Looped Transformers are Better at Learning Learning Algorithms

Transformers have demonstrated effectiveness in in-context solving data-fitting problems from various (latent) models, as reported by Garg et al. (2022). However, the absence of an inherent iterative structure in the transformer architecture presents a challenge in emulating the iterative algorithms, which are commonly employed in traditional machine learning methods. To address this, we propose the utilization of looped transformer architecture and its associated training methodology, with the aim of incorporating iterative characteristics into the transformer architectures. Experimental results suggest that the looped transformer achieves performance comparable to the standard transformer in solving various data-fitting problems, while utilizing less than 10% of the parameter count. Transformers (Vaswani et al., 2017; Brown et al., 2020; Devlin et al., 2019) have emerged as the preferred model in the field of natural language processing (NLP) and other domains requiring sequence-to-sequence modeling. Besides their state-of-art performance in natural language processing tasks, large language models (LLM) such as GPT-3 (Brown et al., 2020) and PaLM (Chowdhery et al., 2022) also exhibit the ability to learn in-context: they can adapt to various downstream tasks based on a brief prompt, thus bypassing the need for additional model fine-tuning. This intriguing ability of in-context learning has sparked interest in the research community, leading numerous studies (Min et al., 2022; Olsson et al., 2022; Li et al., 2023). However, the underlying mechanisms enabling these transformers to perform in-context learning remain unclear. In an effort to understand the in-context learning behavior of LLMs, Garg et al. (2022) investigated the performance of transformers, when trained from scratch, in solving specific function class learning problems in-context. Notably, transformers exhibited strong performance across all tasks, matching or even surpassing traditional solvers. Building on this, Akyürek et al. (2022) explored the transformerbased model's capability to address the linear regression learning problem, interpreting it as an implicit form of established learning algorithms. Their study included both theoretical and empirical perspectives to understand how transformers learn these functions. Subsequently, von Oswald et al. (2022) demonstrated empirically that, when trained to predict the linear function output, a linear self-attention-only transformer inherently learns to perform a single step of gradient descent to solve the linear regression task in-context. While the approach and foundational theory presented by von Oswald et al. (2022) are promising, there exists a significant gap between the simplified architecture they examined and the standard decoder transformer used in practice.