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In this paper, we investigate the Walk on Spheres algorithm (WoS) for motion planning in robotics. WoS is a Monte Carlo method to solve the Dirichlet problem developed in the 50s by Muller and has recently been repopularized by Sawhney and Crane, who showed its applicability for geometry processing in volumetric domains. This paper provides a first study into the applicability of WoS for robot motion planning in configuration spaces, with potential fields defined as the solution of screened Poisson equations. The experiments in this paper empirically indicate the method's trivial parallelization, its dimension-independent convergence characteristic of $O(1/N)$ in the number of walks, and a validation experiment on the RR platform.

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In this paper, we propose Conceptual Codebook Learning (CoCoLe), a novel fine-tuning method for vision-language models (VLMs) to address the challenge of improving the generalization capability of VLMs while fine-tuning them on downstream tasks in a few-shot setting. We recognize that visual concepts, such as textures, shapes, and colors are naturally transferable across domains and play a crucial role in generalization tasks. Motivated by this interesting finding, we learn a conceptual codebook consisting of visual concepts as keys and conceptual prompts as values, which serves as a link between the image encoder's outputs and the text encoder's inputs. Specifically, for a given image, we leverage the codebook to identify the most relevant conceptual prompts associated with the class embeddings to perform the classification. Additionally, we incorporate a handcrafted concept cache as a regularization to alleviate the overfitting issues in low-shot scenarios. We observe that this conceptual codebook learning method is able to achieve enhanced alignment between visual and linguistic modalities. Extensive experimental results demonstrate that our CoCoLe method remarkably outperforms the existing state-of-the-art methods across various evaluation settings, including base-to-new generalization, cross-dataset evaluation, and domain generalization tasks. Detailed ablation studies further confirm the efficacy of each component in CoCoLe.

In this paper, we present a convergence analysis of the Group Projected Subspace Pursuit (GPSP) algorithm proposed by He et al. [HKL+23] (Group Projected subspace pursuit for IDENTification of variable coefficient differential equations (GP-IDENT), Journal of Computational Physics, 494, 112526) and extend its application to general tasks of block sparse signal recovery. We prove that when the sampling matrix satisfies the Block Restricted Isometry Property (BRIP) with a sufficiently small Block Restricted Isometry Constant (BRIC), GPSP exactly recovers the true block sparse signals. When the observations are noisy, this convergence property of GPSP remains valid if the magnitude of true signal is sufficiently large. GPSP selects the features by subspace projection criterion (SPC) for candidate inclusion and response magnitude criterion (RMC) for candidate exclusion. We compare these criteria with counterparts of other state-of-the-art greedy algorithms. Our theoretical analysis and numerical ablation studies reveal that SPC is critical to the superior performances of GPSP, and that RMC can enhance the robustness of feature identification when observations contain noises. We test and compare GPSP with other methods in diverse settings, including heterogeneous random block matrices, inexact observations, face recognition, and PDE identification. We find that GPSP outperforms the other algorithms in most cases for various levels of block sparsity and block sizes, justifying its effectiveness for general applications.

The chaotic nature of fluid flow and the uncertainties in initial conditions limit predictability. Small errors that occur in the initial condition can grow exponentially until they saturate at $\mathcal{O}$(1). Ensemble forecasting averages multiple runs with slightly different initial conditions and other data to produce more accurate results and extend the predictability horizon. However, they can be computationally expensive. We develop a penalty-based ensemble method with a shared coefficient matrix to reduce required memory and computational cost and thereby allow larger ensemble sizes. Penalty methods relax the incompressibility condition to decouple the pressure and velocity, reducing memory requirements. This report gives stability proof and an error estimate of the penalty-based ensemble method, extends it to the Navier-Stokes equations with random variables using Monte Carlo sampling, and validates the method's accuracy and efficiency with three numerical experiments.

This paper discusses developments for a multi-limb morphogenetic UAV, MorphoGear, that is capable of both aerial flight and ground locomotion. A hybrid path planning algorithm based on A* strategy has been developed enabling seamless transition between air-to-ground navigation modes, thereby enhancing robot's mobility in complex environments. Moreover, precise path following is achieved during ground locomotion with a Model Predictive Control (MPC) architecture for its novel walking behaviour. Experimental validation was conducted in the Unity simulation environment utilizing Python scripts to compute control values. The algorithms' performance is validated by the Root Mean Squared Error (RMSE) of 0.91 cm and a maximum error of 1.85 cm, as demonstrated by the results. These developments highlight the adaptability of MorphoGear in navigation through cluttered environments, establishing it as a usable tool in autonomous exploration, both aerial and ground-based.

After a machine learning model has been deployed into production, its predictive performance needs to be monitored. Ideally, such monitoring can be carried out by comparing the model's predictions against ground truth labels. For this to be possible, the ground truth labels must be available relatively soon after inference. However, there are many use cases where ground truth labels are available only after a significant delay, or in the worst case, not at all. In such cases, directly monitoring the model's predictive performance is impossible. Recently, novel methods for estimating the predictive performance of a model when ground truth is unavailable have been developed. Many of these methods leverage model confidence or other uncertainty estimates and are experimentally compared against a naive baseline method, namely Average Confidence (AC), which estimates model accuracy as the average of confidence scores for a given set of predictions. However, until now the theoretical properties of the AC method have not been properly explored. In this paper, we try to fill this gap by reviewing the AC method and show that under certain general assumptions, it is an unbiased and consistent estimator of model accuracy with many desirable properties. We also compare this baseline estimator against some more complex estimators empirically and show that in many cases the AC method is able to beat the others, although the comparative quality of the different estimators is heavily case-dependent.

Graph Neural Networks (GNNs) are state-of-the-art models for performing prediction tasks on graphs. While existing GNNs have shown great performance on various tasks related to graphs, little attention has been paid to the scenario where out-of-distribution (OOD) nodes exist in the graph during training and inference. Borrowing the concept from CV and NLP, we define OOD nodes as nodes with labels unseen from the training set. Since a lot of networks are automatically constructed by programs, real-world graphs are often noisy and may contain nodes from unknown distributions. In this work, we define the problem of graph learning with out-of-distribution nodes. Specifically, we aim to accomplish two tasks: 1) detect nodes which do not belong to the known distribution and 2) classify the remaining nodes to be one of the known classes. We demonstrate that the connection patterns in graphs are informative for outlier detection, and propose Out-of-Distribution Graph Attention Network (OODGAT), a novel GNN model which explicitly models the interaction between different kinds of nodes and separate inliers from outliers during feature propagation. Extensive experiments show that OODGAT outperforms existing outlier detection methods by a large margin, while being better or comparable in terms of in-distribution classification.

In this paper, we focus on the self-supervised learning of visual correspondence using unlabeled videos in the wild. Our method simultaneously considers intra- and inter-video representation associations for reliable correspondence estimation. The intra-video learning transforms the image contents across frames within a single video via the frame pair-wise affinity. To obtain the discriminative representation for instance-level separation, we go beyond the intra-video analysis and construct the inter-video affinity to facilitate the contrastive transformation across different videos. By forcing the transformation consistency between intra- and inter-video levels, the fine-grained correspondence associations are well preserved and the instance-level feature discrimination is effectively reinforced. Our simple framework outperforms the recent self-supervised correspondence methods on a range of visual tasks including video object tracking (VOT), video object segmentation (VOS), pose keypoint tracking, etc. It is worth mentioning that our method also surpasses the fully-supervised affinity representation (e.g., ResNet) and performs competitively against the recent fully-supervised algorithms designed for the specific tasks (e.g., VOT and VOS).

In Multi-Label Text Classification (MLTC), one sample can belong to more than one class. It is observed that most MLTC tasks, there are dependencies or correlations among labels. Existing methods tend to ignore the relationship among labels. In this paper, a graph attention network-based model is proposed to capture the attentive dependency structure among the labels. The graph attention network uses a feature matrix and a correlation matrix to capture and explore the crucial dependencies between the labels and generate classifiers for the task. The generated classifiers are applied to sentence feature vectors obtained from the text feature extraction network (BiLSTM) to enable end-to-end training. Attention allows the system to assign different weights to neighbor nodes per label, thus allowing it to learn the dependencies among labels implicitly. The results of the proposed model are validated on five real-world MLTC datasets. The proposed model achieves similar or better performance compared to the previous state-of-the-art models.

BERT, a pre-trained Transformer model, has achieved ground-breaking performance on multiple NLP tasks. In this paper, we describe BERTSUM, a simple variant of BERT, for extractive summarization. Our system is the state of the art on the CNN/Dailymail dataset, outperforming the previous best-performed system by 1.65 on ROUGE-L. The codes to reproduce our results are available at //github.com/nlpyang/BertSum

Attention mechanism has been used as an ancillary means to help RNN or CNN. However, the Transformer (Vaswani et al., 2017) recently recorded the state-of-the-art performance in machine translation with a dramatic reduction in training time by solely using attention. Motivated by the Transformer, Directional Self Attention Network (Shen et al., 2017), a fully attention-based sentence encoder, was proposed. It showed good performance with various data by using forward and backward directional information in a sentence. But in their study, not considered at all was the distance between words, an important feature when learning the local dependency to help understand the context of input text. We propose Distance-based Self-Attention Network, which considers the word distance by using a simple distance mask in order to model the local dependency without losing the ability of modeling global dependency which attention has inherent. Our model shows good performance with NLI data, and it records the new state-of-the-art result with SNLI data. Additionally, we show that our model has a strength in long sentences or documents.

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