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A significant part of modern topological data analysis is concerned with the design and study of algebraic invariants of poset representations -- often referred to as multi-parameter persistence modules. One such invariant is the minimal rank decomposition, which encodes the ranks of all the structure morphisms of the persistence module by a single ordered pair of rectangle-decomposable modules, interpreted as a signed barcode. This signed barcode generalizes the concept of persistence barcode from one-parameter persistence to any number of parameters, raising the question of its bottleneck stability. We show in this paper that the minimal rank decomposition is not stable under the natural notion of signed bottleneck matching between signed barcodes. We remedy this by turning our focus to the rank exact decomposition, a related signed barcode induced by the minimal projective resolution of the module relative to the so-called rank exact structure, which we prove to be bottleneck stable under signed matchings. As part of our proof, we obtain two intermediate results of independent interest: we compute the global dimension of the rank exact structure on the category of finitely presentable multi-parameter persistence modules, and we prove a bottleneck stability result for hook-decomposable modules. We also give a bound for the size of the rank exact decomposition that is polynomial in the size of the usual minimal projective resolution, we prove a universality result for the dissimilarity function induced by the notion of signed matching, and we compute, in the two-parameter case, the global dimension of a different exact structure related to the upsets of the indexing poset. This set of results combines concepts from topological data analysis and from the representation theory of posets, and we believe is relevant to both areas.

C-based interpreters such as CPython make extensive use of C "extension" code, which is opaque to static analysis tools and faster runtimes with JIT compilers, such as PyPy. Not only are the extensions opaque, but the interface between the dynamic language types and the C types can introduce impedance. We hypothesise that frequent calls to C extension code introduce significant overhead that is often unnecessary. We validate this hypothesis by introducing a simple technique, "typed methods", which allow selected C extension functions to have additional metadata attached to them in a backward-compatible way. This additional metadata makes it much easier for a JIT compiler (and as we show, even an interpreter!) to significantly reduce the call and return overhead. Although we have prototyped typed methods in PyPy, we suspect that the same technique is applicable to a wider variety of language runtimes and that the information can also be consumed by static analysis tooling.

We address an optimal sensor placement problem through Bayesian experimental design for seismic full waveform inversion for the recovery of the associated moment tensor. The objective is that of optimally choosing the location of the sensors (stations) from which to collect the observed data. The Shannon expected information gain is used as the objective function to search for the optimal network of sensors. A closed form for such objective is available due to the linear structure of the forward problem, as well as the Gaussian modeling of the observational errors and prior distribution. The resulting problem being inherently combinatorial, a greedy algorithm is deployed to sequentially select the sensor locations that form the best network for learning the moment tensor. Numerical results are presented and analyzed under several instances of the problem, including: use of full three-dimensional velocity-models, cases in which the earthquake-source location is unknown, as well as moment tensor inversion under model misspecification

Despite recent availability of large transcribed Kinyarwanda speech data, achieving robust speech recognition for Kinyarwanda is still challenging. In this work, we show that using self-supervised pre-training, following a simple curriculum schedule during fine-tuning and using semi-supervised learning to leverage large unlabelled speech data significantly improve speech recognition performance for Kinyarwanda. Our approach focuses on using public domain data only. A new studio-quality speech dataset is collected from a public website, then used to train a clean baseline model. The clean baseline model is then used to rank examples from a more diverse and noisy public dataset, defining a simple curriculum training schedule. Finally, we apply semi-supervised learning to label and learn from large unlabelled data in five successive generations. Our final model achieves 3.2% word error rate (WER) on the new dataset and 15.6% WER on Mozilla Common Voice benchmark, which is state-of-the-art to the best of our knowledge. Our experiments also indicate that using syllabic rather than character-based tokenization results in better speech recognition performance for Kinyarwanda.

We systematically evaluated the performance of seven large language models in generating programming code using various prompt strategies, programming languages, and task difficulties. GPT-4 substantially outperforms other large language models, including Gemini Ultra and Claude 2. The coding performance of GPT-4 varies considerably with different prompt strategies. In most LeetCode and GeeksforGeeks coding contests evaluated in this study, GPT-4 employing the optimal prompt strategy outperforms 85 percent of human participants. Additionally, GPT-4 demonstrates strong capabilities in translating code between different programming languages and in learning from past errors. The computational efficiency of the code generated by GPT-4 is comparable to that of human programmers. These results suggest that GPT-4 has the potential to serve as a reliable assistant in programming code generation and software development.

Average calibration of the uncertainties of machine learning regression tasks can be tested in two ways. One way is to estimate the calibration error (CE) as the difference between the mean absolute error (MSE) and the mean variance (MV) or mean squared uncertainty. The alternative is to compare the mean squared z-scores or scaled errors (ZMS) to 1. Both approaches might lead to different conclusion, as illustrated on an ensemble of datasets from the recent machine learning uncertainty quantification literature. It is shown here that the CE is very sensitive to the distribution of uncertainties, and notably to the presence of outlying uncertainties, and that it cannot be used reliably for calibration testing. By contrast, the ZMS statistic does not present this sensitivity issue and offers the most reliable approach in this context. Implications for the validation of conditional calibration are discussed.

Weak supervision searches have in principle the advantages of both being able to train on experimental data and being able to learn distinctive signal properties. However, the practical applicability of such searches is limited by the fact that successfully training a neural network via weak supervision can require a large amount of signal. In this work, we seek to create neural networks that can learn from less experimental signal by using transfer and meta-learning. The general idea is to first train a neural network on simulations, thereby learning concepts that can be reused or becoming a more efficient learner. The neural network would then be trained on experimental data and should require less signal because of its previous training. We find that transfer and meta-learning can substantially improve the performance of weak supervision searches.

Graph-centric artificial intelligence (graph AI) has achieved remarkable success in modeling interacting systems prevalent in nature, from dynamical systems in biology to particle physics. The increasing heterogeneity of data calls for graph neural architectures that can combine multiple inductive biases. However, combining data from various sources is challenging because appropriate inductive bias may vary by data modality. Multimodal learning methods fuse multiple data modalities while leveraging cross-modal dependencies to address this challenge. Here, we survey 140 studies in graph-centric AI and realize that diverse data types are increasingly brought together using graphs and fed into sophisticated multimodal models. These models stratify into image-, language-, and knowledge-grounded multimodal learning. We put forward an algorithmic blueprint for multimodal graph learning based on this categorization. The blueprint serves as a way to group state-of-the-art architectures that treat multimodal data by choosing appropriately four different components. This effort can pave the way for standardizing the design of sophisticated multimodal architectures for highly complex real-world problems.

The Evidential regression network (ENet) estimates a continuous target and its predictive uncertainty without costly Bayesian model averaging. However, it is possible that the target is inaccurately predicted due to the gradient shrinkage problem of the original loss function of the ENet, the negative log marginal likelihood (NLL) loss. In this paper, the objective is to improve the prediction accuracy of the ENet while maintaining its efficient uncertainty estimation by resolving the gradient shrinkage problem. A multi-task learning (MTL) framework, referred to as MT-ENet, is proposed to accomplish this aim. In the MTL, we define the Lipschitz modified mean squared error (MSE) loss function as another loss and add it to the existing NLL loss. The Lipschitz modified MSE loss is designed to mitigate the gradient conflict with the NLL loss by dynamically adjusting its Lipschitz constant. By doing so, the Lipschitz MSE loss does not disturb the uncertainty estimation of the NLL loss. The MT-ENet enhances the predictive accuracy of the ENet without losing uncertainty estimation capability on the synthetic dataset and real-world benchmarks, including drug-target affinity (DTA) regression. Furthermore, the MT-ENet shows remarkable calibration and out-of-distribution detection capability on the DTA benchmarks.

Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.