Tianhao Zhang

Frank Cole, Yulong Lu, Wuzhe Xu et al.

We study theoretical guarantees for solving linear systems in-context using a linear transformer architecture. For in-domain generalization, we provide neural scaling laws that bound the generalization error in terms of the number of tasks and sizes of samples used in training and inference. For out-of-domain generalization, we find that the behavior of trained transformers under task distribution shifts depends crucially on the distribution of the tasks seen during training. We introduce a novel notion of task diversity and show that it defines a necessary and sufficient condition for pre-trained transformers generalize under task distribution shifts. We also explore applications of learning linear systems in-context, such as to in-context operator learning for PDEs. Finally, we provide some numerical experiments to validate the established theory.

Chunyu Sun, Bingyu Liu, Zhichao Cui et al.

Embedding-based retrieval models have made significant strides in retrieval-augmented generation (RAG) techniques for text and multimodal large language models (LLMs) applications. However, when it comes to speech larage language models (SLLMs), these methods are limited to a two-stage process, where automatic speech recognition (ASR) is combined with text-based retrieval. This sequential architecture suffers from high latency and error propagation. To address these limitations, we propose a unified embedding framework that eliminates the need for intermediate text representations. Specifically, the framework includes separate speech and text encoders, followed by a shared scaling layer that maps both modalities into a common embedding space. Our model reduces pipeline latency by 50\% while achieving higher retrieval accuracy compared to traditional two-stage methods. We also provide a theoretical analysis of the challenges inherent in end-to-end speech retrieval and introduce architectural principles for effective speech-to-document matching. Extensive experiments demonstrate the robustness of our approach across diverse acoustic conditions and speaker variations, paving the way for a new paradigm in multimodal SLLMs retrieval systems.

Frank Cole, Yuxuan Zhao, Yulong Lu et al.

This paper investigates approximation-theoretic aspects of the in-context learning capability of the transformers in representing a family of noisy linear dynamical systems. Our first theoretical result establishes an upper bound on the approximation error of multi-layer transformers with respect to an $L^2$-testing loss uniformly defined across tasks. This result demonstrates that transformers with logarithmic depth can achieve error bounds comparable with those of the least-squares estimator. In contrast, our second result establishes a non-diminishing lower bound on the approximation error for a class of single-layer linear transformers, which suggests a depth-separation phenomenon for transformers in the in-context learning of dynamical systems. Moreover, this second result uncovers a critical distinction in the approximation power of single-layer linear transformers when learning from IID versus non-IID data.

Wei Zhang, Tian-Hao Zhang, Chao Luo et al.

Recently, end-to-end automatic speech recognition has become the mainstream approach in both industry and academia. To optimize system performance in specific scenarios, the Weighted Finite-State Transducer (WFST) is extensively used to integrate acoustic and language models, leveraging its capacity to implicitly fuse language models within static graphs, thereby ensuring robust recognition while also facilitating rapid error correction. However, WFST necessitates a frame-by-frame search of CTC posterior probabilities through autoregression, which significantly hampers inference speed. In this work, we thoroughly investigate the spike property of CTC outputs and further propose the conjecture that adjacent frames to non-blank spikes carry semantic information beneficial to the model. Building on this, we propose the Spike Window Decoding algorithm, which greatly improves the inference speed by making the number of frames decoded in WFST linearly related to the number of spiking frames in the CTC output, while guaranteeing the recognition performance. Our method achieves SOTA recognition accuracy with significantly accelerates decoding speed, proven across both AISHELL-1 and large-scale In-House datasets, establishing a pioneering approach for integrating CTC output with WFST.