$ $Deriving a robot's equation of motion typically requires placing multiple coordinate frames, commonly using the Denavit-Hartenberg convention to express the kinematic and dynamic relationships between segments. This paper presents an alternative using the differential geometric method of Exponential Maps, which reduces the number of coordinate frame choices to two. The traditional and differential geometric methods are compared, and the conceptual and practical differences are detailed. The open-source software, Exp[licit], based on the differential geometric method, is introduced. It is intended for use by researchers and engineers with basic knowledge of geometry and robotics. Code snippets and an example application are provided to demonstrate the benefits of the differential geometric method and assist users to get started with the software.
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Fine-grained open-set recognition (FineOSR) aims to recognize images belonging to classes with subtle appearance differences while rejecting images of unknown classes. A recent trend in OSR shows the benefit of generative models to discriminative unknown detection. As a type of generative model, energy-based models (EBM) are the potential for hybrid modeling of generative and discriminative tasks. However, most existing EBMs suffer from density estimation in high-dimensional space, which is critical to recognizing images from fine-grained classes. In this paper, we explore the low-dimensional latent space with energy-based prior distribution for OSR in a fine-grained visual world. Specifically, based on the latent space EBM, we propose an attribute-aware information bottleneck (AIB), a residual attribute feature aggregation (RAFA) module, and an uncertainty-based virtual outlier synthesis (UVOS) module to improve the expressivity, granularity, and density of the samples in fine-grained classes, respectively. Our method is flexible to take advantage of recent vision transformers for powerful visual classification and generation. The method is validated on both fine-grained and general visual classification datasets while preserving the capability of generating photo-realistic fake images with high resolution.
Neural ordinary differential equations (ODEs) are widely recognized as the standard for modeling physical mechanisms, which help to perform approximate inference in unknown physical or biological environments. In partially observable (PO) environments, how to infer unseen information from raw observations puzzled the agents. By using a recurrent policy with a compact context, context-based reinforcement learning provides a flexible way to extract unobservable information from historical transitions. To help the agent extract more dynamics-related information, we present a novel ODE-based recurrent model combines with model-free reinforcement learning (RL) framework to solve partially observable Markov decision processes (POMDPs). We experimentally demonstrate the efficacy of our methods across various PO continuous control and meta-RL tasks. Furthermore, our experiments illustrate that our method is robust against irregular observations, owing to the ability of ODEs to model irregularly-sampled time series.
Multi-marginal Optimal Transport (mOT), a generalization of OT, aims at minimizing the integral of a cost function with respect to a distribution with some prescribed marginals. In this paper, we consider an entropic version of mOT with a tree-structured quadratic cost, i.e., a function that can be written as a sum of pairwise cost functions between the nodes of a tree. To address this problem, we develop Tree-based Diffusion Schr\"odinger Bridge (TreeDSB), an extension of the Diffusion Schr\"odinger Bridge (DSB) algorithm. TreeDSB corresponds to a dynamic and continuous state-space counterpart of the multimarginal Sinkhorn algorithm. A notable use case of our methodology is to compute Wasserstein barycenters which can be recast as the solution of a mOT problem on a star-shaped tree. We demonstrate that our methodology can be applied in high-dimensional settings such as image interpolation and Bayesian fusion.
We extend the concept of self-consistency for the Fokker-Planck equation (FPE) to the more general McKean-Vlasov equation (MVE). While FPE describes the macroscopic behavior of particles under drift and diffusion, MVE accounts for the additional inter-particle interactions, which are often highly singular in physical systems. Two important examples considered in this paper are the MVE with Coulomb interactions and the vorticity formulation of the 2D Navier-Stokes equation. We show that a generalized self-consistency potential controls the KL-divergence between a hypothesis solution to the ground truth, through entropy dissipation. Built on this result, we propose to solve the MVEs by minimizing this potential function, while utilizing the neural networks for function approximation. We validate the empirical performance of our approach by comparing with state-of-the-art NN-based PDE solvers on several example problems.
It is a long-term vision for Autonomous Driving (AD) community that the perception models can learn from a large-scale point cloud dataset, to obtain unified representations that can achieve promising results on different tasks or benchmarks. Previous works mainly focus on the self-supervised pre-training pipeline, meaning that they perform the pre-training and fine-tuning on the same benchmark, which is difficult to attain the performance scalability and cross-dataset application for the pre-training checkpoint. In this paper, for the first time, we are committed to building a large-scale pre-training point-cloud dataset with diverse data distribution, and meanwhile learning generalizable representations from such a diverse pre-training dataset. We formulate the point-cloud pre-training task as a semi-supervised problem, which leverages the few-shot labeled and massive unlabeled point-cloud data to generate the unified backbone representations that can be directly applied to many baseline models and benchmarks, decoupling the AD-related pre-training process and downstream fine-tuning task. During the period of backbone pre-training, by enhancing the scene- and instance-level distribution diversity and exploiting the backbone's ability to learn from unknown instances, we achieve significant performance gains on a series of downstream perception benchmarks including Waymo, nuScenes, and KITTI, under different baseline models like PV-RCNN++, SECOND, CenterPoint.
Vanilla spiking neurons in Spiking Neural Networks (SNNs) use charge-fire-reset neuronal dynamics, which can only be simulated serially and can hardly learn long-time dependencies. We find that when removing reset, the neuronal dynamics can be reformulated in a non-iterative form and parallelized. By rewriting neuronal dynamics without reset to a general formulation, we propose the Parallel Spiking Neuron (PSN), which generates hidden states that are independent of their predecessors, resulting in parallelizable neuronal dynamics and extremely high simulation speed. The weights of inputs in the PSN are fully connected, which maximizes the utilization of temporal information. To avoid the use of future inputs for step-by-step inference, the weights of the PSN can be masked, resulting in the masked PSN. By sharing weights across time-steps based on the masked PSN, the sliding PSN is proposed to handle sequences of varying lengths. We evaluate the PSN family on simulation speed and temporal/static data classification, and the results show the overwhelming advantage of the PSN family in efficiency and accuracy. To the best of our knowledge, this is the first study about parallelizing spiking neurons and can be a cornerstone for the spiking deep learning research. Our codes are available at \url{//github.com/fangwei123456/Parallel-Spiking-Neuron}.
Zero-shot Learning (ZSL), which aims to predict for those classes that have never appeared in the training data, has arisen hot research interests. The key of implementing ZSL is to leverage the prior knowledge of classes which builds the semantic relationship between classes and enables the transfer of the learned models (e.g., features) from training classes (i.e., seen classes) to unseen classes. However, the priors adopted by the existing methods are relatively limited with incomplete semantics. In this paper, we explore richer and more competitive prior knowledge to model the inter-class relationship for ZSL via ontology-based knowledge representation and semantic embedding. Meanwhile, to address the data imbalance between seen classes and unseen classes, we developed a generative ZSL framework with Generative Adversarial Networks (GANs). Our main findings include: (i) an ontology-enhanced ZSL framework that can be applied to different domains, such as image classification (IMGC) and knowledge graph completion (KGC); (ii) a comprehensive evaluation with multiple zero-shot datasets from different domains, where our method often achieves better performance than the state-of-the-art models. In particular, on four representative ZSL baselines of IMGC, the ontology-based class semantics outperform the previous priors e.g., the word embeddings of classes by an average of 12.4 accuracy points in the standard ZSL across two example datasets (see Figure 4).
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.
Due to their inherent capability in semantic alignment of aspects and their context words, attention mechanism and Convolutional Neural Networks (CNNs) are widely applied for aspect-based sentiment classification. However, these models lack a mechanism to account for relevant syntactical constraints and long-range word dependencies, and hence may mistakenly recognize syntactically irrelevant contextual words as clues for judging aspect sentiment. To tackle this problem, we propose to build a Graph Convolutional Network (GCN) over the dependency tree of a sentence to exploit syntactical information and word dependencies. Based on it, a novel aspect-specific sentiment classification framework is raised. Experiments on three benchmarking collections illustrate that our proposed model has comparable effectiveness to a range of state-of-the-art models, and further demonstrate that both syntactical information and long-range word dependencies are properly captured by the graph convolution structure.
Recently, ensemble has been applied to deep metric learning to yield state-of-the-art results. Deep metric learning aims to learn deep neural networks for feature embeddings, distances of which satisfy given constraint. In deep metric learning, ensemble takes average of distances learned by multiple learners. As one important aspect of ensemble, the learners should be diverse in their feature embeddings. To this end, we propose an attention-based ensemble, which uses multiple attention masks, so that each learner can attend to different parts of the object. We also propose a divergence loss, which encourages diversity among the learners. The proposed method is applied to the standard benchmarks of deep metric learning and experimental results show that it outperforms the state-of-the-art methods by a significant margin on image retrieval tasks.
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