Yingyu Liang

Zhuoyan Xu, Zhenmei Shi, Junyi Wei et al.

Foundation models have emerged as a powerful tool for many AI problems. Despite the tremendous success of foundation models, effective adaptation to new tasks, particularly those with limited labels, remains an open question and lacks theoretical understanding. An emerging solution with recent success in vision and NLP involves finetuning a foundation model on a selection of relevant tasks, before its adaptation to a target task with limited labeled samples. In this paper, we study the theoretical justification of this multitask finetuning approach. Our theoretical analysis reveals that with a diverse set of related tasks, this multitask finetuning leads to reduced error in the target task, in comparison to directly adapting the same pretrained model. We quantify the relationship between finetuning tasks and target tasks by diversity and consistency metrics, and further propose a practical task selection algorithm. We substantiate our theoretical claims with extensive empirical evidence. Further, we present results affirming our task selection algorithm adeptly chooses related finetuning tasks, providing advantages to the model performance on target tasks. We believe our study shed new light on the effective adaptation of foundation models to new tasks that lack abundant labels. Our code is available at https://github.com/OliverXUZY/Foudation-Model_Multitask.

Yekun Ke, Yingyu Liang, Zhenmei Shi et al.

The application of transformer-based models on time series forecasting (TSF) tasks has long been popular to study. However, many of these works fail to beat the simple linear residual model, and the theoretical understanding of this issue is still limited. In this work, we propose the first theoretical explanation of the inefficiency of transformers on TSF tasks. We attribute the mechanism behind it to {\bf Asymmetric Learning} in training attention networks. When the sign of the previous step is inconsistent with the sign of the current step in the next-step-prediction time series, attention fails to learn the residual features. This makes it difficult to generalize on out-of-distribution (OOD) data, especially on the sign-inconsistent next-step-prediction data, with the same representation pattern, whereas a linear residual network could easily accomplish it. We hope our theoretical insights provide important necessary conditions for designing the expressive and efficient transformer-based architecture for practitioners.

Yifang Chen, Xiaoyu Li, Yingyu Liang et al.

We investigate the fundamental limits of transformer-based foundation models, extending our analysis to include Visual Autoregressive (VAR) transformers. VAR represents a big step toward generating images using a novel, scalable, coarse-to-fine ``next-scale prediction'' framework. These models set a new quality bar, outperforming all previous methods, including Diffusion Transformers, while having state-of-the-art performance for image synthesis tasks. Our primary contributions establish that, for single-head VAR transformers with a single self-attention layer and single interpolation layer, the VAR Transformer is universal. From the statistical perspective, we prove that such simple VAR transformers are universal approximators for any image-to-image Lipschitz functions. Furthermore, we demonstrate that flow-based autoregressive transformers inherit similar approximation capabilities. Our results provide important design principles for effective and computationally efficient VAR Transformer strategies that can be used to extend their utility to more sophisticated VAR models in image generation and other related areas.

Zhuoyan Xu, Khoi Duc Nguyen, Preeti Mukherjee et al.

Multimodal Large Language Models (MLLMs) have shown impressive capabilities in visual reasoning, yet come with substantial computational cost, limiting their deployment in resource-constrained settings. Despite recent effort on improving the efficiency of MLLMs, prior solutions fall short in responding to varying runtime conditions, in particular changing resource availability (e.g., contention due to the execution of other programs on the device). To bridge this gap, we introduce AdaLLaVA, an adaptive inference framework that learns to dynamically reconfigure operations in an MLLM during inference, accounting for the input data and a latency budget. We conduct extensive experiments across benchmarks involving question-answering, reasoning, and hallucination. Our results show that AdaLLaVA effectively adheres to input latency budget, achieving varying accuracy and latency tradeoffs at runtime. Further, we demonstrate that AdaLLaVA adapts to both input latency and content, can be integrated with token selection for enhanced efficiency, and generalizes across MLLMs. Our project webpage with code release is at https://zhuoyan-xu.github.io/ada-llava/.

Yingyu Liang, Zhizhou Sha, Zhenmei Shi et al.

Flow Matching and Transformer architectures have demonstrated remarkable performance in image generation tasks, with recent work FlowAR [Ren et al., 2024] synergistically integrating both paradigms to advance synthesis fidelity. However, current FlowAR implementations remain constrained by first-order trajectory modeling during the generation process. This paper introduces a novel framework that systematically enhances flow autoregressive transformers through high-order supervision. We provide theoretical analysis and empirical evaluation showing that our High-Order FlowAR (HOFAR) demonstrates measurable improvements in generation quality compared to baseline models. The proposed approach advances the understanding of flow-based autoregressive modeling by introducing a systematic framework for analyzing trajectory dynamics through high-order expansion.

Yifang Chen, Xuyang Guo, Xiaoyu Li et al.

Recently, Large Language Models (LLMs) have achieved remarkable success. A key factor behind this success is the scaling law observed by OpenAI. Specifically, for models with Transformer architecture, the test loss exhibits a power-law relationship with model size, dataset size, and the amount of computation used in training, demonstrating trends that span more than seven orders of magnitude. This scaling law challenges traditional machine learning wisdom, notably the Oscar Scissors principle, which suggests that an overparametrized algorithm will overfit the training datasets, resulting in poor test performance. Recent research has also identified the scaling law in simpler machine learning contexts, such as linear regression. However, fully explaining the scaling law in large practical models remains an elusive goal. In this work, we advance our understanding by demonstrating that the scaling law phenomenon extends to multiple regression and kernel regression settings, which are significantly more expressive and powerful than linear methods. Our analysis provides deeper insights into the scaling law, potentially enhancing our understanding of LLMs.

Yang Guo, Yutian Tao, Yifei Ming et al.

Retrieval-augmented generation (RAG) has seen many empirical successes in recent years by aiding the LLM with external knowledge. However, its theoretical aspect has remained mostly unexplored. In this paper, we propose the first finite-sample generalization bound for RAG in in-context linear regression and derive an exact bias-variance tradeoff. Our framework views the retrieved texts as query-dependent noisy in-context examples and recovers the classical in-context learning (ICL) and standard RAG as the limit cases. Our analysis suggests that an intrinsic ceiling on generalization error exists on RAG as opposed to the ICL. Furthermore, our framework is able to model retrieval both from the training data and from external corpora by introducing uniform and non-uniform RAG noise. In line with our theory, we show the sample efficiency of ICL and RAG empirically with experiments on common QA benchmarks, such as Natural Questions and TriviaQA.

Bo Chen, Xiaoyu Li, Yekun Ke et al.

A fundamental challenge in Visual Autoregressive models is the substantial memory overhead required during inference to store previously generated representations. Despite various attempts to mitigate this issue through compression techniques, prior works have not explicitly formalized the problem of KV-cache compression in this context. In this work, we take the first step in formally defining the KV-cache compression problem for Visual Autoregressive transformers. We then establish a fundamental negative result, proving that any mechanism for sequential visual token generation under attention-based architectures must use at least $Ω(n^2 d)$ memory, when $d = Ω(\log n)$, where $n$ is the number of tokens generated and $d$ is the embedding dimensionality. This result demonstrates that achieving truly sub-quadratic memory usage is impossible without additional structural constraints. Our proof is constructed via a reduction from a computational lower bound problem, leveraging randomized embedding techniques inspired by dimensionality reduction principles. Finally, we discuss how sparsity priors on visual representations can influence memory efficiency, presenting both impossibility results and potential directions for mitigating memory overhead.