In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures, finitely additive probability measures, plausibilty measures (and their duals, belief functions), and possibility measures. We give axioms and inference rules for the associated system of coalgebraic modal logic, and construct the canonical coalgebras to prove a completeness result.
Compared to minutia-based fingerprint representations, fixed-length representations are attractive due to simple and efficient matching. However, fixed-length fingerprint representations are limited in accuracy when matching fingerprints with different visible areas, which can occur due to different finger poses or acquisition methods. To address this issue, we propose a localized deep representation of fingerprint, named LDRF. By focusing on the discriminative characteristics within local regions, LDRF provides a more robust and accurate fixed-length representation for fingerprints with variable visible areas. LDRF can be adapted to retain information within any valid area, making it highly flexible. The matching scores produced by LDRF also exhibit intuitive statistical characteristics, which led us to propose a matching score normalization technique to mitigate the uncertainty in the cases of very small overlapping area. With this new technique, we can maintain a high level of accuracy and reliability in our fingerprint matching, even as the size of the database grows rapidly. Our experimental results on 21 datasets containing over 140K fingerprints of various finger poses and impression types show that LDRF outperforms other fixed-length representations and is robust to sensing technologies and impression types. Besides, the proposed matching score normalization effectively reduces the false match rate (FMR) in large-scale identification experiments comprising over 5.11 million fingerprints. Specifically, this technique results in a reduction of two orders of magnitude compared to matching without matching score normalization and five orders of magnitude compared to prior works.
In this study, we propose a multitask reinforcement learning algorithm for foundational policy acquisition to generate novel motor skills. Inspired by human sensorimotor adaptation mechanisms, we aim to train encoder-decoder networks that can be commonly used to learn novel motor skills in a single movement category. To train the policy network, we develop the multitask reinforcement learning method, where the policy needs to cope with changes in goals or environments with different reward functions or physical parameters of the environment in dynamic movement generation tasks. Here, as a concrete task, we evaluated the proposed method with the ball heading task using a monopod robot model. The results showed that the proposed method could adapt to novel target positions or inexperienced ball restitution coefficients. Furthermore, we demonstrated that the acquired foundational policy network originally learned for heading motion, can be used to generate an entirely new overhead kicking skill.
Aggregated HPC resources have rigid allocation systems and programming models which struggle to adapt to diverse and changing workloads. Consequently, HPC systems fail to efficiently use the large pools of unused memory and increase the utilization of idle computing resources. Prior work attempted to increase the throughput and efficiency of supercomputing systems through workload co-location and resource disaggregation. However, these methods fall short of providing a solution that can be applied to existing systems without major hardware modifications and performance losses. In this paper, we improve the utilization of supercomputers by employing the new cloud paradigm of serverless computing. We show how serverless functions provide fine-grained access to the resources of batch-managed cluster nodes. We present an HPC-oriented Function-as-a-Service (FaaS) that satisfies the requirements of high-performance applications. We demonstrate a software resource disaggregation approach where placing functions on unallocated and underutilized nodes allows idle cores and accelerators to be utilized while retaining near-native performance.
In this paper, we present a novel approach that combines deep metric learning and synthetic data generation using diffusion models for out-of-distribution (OOD) detection. One popular approach for OOD detection is outlier exposure, where models are trained using a mixture of in-distribution (ID) samples and ``seen" OOD samples. For the OOD samples, the model is trained to minimize the KL divergence between the output probability and the uniform distribution while correctly classifying the in-distribution (ID) data. In this paper, we propose a label-mixup approach to generate synthetic OOD data using Denoising Diffusion Probabilistic Models (DDPMs). Additionally, we explore recent advancements in metric learning to train our models. In the experiments, we found that metric learning-based loss functions perform better than the softmax. Furthermore, the baseline models (including softmax, and metric learning) show a significant improvement when trained with the generated OOD data. Our approach outperforms strong baselines in conventional OOD detection metrics.
In this paper, we present some enhanced error estimates for augmented subspace methods with the nonconforming Crouzeix-Raviart (CR) element. Before the novel estimates, we derive the explicit error estimates for the case of single eigenpair and multiple eigenpairs based on our defined spectral projection operators, respectively. Then we first strictly prove that the CR element based augmented subspace method exhibits the second-order convergence rate between the two steps of the augmented subspace iteration, which coincides with the practical experimental results. The algebraic error estimates of second order for the augmented subspace method explicitly elucidate the dependence of the convergence rate of the algebraic error on the coarse space, which provides new insights into the performance of the augmented subspace method. Numerical experiments are finally supplied to verify these new estimate results and the efficiency of our algorithms.
In this paper, a parallel symmetric eigensolver with very small matrices in massively parallel processing is considered. We define very small matrices that fit the sizes of caches per node in a supercomputer. We assume that the sizes also fit the exa-scale computing requirements of current production runs of an application. To minimize communication time, we added several communication avoiding and communication reducing algorithms based on Message Passing Interface (MPI) non-blocking implementations. A performance evaluation with up to full nodes of the FX10 system indicates that (1) the MPI non-blocking implementation is 3x as efficient as the baseline implementation, (2) the hybrid MPI execution is 1.9x faster than the pure MPI execution, (3) our proposed solver is 2.3x and 22x faster than a ScaLAPACK routine with optimized blocking size and cyclic-cyclic distribution, respectively.
Developing theoretical guarantees on the sample complexity of offline RL methods is an important step towards making data-hungry RL algorithms practically viable. Currently, most results hinge on unrealistic assumptions about the data distribution -- namely that it comprises a set of i.i.d. trajectories collected by a single logging policy. We consider a more general setting where the dataset may have been gathered adaptively. We develop theory for the TMIS Offline Policy Evaluation (OPE) estimator in this generalized setting for tabular MDPs, deriving high-probability, instance-dependent bounds on its estimation error. We also recover minimax-optimal offline learning in the adaptive setting. Finally, we conduct simulations to empirically analyze the behavior of these estimators under adaptive and non-adaptive regimes.
In this paper, we tackle two challenges in multimodal learning for visual recognition: 1) when missing-modality occurs either during training or testing in real-world situations; and 2) when the computation resources are not available to finetune on heavy transformer models. To this end, we propose to utilize prompt learning and mitigate the above two challenges together. Specifically, our modality-missing-aware prompts can be plugged into multimodal transformers to handle general missing-modality cases, while only requiring less than 1% learnable parameters compared to training the entire model. We further explore the effect of different prompt configurations and analyze the robustness to missing modality. Extensive experiments are conducted to show the effectiveness of our prompt learning framework that improves the performance under various missing-modality cases, while alleviating the requirement of heavy model re-training. Code is available.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.