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This paper presents a simple method to boost the robustness of quadrotors in trajectory tracking. The presented method features a high-gain disturbance observer (HGDO) that provides disturbance estimates in real-time. The estimates are then used in a trajectory control law to compensate for disturbance effects. We present theoretical convergence results showing that the proposed HGDO can quickly converge to an adjustable neighborhood of actual disturbance values. We will then integrate the disturbance estimates with a typical robust trajectory controller, namely sliding mode control (SMC), and present Lyapunov stability analysis to establish the boundedness of trajectory tracking errors. However, our stability analysis can be easily extended to other Lyapunov-based controllers to develop different HGDO-based controllers with formal stability guarantees. We evaluate the proposed HGDO-based control method using both simulation and laboratory experiments in various scenarios and in the presence of external disturbances. Our results indicate that the addition of HGDO to a quadrotor trajectory controller can significantly improve the accuracy and precision of trajectory tracking in the presence of external disturbances.

We prove that training neural networks on 1-D data is equivalent to solving a convex Lasso problem with a fixed, explicitly defined dictionary matrix of features. The specific dictionary depends on the activation and depth. We consider 2-layer networks with piecewise linear activations, deep narrow ReLU networks with up to 4 layers, and rectangular and tree networks with sign activation and arbitrary depth. Interestingly in ReLU networks, a fourth layer creates features that represent reflections of training data about themselves. The Lasso representation sheds insight to globally optimal networks and the solution landscape.

The Segment Anything Model (SAM) has recently emerged as a groundbreaking foundation model for prompt-driven image segmentation tasks. However, both the original SAM and its medical variants require slice-by-slice manual prompting of target structures, which directly increase the burden for applications. Despite attempts of auto-prompting to turn SAM into a fully automatic manner, it still exhibits subpar performance and lacks of reliability especially in the field of medical imaging. In this paper, we propose UR-SAM, an uncertainty rectified SAM framework to enhance the reliability for auto-prompting medical image segmentation. Building upon a localization framework for automatic prompt generation, our method incorporates a prompt augmentation module to obtain a series of input prompts for SAM for uncertainty estimation and an uncertainty-based rectification module to further utilize the distribution of estimated uncertainty to improve the segmentation performance. Extensive experiments on two public 3D medical datasets covering the segmentation of 35 organs demonstrate that without supplementary training or fine-tuning, our method further improves the segmentation performance with up to 10.7 % and 13.8 % in dice similarity coefficient, demonstrating efficiency and broad capabilities for medical image segmentation without manual prompting.

Despite the progress of learning-based methods for 6D object pose estimation, the trade-off between accuracy and scalability for novel objects still exists. Specifically, previous methods for novel objects do not make good use of the target object's 3D shape information since they focus on generalization by processing the shape indirectly, making them less effective. We present GenFlow, an approach that enables both accuracy and generalization to novel objects with the guidance of the target object's shape. Our method predicts optical flow between the rendered image and the observed image and refines the 6D pose iteratively. It boosts the performance by a constraint of the 3D shape and the generalizable geometric knowledge learned from an end-to-end differentiable system. We further improve our model by designing a cascade network architecture to exploit the multi-scale correlations and coarse-to-fine refinement. GenFlow ranked first on the unseen object pose estimation benchmarks in both the RGB and RGB-D cases. It also achieves performance competitive with existing state-of-the-art methods for the seen object pose estimation without any fine-tuning.

An effective technique for obtaining high-quality representations is adding a projection head on top of the encoder during training, then discarding it and using the pre-projection representations. Despite its proven practical effectiveness, the reason behind the success of this technique is poorly understood. The pre-projection representations are not directly optimized by the loss function, raising the question: what makes them better? In this work, we provide a rigorous theoretical answer to this question. We start by examining linear models trained with self-supervised contrastive loss. We reveal that the implicit bias of training algorithms leads to layer-wise progressive feature weighting, where features become increasingly unequal as we go deeper into the layers. Consequently, lower layers tend to have more normalized and less specialized representations. We theoretically characterize scenarios where such representations are more beneficial, highlighting the intricate interplay between data augmentation and input features. Additionally, we demonstrate that introducing non-linearity into the network allows lower layers to learn features that are completely absent in higher layers. Finally, we show how this mechanism improves the robustness in supervised contrastive learning and supervised learning. We empirically validate our results through various experiments on CIFAR-10/100, UrbanCars and shifted versions of ImageNet. We also introduce a potential alternative to projection head, which offers a more interpretable and controllable design.

We present a comparative study between cross-encoder and LLMs rerankers in the context of re-ranking effective SPLADE retrievers. We conduct a large evaluation on TREC Deep Learning datasets and out-of-domain datasets such as BEIR and LoTTE. In the first set of experiments, we show how cross-encoder rerankers are hard to distinguish when it comes to re-rerank SPLADE on MS MARCO. Observations shift in the out-of-domain scenario, where both the type of model and the number of documents to re-rank have an impact on effectiveness. Then, we focus on listwise rerankers based on Large Language Models -- especially GPT-4. While GPT-4 demonstrates impressive (zero-shot) performance, we show that traditional cross-encoders remain very competitive. Overall, our findings aim to to provide a more nuanced perspective on the recent excitement surrounding LLM-based re-rankers -- by positioning them as another factor to consider in balancing effectiveness and efficiency in search systems.

We study dual number symmetric matrices, dual complex Hermitian matrices and dual quaternion Hermitian matrices in a unified frame of dual Hermitian matrices. Suppose we have a ring, which can be the real field, the complex field, or the quaternion ring. Then an $n \times n$ dual Hermitian matrix has $n$ dual number eigenvalues. We define supplement matrices for a dual Hermitian matrix. Supplement matrices are Hermitian matrices in the original ring. The standard parts of the eigenvalues of that dual Hermitian matrix are the eigenvalues of the standard part Hermitian matrix in the original ring, while the dual parts of the eigenvalues of that dual Hermitian matrix are the eigenvalues of those {supplement} matrices. Hence, by apply any practical method for computing eigenvalues of Hermitian matrices in the original ring, we have a practical method for computing eigenvalues of a dual Hermitian matrix. We call this method the supplement matrix method. Applications to low rank approximation and generalized inverses of dual matrices, dual least squares problem and formation control are discussed. Numerical experiments are reported.

Large language models (LLMs) can achieve highly effective performance on various reasoning tasks by incorporating step-by-step chain-of-thought (CoT) prompting as demonstrations. However, the reasoning chains of demonstrations generated by LLMs are prone to errors, which can subsequently lead to incorrect reasoning during inference. Furthermore, inappropriate exemplars (overly simplistic or complex), can affect overall performance among varying levels of difficulty. We introduce Iter-CoT (Iterative bootstrapping in Chain-of-Thoughts Prompting), an iterative bootstrapping approach for selecting exemplars and generating reasoning chains. By utilizing iterative bootstrapping, our approach enables LLMs to autonomously rectify errors, resulting in more precise and comprehensive reasoning chains. Simultaneously, our approach selects challenging yet answerable questions accompanied by reasoning chains as exemplars with a moderate level of difficulty, which enhances the LLMs' generalizability across varying levels of difficulty. Experimental results indicate that Iter-CoT exhibits superiority, achieving competitive performance across three distinct reasoning tasks on ten datasets.

We propose EmoDistill, a novel speech emotion recognition (SER) framework that leverages cross-modal knowledge distillation during training to learn strong linguistic and prosodic representations of emotion from speech. During inference, our method only uses a stream of speech signals to perform unimodal SER thus reducing computation overhead and avoiding run-time transcription and prosodic feature extraction errors. During training, our method distills information at both embedding and logit levels from a pair of pre-trained Prosodic and Linguistic teachers that are fine-tuned for SER. Experiments on the IEMOCAP benchmark demonstrate that our method outperforms other unimodal and multimodal techniques by a considerable margin, and achieves state-of-the-art performance of 77.49% unweighted accuracy and 78.91% weighted accuracy. Detailed ablation studies demonstrate the impact of each component of our method.

The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.