Peng Ding

Dennis Shen, Dogyoon Song, Peng Ding et al.

Deep learning research has uncovered the phenomenon of benign overfitting for overparameterized statistical models, which has drawn significant theoretical interest in recent years. Given its simplicity and practicality, the ordinary least squares (OLS) interpolator has become essential to gain foundational insights into this phenomenon. While properties of OLS are well established in classical, underparameterized settings, its behavior in high-dimensional, overparameterized regimes is less explored (unlike for ridge or lasso regression) though significant progress has been made of late. We contribute to this growing literature by providing fundamental algebraic and statistical results for the minimum $\ell_2$-norm OLS interpolator. In particular, we provide algebraic equivalents of (i) the leave-$k$-out residual formula, (ii) Cochran's formula, and (iii) the Frisch-Waugh-Lovell theorem in the overparameterized regime. These results aid in understanding the OLS interpolator's ability to generalize and have substantive implications for causal inference. Under the Gauss-Markov model, we present statistical results such as an extension of the Gauss-Markov theorem and an analysis of variance estimation under homoskedastic errors for the overparameterized regime. To substantiate our theoretical contributions, we conduct simulations that further explore the stochastic properties of the OLS interpolator.

Zhan Shi, Xin Ding, Peng Ding et al.

Ship orientation angle prediction (SOAP) with optical remote sensing images is an important image processing task, which often relies on deep convolutional neural networks (CNNs) to make accurate predictions. This paper proposes a novel framework to reduce the model sizes and computational costs of SOAP models without harming prediction accuracy. First, a new SOAP model called Mobile-SOAP is designed based on MobileNetV2, achieving state-of-the-art prediction accuracy. Four tiny SOAP models are also created by replacing the convolutional blocks in Mobile-SOAP with four small-scale networks, respectively. Then, to transfer knowledge from Mobile-SOAP to four lightweight models, we propose a novel knowledge distillation (KD) framework termed SOAP-KD consisting of a novel feature-based guidance loss and an optimized synthetic samples-based knowledge transfer mechanism. Lastly, extensive experiments on the FGSC-23 dataset confirm the superiority of Mobile-SOAP over existing models and also demonstrate the effectiveness of SOAP-KD in improving the prediction performance of four specially designed tiny models. Notably, by using SOAP-KD, the test mean absolute error of the ShuffleNetV2x1.0-based model is only 8% higher than that of Mobile-SOAP, but its number of parameters and multiply-accumulate operations (MACs) are respectively 61.6% and 60.8% less.

Peng Ding, Jiading Fang, Peng Li et al.

Large language models such as ChatGPT and GPT-4 have recently achieved astonishing performance on a variety of natural language processing tasks. In this paper, we propose MANGO, a benchmark to evaluate their capabilities to perform text-based mapping and navigation. Our benchmark includes 53 mazes taken from a suite of textgames: each maze is paired with a walkthrough that visits every location but does not cover all possible paths. The task is question-answering: for each maze, a large language model reads the walkthrough and answers hundreds of mapping and navigation questions such as "How should you go to Attic from West of House?" and "Where are we if we go north and east from Cellar?". Although these questions are easy to humans, it turns out that even GPT-4, the best-to-date language model, performs poorly at answering them. Further, our experiments suggest that a strong mapping and navigation ability would benefit large language models in performing relevant downstream tasks, such as playing textgames. Our MANGO benchmark will facilitate future research on methods that improve the mapping and navigation capabilities of language models. We host our leaderboard, data, code, and evaluation program at https://mango.ttic.edu and https://github.com/oaklight/mango/.

Xiaofeng Liu, Yang Zou, Tong Che et al.

This paper targets the task with discrete and periodic class labels ($e.g.,$ pose/orientation estimation) in the context of deep learning. The commonly used cross-entropy or regression loss is not well matched to this problem as they ignore the periodic nature of the labels and the class similarity, or assume labels are continuous value. We propose to incorporate inter-class correlations in a Wasserstein training framework by pre-defining ($i.e.,$ using arc length of a circle) or adaptively learning the ground metric. We extend the ground metric as a linear, convex or concave increasing function $w.r.t.$ arc length from an optimization perspective. We also propose to construct the conservative target labels which model the inlier and outlier noises using a wrapped unimodal-uniform mixture distribution. Unlike the one-hot setting, the conservative label makes the computation of Wasserstein distance more challenging. We systematically conclude the practical closed-form solution of Wasserstein distance for pose data with either one-hot or conservative target label. We evaluate our method on head, body, vehicle and 3D object pose benchmarks with exhaustive ablation studies. The Wasserstein loss obtaining superior performance over the current methods, especially using convex mapping function for ground metric, conservative label, and closed-form solution.