In this paper, a model predictive control (MPC) framework is employed to realize autonomous rendezvous and docking (AR&D) with a tumbling target, using the piecewise affine (PWA) model of the 3-D line-of-sight (LOS) dynamics and Euler attitude dynamics. Consider the error between the predictions obtained by the approximate linear model and the actual states of nonlinear dynamics, a sampling-based PWA MPC is proposed to sample the predictions in the closer neighborhood of the actual states. Besides, novel constructions of constraints are presented to reduce the on-board computation cost and time-delay. Furthermore, a singularity-free strategy is provided to realize crossing the singularity of angle states smoothly. Then, the mission is achieved by continuous 6-DOF pose (position and attitude) tracking of the target's docking port, with the coupling between the position and attitude of the target's docking port is taken into account. Finally, numerical results are presented to demonstrate the above theories.
Model uncertainty has been one prominent issue both in the theory of risk measures and in practice such as financial risk management and regulation. Motivated by this observation, in this paper, we take a new perspective to describe the model uncertainty, and thus propose a new class of risk measures under model uncertainty. More precisely, we use an auxiliary random variable to describe the model uncertainty. We first establish a conditional distortion risk measure under an auxiliary random variable. Then we axiomatically characterize it by proposing a set of new axioms. Moreover, its coherence and dual representation are investigated. Finally, we make comparisons with some known risk measures such as weighted value at risk (WVaR), range value at risk (RVaR) and $\sQ-$ mixture of ES. One advantage of our modeling is in its flexibility, as the auxiliary random variable can describe various contexts including model uncertainty. To illustrate the proposed framework, we also deduce new risk measures in the presence of background risk.This paper provides some theoretical results about risk measures under model uncertainty, being expected to make meaningful complement to the study of risk measures under model uncertainty.
In the prospect theory, value function is typically concave for gains, commonly convex for losses, with losses usually having a steeper slope than gains. The neural system largely differs from the loss and gains sides. Five new studies on neurons related to this issue have examined neuronal responses to losses, gains, and reference points. This study investigates a new concept of the value function. A value function with a neuronal cusp may show variations and behavior cusps with catastrophe where a trader closes one's position.
In soccer games, the goalkeeper's performance is an important factor to the success of the whole team. Despite the goalkeeper's importance, little attention has been paid to their performance in events and tracking data. Here, we developed a model to predict which movements would be most effective for shot-stopping and compare it to the real-life behavior of goalkeepers. This model evaluates the performance of goalkeepers based on their position and dive radius. We found that contrary to the movements that were considered most effective by our model, real-life goalkeepers' movements were more diverse. We further used our model to develop a tool to analyse goalkeepers' behavior in real-life soccer games. In addition, a simulator function allows team analysts or couches to identify situations that allow further improvement of the reaction of the goalkeeper.
We propose an end-to-end solution to address the problem of object localisation in partial scenes, where we aim to estimate the position of an object in an unknown area given only a partial 3D scan of the scene. We propose a novel scene representation to facilitate the geometric reasoning, Directed Spatial Commonsense Graph (D-SCG), a spatial scene graph that is enriched with additional concept nodes from a commonsense knowledge base. Specifically, the nodes of D-SCG represent the scene objects and the edges are their relative positions. Each object node is then connected via different commonsense relationships to a set of concept nodes. With the proposed graph-based scene representation, we estimate the unknown position of the target object using a Graph Neural Network that implements a novel attentional message passing mechanism. The network first predicts the relative positions between the target object and each visible object by learning a rich representation of the objects via aggregating both the object nodes and the concept nodes in D-SCG. These relative positions then are merged to obtain the final position. We evaluate our method using Partial ScanNet, improving the state-of-the-art by 5.9% in terms of the localisation accuracy at a 8x faster training speed.
Rejecting correspondence outliers enables to boost the correspondence quality, which is a critical step in achieving high point cloud registration accuracy. The current state-of-the-art correspondence outlier rejection methods only utilize the structure features of the correspondences. However, texture information is critical to reject the correspondence outliers in our human vision system. In this paper, we propose General Multimodal Fusion (GMF) to learn to reject the correspondence outliers by leveraging both the structure and texture information. Specifically, two cross-attention-based fusion layers are proposed to fuse the texture information from paired images and structure information from point correspondences. Moreover, we propose a convolutional position encoding layer to enhance the difference between Tokens and enable the encoding feature pay attention to neighbor information. Our position encoding layer will make the cross-attention operation integrate both local and global information. Experiments on multiple datasets(3DMatch, 3DLoMatch, KITTI) and recent state-of-the-art models (3DRegNet, DGR, PointDSC) prove that our GMF achieves wide generalization ability and consistently improves the point cloud registration accuracy. Furthermore, several ablation studies demonstrate the robustness of the proposed GMF on different loss functions, lighting conditions and noises.The code is available at https://github.com/XiaoshuiHuang/GMF.
Data-efficient learning on graphs (GEL) is essential in real-world applications. Existing GEL methods focus on learning useful representations for nodes, edges, or entire graphs with ``small'' labeled data. But the problem of data-efficient learning for subgraph prediction has not been explored. The challenges of this problem lie in the following aspects: 1) It is crucial for subgraphs to learn positional features to acquire structural information in the base graph in which they exist. Although the existing subgraph neural network method is capable of learning disentangled position encodings, the overall computational complexity is very high. 2) Prevailing graph augmentation methods for GEL, including rule-based, sample-based, adaptive, and automated methods, are not suitable for augmenting subgraphs because a subgraph contains fewer nodes but richer information such as position, neighbor, and structure. Subgraph augmentation is more susceptible to undesirable perturbations. 3) Only a small number of nodes in the base graph are contained in subgraphs, which leads to a potential ``bias'' problem that the subgraph representation learning is dominated by these ``hot'' nodes. By contrast, the remaining nodes fail to be fully learned, which reduces the generalization ability of subgraph representation learning. In this paper, we aim to address the challenges above and propose a Position-Aware Data-Efficient Learning framework for subgraph neural networks called PADEL. Specifically, we propose a novel node position encoding method that is anchor-free, and design a new generative subgraph augmentation method based on a diffused variational subgraph autoencoder, and we propose exploratory and exploitable views for subgraph contrastive learning. Extensive experiment results on three real-world datasets show the superiority of our proposed method over state-of-the-art baselines.
Greedy sparse recovery has become a popular tool in many applications, although its complexity is still prohibitive when large sparsifying dictionaries or sensing matrices have to be exploited. In this paper, we formulate first a new class of sparse recovery problems that exploit multidimensional dictionaries and the separability of the measurement matrices that appear in certain problems. Then we develop a new algorithm, Separable Multidimensional Orthogonal Matching Pursuit (SMOMP), which can solve this class of problems with low complexity. Finally, we apply SMOMP to the problem of joint localization and communication at mmWave, and numerically show its effectiveness to provide, at a reasonable complexity, high accuracy channel and position estimations.
Online retailers and platforms typically present alternatives using ranked product lists. By adjusting the ranking, these platforms influence consumers' choices and, in turn, conversions, platform revenues, and consumer welfare. In this paper, I study the trade-offs between ranking algorithms that target these different objectives. First, I highlight and provide reduced-form evidence for a key factor shaping these trade-offs: cross-product heterogeneity in position effects. To quantify the effects of different rankings, I then develop an empirical framework based on the search and discovery model of Greminger (2022). For this framework, I show that the ranking that maximizes conversions also maximizes consumer welfare, implying no trade-off between these two objectives. Moreover, I develop and test a heuristic ranking algorithm to maximize revenues. Finally, I estimate the model and compare the effects of the rankings developed for the different objectives. The results highlight the effectiveness of the different rankings and reveal that the proposed heuristic to maximize revenues also increases consumer welfare, suggesting that the trade-off between revenue maximization and consumer welfare also is limited.
In this paper, we present our approach and empirical observations for Cause-Effect Signal Span Detection -- Subtask 2 of Shared task 3~\cite{tan-etal-2022-event} at CASE 2022. The shared task aims to extract the cause, effect, and signal spans from a given causal sentence. We model the task as a reading comprehension (RC) problem and apply a token-level RC-based span prediction paradigm to the task as the baseline. We explore different training objectives to fine-tune the model, as well as data augmentation (DA) tricks based on the language model (LM) for performance improvement. Additionally, we propose an efficient beam-search post-processing strategy to due with the drawbacks of span detection to obtain a further performance gain. Our approach achieves an average $F_1$ score of 54.15 and ranks \textbf{$1^{st}$} in the CASE competition. Our code is available at \url{https://github.com/Gzhang-umich/1CademyTeamOfCASE}.
Recently, self-attention (SA) structures became popular in computer vision fields. They have locally independent filters and can use large kernels, which contradicts the previously popular convolutional neural networks (CNNs). CNNs success was attributed to the hard-coded inductive biases of locality and spatial invariance. However, recent studies have shown that inductive biases in CNNs are too restrictive. On the other hand, the relative position encodings, similar to depthwise (DW) convolution, are necessary for the local SA networks, which indicates that the SA structures are not entirely spatially variant. Hence, we would like to determine which part of inductive biases contributes to the success of the local SA structures. To do so, we introduced context-aware decomposed attention (CADA), which decomposes attention maps into multiple trainable base kernels and accumulates them using context-aware (CA) parameters. This way, we could identify the link between the CNNs and SA networks. We conducted ablation studies using the ResNet50 applied to the ImageNet classification task. DW convolution could have a large locality without increasing computational costs compared to CNNs, but the accuracy saturates with larger kernels. CADA follows this characteristic of locality. We showed that context awareness was the crucial property; however, large local information was not necessary to construct CA parameters. Even though no spatial invariance makes training difficult, more relaxed spatial invariance gave better accuracy than strict spatial invariance. Also, additional strong spatial invariance through relative position encoding was preferable. We extended these experiments to filters for downsampling and showed that locality bias is more critical for downsampling but can remove the strong locality bias using relaxed spatial invariance.
Transformers have demonstrated a competitive performance across a wide range of vision tasks, while it is very expensive to compute the global self-attention. Many methods limit the range of attention within a local window to reduce computation complexity. However, their approaches cannot save the number of parameters; meanwhile, the self-attention and inner position bias (inside the softmax function) cause each query to focus on similar and close patches. Consequently, this paper presents a light self-limited-attention (LSLA) consisting of a light self-attention mechanism (LSA) to save the computation cost and the number of parameters, and a self-limited-attention mechanism (SLA) to improve the performance. Firstly, the LSA replaces the K (Key) and V (Value) of self-attention with the X(origin input). Applying it in vision Transformers which have encoder architecture and self-attention mechanism, can simplify the computation. Secondly, the SLA has a positional information module and a limited-attention module. The former contains a dynamic scale and an inner position bias to adjust the distribution of the self-attention scores and enhance the positional information. The latter uses an outer position bias after the softmax function to limit some large values of attention weights. Finally, a hierarchical Vision Transformer with Light self-Limited-attention (ViT-LSLA) is presented. The experiments show that ViT-LSLA achieves 71.6% top-1 accuracy on IP102 (2.4% absolute improvement of Swin-T); 87.2% top-1 accuracy on Mini-ImageNet (3.7% absolute improvement of Swin-T). Furthermore, it greatly reduces FLOPs (3.5GFLOPs vs. 4.5GFLOPs of Swin-T) and parameters (18.9M vs. 27.6M of Swin-T).
Implant prosthesis is the most appropriate treatment for dentition defect or dentition loss, which usually involves a surgical guide design process to decide the implant position. However, such design heavily relies on the subjective experiences of dentists. In this paper, a transformer-based Implant Position Regression Network, ImplantFormer, is proposed to automatically predict the implant position based on the oral CBCT data. We creatively propose to predict the implant position using the 2D axial view of the tooth crown area and fit a centerline of the implant to obtain the actual implant position at the tooth root. Convolutional stem and decoder are designed to coarsely extract image features before the operation of patch embedding and integrate multi-level feature maps for robust prediction, respectively. As both long-range relationship and local features are involved, our approach can better represent global information and achieves better location performance. Extensive experiments on a dental implant dataset through five-fold cross-validation demonstrated that the proposed ImplantFormer achieves superior performance than existing methods.
In conventional multichannel audio signal enhancement, spatial and spectral filtering are often performed sequentially. In contrast, it has been shown that for neural spatial filtering a joint approach of spectro-spatial filtering is more beneficial. In this contribution, we investigate the spatial filtering performed by such a time-varying spectro-spatial filter. We extend the recently proposed complex-valued spatial autoencoder (COSPA) for the task of target speaker extraction by leveraging its interpretable structure and purposefully informing the network of the target speaker's position. We show that the resulting informed COSPA (iCOSPA) effectively and flexibly extracts a target speaker from a mixture of speakers. We also find that the proposed architecture is well capable of learning pronounced spatial selectivity patterns and show that the results depend significantly on the training target and the reference signal when computing various evaluation metrics.
Extractive question answering (QA) models tend to exploit spurious correlations to make predictions when a training set has unintended biases. This tendency results in models not being generalizable to examples where the correlations do not hold. Determining the spurious correlations QA models can exploit is crucial in building generalizable QA models in real-world applications; moreover, a method needs to be developed that prevents these models from learning the spurious correlations even when a training set is biased. In this study, we discovered that the relative position of an answer, which is defined as the relative distance from an answer span to the closest question-context overlap word, can be exploited by QA models as superficial cues for making predictions. Specifically, we find that when the relative positions in a training set are biased, the performance on examples with relative positions unseen during training is significantly degraded. To mitigate the performance degradation for unseen relative positions, we propose an ensemble-based debiasing method that does not require prior knowledge about the distribution of relative positions. We demonstrate that the proposed method mitigates the models' reliance on relative positions using the biased and full SQuAD dataset. We hope that this study can help enhance the generalization ability of QA models in real-world applications.
Inference is a significant part of ML software infrastructure. Despite the variety of inference frameworks available, the field as a whole can be considered in its early days. This position paper puts forth a range of important qualities that next generation of inference platforms should be aiming for. We present our rationale for the importance of each quality, and discuss ways to achieve it in practice. We propose to focus on data-centricity as the overarching design pattern which enables smarter ML system deployment and operation at scale.
Recent data- and learning-based sound source localization (SSL) methods have shown strong performance in challenging acoustic scenarios. However, little work has been done on adapting such methods to track consistently multiple sources appearing and disappearing, as would occur in reality. In this paper, we present a new training strategy for deep learning SSL models with a straightforward implementation based on the mean squared error of the optimal association between estimated and reference positions in the preceding time frames. It optimizes the desired properties of a tracking system: handling a time-varying number of sources and ordering localization estimates according to their trajectories, minimizing identity switches (IDSs). Evaluation on simulated data of multiple reverberant moving sources and on two model architectures proves its effectiveness on reducing identity switches without compromising frame-wise localization accuracy.
Bruch's membrane (BM) segmentation on optical coherence tomography (OCT) is a pivotal step for the diagnosis and follow-up of age-related macular degeneration (AMD), one of the leading causes of blindness in the developed world. Automated BM segmentation methods exist, but they usually do not account for the anatomical coherence of the results, neither provide feedback on the confidence of the prediction. These factors limit the applicability of these systems in real-world scenarios. With this in mind, we propose an end-to-end deep learning method for automated BM segmentation in AMD patients. An Attention U-Net is trained to output a probability density function of the BM position, while taking into account the natural curvature of the surface. Besides the surface position, the method also estimates an A-scan wise uncertainty measure of the segmentation output. Subsequently, the A-scans with high uncertainty are interpolated using thin plate splines (TPS). We tested our method with ablation studies on an internal dataset with 138 patients covering all three AMD stages, and achieved a mean absolute localization error of 4.10 um. In addition, the proposed segmentation method was compared against the state-of-the-art methods and showed a superior performance on an external publicly available dataset from a different patient cohort and OCT device, demonstrating strong generalization ability.
The authors present a novel face tracking approach where optical flow information is incorporated into a modified version of the Viola Jones detection algorithm. In the original algorithm, detection is static, as information from previous frames is not considered. In addition, candidate windows have to pass all stages of the classification cascade, otherwise they are discarded as containing no face. In contrast, the proposed tracker preserves information about the number of classification stages passed by each window. Such information is used to build a likelihood map, which represents the probability of having a face located at that position. Tracking capabilities are provided by extrapolating the position of the likelihood map to the next frame by optical flow computation. The proposed algorithm works in real time on a standard laptop. The system is verified on the Boston Head Tracking Database, showing that the proposed algorithm outperforms the standard Viola Jones detector in terms of detection rate and stability of the output bounding box, as well as including the capability to deal with occlusions. The authors also evaluate two recently published face detectors based on convolutional networks and deformable part models with their algorithm showing a comparable accuracy at a fraction of the computation time.
Transformer language models encode the notion of word order using positional information. Most commonly, this positional information is represented by absolute position embeddings (APEs), that are learned from the pretraining data. However, in natural language, it is not absolute position that matters, but relative position, and the extent to which APEs can capture this type of information has not been investigated. In this work, we observe that models trained with APE over-rely on positional information to the point that they break-down when subjected to sentences with shifted position information. Specifically, when models are subjected to sentences starting from a non-zero position (excluding the effect of priming), they exhibit noticeably degraded performance on zero to full-shot tasks, across a range of model families and model sizes. Our findings raise questions about the efficacy of APEs to model the relativity of position information, and invite further introspection on the sentence and word order processing strategies employed by these models.