while offering significant savings. However, one may ask that, can Mamba always enjoy the ``free lunch"? In this paper, we focus on analyzing the expressive ability of Mamba from a theoretical standpoint. First, inspired by the connection between Mamba and linear attention, we investigate potential shortcomings of the Mamba when performing the COPY operation. Our results indicate that Mamba with constant size may encounter bottlenecks when handling COPY, while it can achieve perfect performance when the size scales linearly with sequence length. Based on this observation, we analyze Mamba's ability to tackle DP problems when equipped with Chain of Thought (CoT). Our findings suggest that to solve arbitrary DP problems, the total cost of Mamba is comparable to standard and efficient Transformers. However, similar to efficient Transformers, when facing DP problems with favorable properties such as locality, Mamba can provide savings in overhead. Our results contribute to a deeper understanding of Mamba.

In-context Learning with Transformer Is Really Equivalent to a Contrastive Learning Pattern

Pre-trained large language models based on Transformers have demonstrated amazing in-context learning (ICL) abilities. Given several demonstration examples, the models can implement new tasks without any parameter updates. However, it is still an open question to understand the mechanism of ICL. In this paper, we interpret the inference process of ICL as a gradient descent process in a contrastive learning pattern. Firstly, leveraging kernel methods, we establish the relationship between gradient descent and self-attention mechanism under generally used softmax attention setting instead of linear attention setting. Then, we analyze the corresponding gradient descent process of ICL from the perspective of contrastive learning without negative samples and discuss possible improvements of this contrastive learning pattern, based on which the self-attention layer can be further modified. Finally, we design experiments to support our opinions. To the best of our knowledge, our work is the first to provide the understanding of ICL from the perspective of contrastive learning and has the potential to facilitate future model design by referring to related works on contrastive learning.