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Ordered sequences of data, specified with a join operation to combine sequences, serve as a foundation for the implementation of parallel functional algorithms. This abstract data type can be elegantly and efficiently implemented using balanced binary trees, where a join operation is provided to combine two trees and rebalance as necessary. In this work, we present a verified implementation and cost analysis of joinable red-black trees in $\textbf{calf}$, a dependent type theory for cost analysis. We implement red-black trees and auxiliary intermediate data structures in such a way that all correctness invariants are intrinsically maintained. Then, we describe and verify precise cost bounds on the operations, making use of the red-black tree invariants. Finally, we implement standard algorithms on sequences using the simple join-based signature and bound their cost in the case that red-black trees are used as the underlying implementation. All proofs are formally mechanized using the embedding of $\textbf{calf}$ in the Agda theorem prover.

The problem of function approximation by neural dynamical systems has typically been approached in a top-down manner: Any continuous function can be approximated to an arbitrary accuracy by a sufficiently complex model with a given architecture. This can lead to high-complexity controls which are impractical in applications. In this paper, we take the opposite, constructive approach: We impose various structural restrictions on system dynamics and consequently characterize the class of functions that can be realized by such a system. The systems are implemented as a cascade interconnection of a neural stochastic differential equation (Neural SDE), a deterministic dynamical system, and a readout map. Both probabilistic and geometric (Lie-theoretic) methods are used to characterize the classes of functions realized by such systems.

Accurate load forecasting plays a vital role in numerous sectors, but accurately capturing the complex dynamics of dynamic power systems remains a challenge for traditional statistical models. For these reasons, time-series models (ARIMA) and deep-learning models (ANN, LSTM, GRU, etc.) are commonly deployed and often experience higher success. In this paper, we analyze the efficacy of the recently developed Transformer-based Neural Network model in Load forecasting. Transformer models have the potential to improve Load forecasting because of their ability to learn long-range dependencies derived from their Attention Mechanism. We apply several metaheuristics namely Differential Evolution to find the optimal hyperparameters of the Transformer-based Neural Network to produce accurate forecasts. Differential Evolution provides scalable, robust, global solutions to non-differentiable, multi-objective, or constrained optimization problems. Our work compares the proposed Transformer based Neural Network model integrated with different metaheuristic algorithms by their performance in Load forecasting based on numerical metrics such as Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). Our findings demonstrate the potential of metaheuristic-enhanced Transformer-based Neural Network models in Load forecasting accuracy and provide optimal hyperparameters for each model.

Prompt Tuning is emerging as a scalable and cost-effective method to fine-tune Pretrained Language Models (PLMs). This study benchmarks the performance and computational efficiency of Prompt Tuning and baseline methods on a multi-label text classification task. This is applied to the use case of classifying companies into an investment firm's proprietary industry taxonomy, supporting their thematic investment strategy. Text-to-text classification with PLMs is frequently reported to outperform classification with a classification head, but has several limitations when applied to a multi-label classification problem where each label consists of multiple tokens: (a) Generated labels may not match any label in the industry taxonomy; (b) During fine-tuning, multiple labels must be provided in an arbitrary order; (c) The model provides a binary decision for each label, rather than an appropriate confidence score. Limitation (a) is addressed by applying constrained decoding using Trie Search, which slightly improves classification performance. All limitations (a), (b), and (c) are addressed by replacing the PLM's language head with a classification head. This improves performance significantly, while also reducing computational costs during inference. The results indicate the continuing need to adapt state-of-the-art methods to domain-specific tasks, even in the era of PLMs with strong generalization abilities.

We prove the undecidability of the third order pattern matching problem in typed lambda-calculi with dependent types and in those with type constructors by reducing the second order unification problem to them.

The problem of predicting the training time of machine learning (ML) models has become extremely relevant in the scientific community. Being able to predict a priori the training time of an ML model would enable the automatic selection of the best model both in terms of energy efficiency and in terms of performance in the context of, for instance, MLOps architectures. In this paper, we present the work we are conducting towards this direction. In particular, we present an extensive empirical study of the Full Parameter Time Complexity (FPTC) approach by Zheng et al., which is, to the best of our knowledge, the only approach formalizing the training time of ML models as a function of both dataset's and model's parameters. We study the formulations proposed for the Logistic Regression and Random Forest classifiers, and we highlight the main strengths and weaknesses of the approach. Finally, we observe how, from the conducted study, the prediction of training time is strictly related to the context (i.e., the involved dataset) and how the FPTC approach is not generalizable.

We consider the problem of training private recommendation models with access to public item features. Training with Differential Privacy (DP) offers strong privacy guarantees, at the expense of loss in recommendation quality. We show that incorporating public item features during training can help mitigate this loss in quality. We propose a general approach based on collective matrix factorization (CMF), that works by simultaneously factorizing two matrices: the user feedback matrix (representing sensitive data) and an item feature matrix that encodes publicly available (non-sensitive) item information. The method is conceptually simple, easy to tune, and highly scalable. It can be applied to different types of public item data, including: (1) categorical item features; (2) item-item similarities learned from public sources; and (3) publicly available user feedback. Furthermore, these data modalities can be collectively utilized to fully leverage public data. Evaluating our method on a standard DP recommendation benchmark, we find that using public item features significantly narrows the quality gap between private models and their non-private counterparts. As privacy constraints become more stringent, models rely more heavily on public side features for recommendation. This results in a smooth transition from collaborative filtering to item-based contextual recommendations.

The concept of causality plays an important role in human cognition . In the past few decades, causal inference has been well developed in many fields, such as computer science, medicine, economics, and education. With the advancement of deep learning techniques, it has been increasingly used in causal inference against counterfactual data. Typically, deep causal models map the characteristics of covariates to a representation space and then design various objective optimization functions to estimate counterfactual data unbiasedly based on the different optimization methods. This paper focuses on the survey of the deep causal models, and its core contributions are as follows: 1) we provide relevant metrics under multiple treatments and continuous-dose treatment; 2) we incorporate a comprehensive overview of deep causal models from both temporal development and method classification perspectives; 3) we assist a detailed and comprehensive classification and analysis of relevant datasets and source code.

Data processing and analytics are fundamental and pervasive. Algorithms play a vital role in data processing and analytics where many algorithm designs have incorporated heuristics and general rules from human knowledge and experience to improve their effectiveness. Recently, reinforcement learning, deep reinforcement learning (DRL) in particular, is increasingly explored and exploited in many areas because it can learn better strategies in complicated environments it is interacting with than statically designed algorithms. Motivated by this trend, we provide a comprehensive review of recent works focusing on utilizing DRL to improve data processing and analytics. First, we present an introduction to key concepts, theories, and methods in DRL. Next, we discuss DRL deployment on database systems, facilitating data processing and analytics in various aspects, including data organization, scheduling, tuning, and indexing. Then, we survey the application of DRL in data processing and analytics, ranging from data preparation, natural language processing to healthcare, fintech, etc. Finally, we discuss important open challenges and future research directions of using DRL in data processing and analytics.

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.