In this paper, we focus on exploiting the group structure for large-dimensional factor models, which captures the homogeneous effects of common factors on individuals within the same group. In view of the fact that datasets in macroeconomics and finance are typically heavy-tailed, we propose to identify the unknown group structure using the agglomerative hierarchical clustering algorithm and an information criterion with the robust two-step (RTS) estimates as initial values. The loadings and factors are then re-estimated conditional on the identified groups. Theoretically, we demonstrate the consistency of the estimators for both group membership and the number of groups determined by the information criterion. Under finite second moment condition, we provide the convergence rate for the newly estimated factor loadings with group information, which are shown to achieve efficiency gains compared to those obtained without group structure information. Numerical simulations and real data analysis demonstrate the nice finite sample performance of our proposed approach in the presence of both group structure and heavy-tailedness.
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This paper presents a novel approach to address the challenging problem of autonomous on-ramp merging, where a self-driving vehicle needs to seamlessly integrate into a flow of vehicles on a multi-lane highway. We introduce the Lane-keeping, Lane-changing with Latent-state Inference and Safety Controller (L3IS) agent, designed to perform the on-ramp merging task safely without comprehensive knowledge about surrounding vehicles' intents or driving styles. We also present an augmentation of this agent called AL3IS that accounts for observation delays, allowing the agent to make more robust decisions in real-world environments with vehicle-to-vehicle (V2V) communication delays. By modeling the unobservable aspects of the environment through latent states, such as other drivers' intents, our approach enhances the agent's ability to adapt to dynamic traffic conditions, optimize merging maneuvers, and ensure safe interactions with other vehicles. We demonstrate the effectiveness of our method through extensive simulations generated from real traffic data and compare its performance with existing approaches. L3IS shows a 99.90% success rate in a challenging on-ramp merging case generated from the real US Highway 101 data. We further perform a sensitivity analysis on AL3IS to evaluate its robustness against varying observation delays, which demonstrates an acceptable performance of 93.84% success rate in 1-second V2V communication delay.
Advancements in model algorithms, the growth of foundational models, and access to high-quality datasets have propelled the evolution of Artificial Intelligence Generated Content (AIGC). Despite its notable successes, AIGC still faces hurdles such as updating knowledge, handling long-tail data, mitigating data leakage, and managing high training and inference costs. Retrieval-Augmented Generation (RAG) has recently emerged as a paradigm to address such challenges. In particular, RAG introduces the information retrieval process, which enhances the generation process by retrieving relevant objects from available data stores, leading to higher accuracy and better robustness. In this paper, we comprehensively review existing efforts that integrate RAG technique into AIGC scenarios. We first classify RAG foundations according to how the retriever augments the generator, distilling the fundamental abstractions of the augmentation methodologies for various retrievers and generators. This unified perspective encompasses all RAG scenarios, illuminating advancements and pivotal technologies that help with potential future progress. We also summarize additional enhancements methods for RAG, facilitating effective engineering and implementation of RAG systems. Then from another view, we survey on practical applications of RAG across different modalities and tasks, offering valuable references for researchers and practitioners. Furthermore, we introduce the benchmarks for RAG, discuss the limitations of current RAG systems, and suggest potential directions for future research. Github: //github.com/PKU-DAIR/RAG-Survey.
Despite the success of existing instruction-tuned models, we find that they usually struggle to respond to queries with multiple instructions. This impairs their performance in complex problems whose solution consists of multiple intermediate tasks. Thus, we contend that part of the fine-tuning data mixture should be sequential--containing a chain of interrelated tasks. We first approach sequential instruction tuning from a task-driven perspective, manually creating interpretable intermediate tasks for multilingual and visual question answering: namely "translate then predict" and "caption then answer". Next, we automate this process by turning instructions in existing datasets (e.g., Alpaca and FlanCoT) into diverse and complex sequential instructions, making our method general-purpose. Models that underwent our sequential instruction tuning show improved results in coding, maths, and open-ended generation. Moreover, we put forward a new benchmark named SeqEval to evaluate a model's ability to follow all the instructions in a sequence, which further corroborates the benefits of our fine-tuning method. We hope that our endeavours will open new research avenues on instruction tuning for complex tasks.
In this work, we propose using mechanistic interpretability -- techniques for reverse engineering model weights into human-interpretable algorithms -- to derive and compactly prove formal guarantees on model performance. We prototype this approach by formally proving lower bounds on the accuracy of 151 small transformers trained on a Max-of-$K$ task. We create 102 different computer-assisted proof strategies and assess their length and tightness of bound on each of our models. Using quantitative metrics, we find that shorter proofs seem to require and provide more mechanistic understanding. Moreover, we find that more faithful mechanistic understanding leads to tighter performance bounds. We confirm these connections by qualitatively examining a subset of our proofs. Finally, we identify compounding structureless noise as a key challenge for using mechanistic interpretability to generate compact proofs on model performance.
In this paper, we aim to improve the performance of a deep learning model towards image classification tasks, proposing a novel anchor-based training methodology, named \textit{Online Anchor-based Training} (OAT). The OAT method, guided by the insights provided in the anchor-based object detection methodologies, instead of learning directly the class labels, proposes to train a model to learn percentage changes of the class labels with respect to defined anchors. We define as anchors the batch centers at the output of the model. Then, during the test phase, the predictions are converted back to the original class label space, and the performance is evaluated. The effectiveness of the OAT method is validated on four datasets.
Current formations commonly rely on invariant hierarchical structures, such as predetermined leaders or enumerated formation shapes. These structures could be unidirectional and sluggish, constraining their adaptability and agility when encountering cluttered environments. To surmount these constraints, this work proposes an omnidirectional affine formation approach with hierarchical reorganizations. We first delineate the critical conditions requisite for facilitating hierarchical reorganizations within formations, which informs the development of the omnidirectional affine criterion. Central to our approach is the fluid leadership and authority redistribution, for which we develop a minimum time-driven leadership evaluation algorithm and a power transition control algorithm. These algorithms facilitate autonomous leader selection and ensure smooth power transitions, enabling the swarm to adapt hierarchically in alignment with the external environment. Furthermore, we deploy a power-centric topology switching mechanism tailored for the dynamic reorganization of in-team connections. Finally, simulations and experiments demonstrate the performance of the proposed method. The formation successfully performs several hierarchical reorganizations, with the longest reorganization taking only 0.047s. This swift adaptability allows five aerial robots to carry out complex tasks, including executing swerving movements and navigating through hoops at velocities up to 1.9m/s.
Given a sample of i.i.d. high-dimensional centered random vectors, we consider a problem of estimation of their covariance matrix $\Sigma$ with an additional assumption that $\Sigma$ can be represented as a sum of a few Kronecker products of smaller matrices. Under mild conditions, we derive the first non-asymptotic dimension-free high-probability bound on the Frobenius distance between $\Sigma$ and a widely used penalized permuted least squares estimate. Because of the hidden structure, the established rate of convergence is faster than in the standard covariance estimation problem.
In this paper, we delve into the statistical analysis of the fitted Q-evaluation (FQE) method, which focuses on estimating the value of a target policy using offline data generated by some behavior policy. We provide a comprehensive theoretical understanding of FQE estimators under both parameteric and nonparametric models on the $Q$-function. Specifically, we address three key questions related to FQE that remain largely unexplored in the current literature: (1) Is the optimal convergence rate for estimating the policy value regarding the sample size $n$ ($n^{-1/2}$) achievable for FQE under a non-parametric model with a fixed horizon ($T$)? (2) How does the error bound depend on the horizon $T$? (3) What is the role of the probability ratio function in improving the convergence of FQE estimators? Specifically, we show that under the completeness assumption of $Q$-functions, which is mild in the non-parametric setting, the estimation errors for policy value using both parametric and non-parametric FQE estimators can achieve an optimal rate in terms of $n$. The corresponding error bounds in terms of both $n$ and $T$ are also established. With an additional realizability assumption on ratio functions, the rate of estimation errors can be improved from $T^{1.5}/\sqrt{n}$ to $T/\sqrt{n}$, which matches the sharpest known bound in the current literature under the tabular setting.
Analysing Multi-Task Regression via Random Matrix Theory with Application to Time Series Forecasting
In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a multi-task optimization problem as a regularization technique to enable single-task models to leverage multi-task learning information. We derive a closed-form solution for multi-task optimization in the context of linear models. Our analysis provides valuable insights by linking the multi-task learning performance to various model statistics such as raw data covariances, signal-generating hyperplanes, noise levels, as well as the size and number of datasets. We finally propose a consistent estimation of training and testing errors, thereby offering a robust foundation for hyperparameter optimization in multi-task regression scenarios. Experimental validations on both synthetic and real-world datasets in regression and multivariate time series forecasting demonstrate improvements on univariate models, incorporating our method into the training loss and thus leveraging multivariate information.
In this paper, we tackle two challenges in multimodal learning for visual recognition: 1) when missing-modality occurs either during training or testing in real-world situations; and 2) when the computation resources are not available to finetune on heavy transformer models. To this end, we propose to utilize prompt learning and mitigate the above two challenges together. Specifically, our modality-missing-aware prompts can be plugged into multimodal transformers to handle general missing-modality cases, while only requiring less than 1% learnable parameters compared to training the entire model. We further explore the effect of different prompt configurations and analyze the robustness to missing modality. Extensive experiments are conducted to show the effectiveness of our prompt learning framework that improves the performance under various missing-modality cases, while alleviating the requirement of heavy model re-training. Code is available.
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