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In this preliminary study, we provide two methods for estimating the gradients of functions of real value. Both methods are built on derivative estimations that are calculated using the standard method or the Squire-Trapp method for any given direction. Gradients are computed as the average of derivatives in uniformly sampled directions. The first method uses a uniformly distributed set of axes that consists of orthogonal unit vectors that span the space. The second method only uses a uniformly distributed set of unit vectors. Both methods essentially minimize the error through an average of estimations to cancel error terms. Both methods are essentially a conceptual generalization of the method used to estimate normal fractal surfaces.

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Memory bandwidth is known to be a performance bottleneck for FPGA accelerators, especially when they deal with large multi-dimensional data-sets. A large body of work focuses on reducing of off-chip transfers, but few authors try to improve the efficiency of transfers. This paper addresses the later issue by proposing (i) a compiler-based approach to accelerator's data layout to maximize contiguous access to off-chip memory, and (ii) data packing and runtime compression techniques that take advantage of this layout to further improve memory performance. We show that our approach can decrease the I/O cycles up to $7\times$ compared to un-optimized memory accesses.

Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn a conjecture with missing assumptions and with an under-specified goal into a proper theorem. Also, the proposed framework can help in completing a proof sketch into a human-readable and machine-checkable proof. Our approach is focused on synthetic geometry, and uses coherent logic and constraint solving. The proposed approach is uniform for all three kinds of tasks, flexible and, to our knowledge, unique such approach.

Computational complexity is a key limitation of genomic analyses. Thus, over the last 30 years, researchers have proposed numerous fast heuristic methods that provide computational relief. Comparing genomic sequences is one of the most fundamental computational steps in most genomic analyses. Due to its high computational complexity, optimized exact and heuristic algorithms are still being developed. We find that these methods are highly sensitive to the underlying data, its quality, and various hyperparameters. Despite their wide use, no in-depth analysis has been performed, potentially falsely discarding genetic sequences from further analysis and unnecessarily inflating computational costs. We provide the first analysis and benchmark of this heterogeneity. We deliver an actionable overview of the 11 most widely used state-of-the-art methods for comparing genomic sequences. We also inform readers about their advantages and downsides using thorough experimental evaluation and different real datasets from all major manufacturers (i.e., Illumina, ONT, and PacBio). SequenceLab is publicly available at //github.com/CMU-SAFARI/SequenceLab.

Interactive systems that facilitate exposure to examples can augment problem solving performance. However designers of such systems are often faced with many practical design decisions about how users will interact with examples, with little clear theoretical guidance. To understand how example interaction design choices affect whether/how people benefit from examples, we conducted an experiment where 182 participants worked on a controlled analog to an exploratory creativity task, with access to examples of varying diversity and presentation interfaces. Task performance was worse when examples were presented in a list, compared to contextualized in the exploration space or shown in a dropdown list. Example lists were associated with more fixation, whereas contextualized examples were associated with using examples to formulate a model of the problem space to guide exploration. We discuss implications of these results for a theoretical framework that maps design choices to fundamental psychological mechanisms of creative inspiration from examples.

Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence analysis of fractional gradient descent is currently limited both in the methods analyzed and the settings analyzed. This paper aims to fill in these gaps by analyzing variations of fractional gradient descent in smooth and convex, smooth and strongly convex, and smooth and non-convex settings. First, novel bounds will be established bridging fractional and integer derivatives. Then, these bounds will be applied to the aforementioned settings to prove linear convergence for smooth and strongly convex functions and $O(1/T)$ convergence for smooth and convex functions. Additionally, we prove $O(1/T)$ convergence for smooth and non-convex functions using an extended notion of smoothness - H\"older smoothness - that is more natural for fractional derivatives. Finally, empirical results will be presented on the potential speed up of fractional gradient descent over standard gradient descent as well as the challenges of predicting which will be faster in general.

Adversarial attacks on learning-based trajectory predictors have already been demonstrated. However, there are still open questions about the effects of perturbations on trajectory predictor inputs other than state histories, and how these attacks impact downstream planning and control. In this paper, we conduct a sensitivity analysis on two trajectory prediction models, Trajectron++ and AgentFormer. We observe that between all inputs, almost all of the perturbation sensitivities for Trajectron++ lie only within the most recent state history time point, while perturbation sensitivities for AgentFormer are spread across state histories over time. We additionally demonstrate that, despite dominant sensitivity on state history perturbations, an undetectable image map perturbation made with the Fast Gradient Sign Method can induce large prediction error increases in both models. Even though image maps may contribute slightly to the prediction output of both models, this result reveals that rather than being robust to adversarial image perturbations, trajectory predictors are susceptible to image attacks. Using an optimization-based planner and example perturbations crafted from sensitivity results, we show how this vulnerability can cause a vehicle to come to a sudden stop from moderate driving speeds.

In the past decade, we have witnessed the rise of deep learning to dominate the field of artificial intelligence. Advances in artificial neural networks alongside corresponding advances in hardware accelerators with large memory capacity, together with the availability of large datasets enabled researchers and practitioners alike to train and deploy sophisticated neural network models that achieve state-of-the-art performance on tasks across several fields spanning computer vision, natural language processing, and reinforcement learning. However, as these neural networks become bigger, more complex, and more widely used, fundamental problems with current deep learning models become more apparent. State-of-the-art deep learning models are known to suffer from issues that range from poor robustness, inability to adapt to novel task settings, to requiring rigid and inflexible configuration assumptions. Ideas from collective intelligence, in particular concepts from complex systems such as self-organization, emergent behavior, swarm optimization, and cellular systems tend to produce solutions that are robust, adaptable, and have less rigid assumptions about the environment configuration. It is therefore natural to see these ideas incorporated into newer deep learning methods. In this review, we will provide a historical context of neural network research's involvement with complex systems, and highlight several active areas in modern deep learning research that incorporate the principles of collective intelligence to advance its current capabilities. To facilitate a bi-directional flow of ideas, we also discuss work that utilize modern deep learning models to help advance complex systems research. We hope this review can serve as a bridge between complex systems and deep learning communities to facilitate the cross pollination of ideas and foster new collaborations across disciplines.

With the advances of data-driven machine learning research, a wide variety of prediction problems have been tackled. It has become critical to explore how machine learning and specifically deep learning methods can be exploited to analyse healthcare data. A major limitation of existing methods has been the focus on grid-like data; however, the structure of physiological recordings are often irregular and unordered which makes it difficult to conceptualise them as a matrix. As such, graph neural networks have attracted significant attention by exploiting implicit information that resides in a biological system, with interactive nodes connected by edges whose weights can be either temporal associations or anatomical junctions. In this survey, we thoroughly review the different types of graph architectures and their applications in healthcare. We provide an overview of these methods in a systematic manner, organized by their domain of application including functional connectivity, anatomical structure and electrical-based analysis. We also outline the limitations of existing techniques and discuss potential directions for future research.

Current deep learning research is dominated by benchmark evaluation. A method is regarded as favorable if it empirically performs well on the dedicated test set. This mentality is seamlessly reflected in the resurfacing area of continual learning, where consecutively arriving sets of benchmark data are investigated. The core challenge is framed as protecting previously acquired representations from being catastrophically forgotten due to the iterative parameter updates. However, comparison of individual methods is nevertheless treated in isolation from real world application and typically judged by monitoring accumulated test set performance. The closed world assumption remains predominant. It is assumed that during deployment a model is guaranteed to encounter data that stems from the same distribution as used for training. This poses a massive challenge as neural networks are well known to provide overconfident false predictions on unknown instances and break down in the face of corrupted data. In this work we argue that notable lessons from open set recognition, the identification of statistically deviating data outside of the observed dataset, and the adjacent field of active learning, where data is incrementally queried such that the expected performance gain is maximized, are frequently overlooked in the deep learning era. Based on these forgotten lessons, we propose a consolidated view to bridge continual learning, active learning and open set recognition in deep neural networks. Our results show that this not only benefits each individual paradigm, but highlights the natural synergies in a common framework. We empirically demonstrate improvements when alleviating catastrophic forgetting, querying data in active learning, selecting task orders, while exhibiting robust open world application where previously proposed methods fail.

Deep neural models in recent years have been successful in almost every field, including extremely complex problem statements. However, these models are huge in size, with millions (and even billions) of parameters, thus demanding more heavy computation power and failing to be deployed on edge devices. Besides, the performance boost is highly dependent on redundant labeled data. To achieve faster speeds and to handle the problems caused by the lack of data, knowledge distillation (KD) has been proposed to transfer information learned from one model to another. KD is often characterized by the so-called `Student-Teacher' (S-T) learning framework and has been broadly applied in model compression and knowledge transfer. This paper is about KD and S-T learning, which are being actively studied in recent years. First, we aim to provide explanations of what KD is and how/why it works. Then, we provide a comprehensive survey on the recent progress of KD methods together with S-T frameworks typically for vision tasks. In general, we consider some fundamental questions that have been driving this research area and thoroughly generalize the research progress and technical details. Additionally, we systematically analyze the research status of KD in vision applications. Finally, we discuss the potentials and open challenges of existing methods and prospect the future directions of KD and S-T learning.

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