Renpu Liu

Renpu Liu, Jing Yang

Large language models (LLMs) exhibit impressive in-context learning (ICL) capabilities, yet the quality of their predictions is fundamentally limited by the few costly labeled demonstrations that can fit into a prompt. Meanwhile, there exist vast and continuously growing amounts of unlabeled data that may be closely related to the ICL task. How to utilize such unlabeled data to provably enhance the performance of ICL thus becomes an emerging fundamental question. In this work, we propose a novel augmented ICL framework, in which the prompt includes a small set of labeled examples alongside a block of unlabeled inputs. We focus on the multi-class linear classification setting and demonstrate that, with chain-of-thought (CoT) prompting, a multi-layer transformer can effectively emulate an expectation-maximization (EM) algorithm. This enables the transformer to implicitly extract useful information from both labeled and unlabeled data, leading to provable improvements in ICL accuracy. Moreover, we show that such a transformer can be trained via teacher forcing, with its parameters converging to the desired solution at a linear rate. Experiments demonstrate that the augmented ICL framework consistently outperforms conventional few-shot ICL, providing empirical support for our theoretical findings. To the best of our knowledge, this is the first theoretical study on the impact of unlabeled data on the ICL performance of transformers.

Renpu Liu, Cong Shen, Jing Yang

Federated representation learning (FRL) is a popular personalized federated learning (FL) framework where clients work together to train a common representation while retaining their personalized heads. Existing studies, however, largely focus on the over-parameterized regime. In this paper, we make the initial efforts to investigate FRL in the under-parameterized regime, where the FL model is insufficient to express the variations in all ground-truth models. We propose a novel FRL algorithm FLUTE, and theoretically characterize its sample complexity and convergence rate for linear models in the under-parameterized regime. To the best of our knowledge, this is the first FRL algorithm with provable performance guarantees in this regime. FLUTE features a data-independent random initialization and a carefully designed objective function that aids the distillation of subspace spanned by the global optimal representation from the misaligned local representations. On the technical side, we bridge low-rank matrix approximation techniques with the FL analysis, which may be of broad interest. We also extend FLUTE beyond linear representations. Experimental results demonstrate that FLUTE outperforms state-of-the-art FRL solutions in both synthetic and real-world tasks.