We formulate, in lattice-theoretic terms, two novel algorithms inspired by Bradley's property directed reachability algorithm. For finding safe invariants or counterexamples, the first algorithm exploits over-approximations of both forward and backward transition relations, expressed abstractly by the notion of adjoints. In the absence of adjoints, one can use the second algorithm, which exploits lower sets and their principals. As a notable example of application, we consider quantitative reachability problems for Markov Decision Processes.
相關內容
Text-to-motion generation is a formidable task, aiming to produce human motions that align with the input text while also adhering to human capabilities and physical laws. While there have been advancements in diffusion models, their application in discrete spaces remains underexplored. Current methods often overlook the varying significance of different motions, treating them uniformly. It is essential to recognize that not all motions hold the same relevance to a particular textual description. Some motions, being more salient and informative, should be given precedence during generation. In response, we introduce a Priority-Centric Motion Discrete Diffusion Model (M2DM), which utilizes a Transformer-based VQ-VAE to derive a concise, discrete motion representation, incorporating a global self-attention mechanism and a regularization term to counteract code collapse. We also present a motion discrete diffusion model that employs an innovative noise schedule, determined by the significance of each motion token within the entire motion sequence. This approach retains the most salient motions during the reverse diffusion process, leading to more semantically rich and varied motions. Additionally, we formulate two strategies to gauge the importance of motion tokens, drawing from both textual and visual indicators. Comprehensive experiments on the HumanML3D and KIT-ML datasets confirm that our model surpasses existing techniques in fidelity and diversity, particularly for intricate textual descriptions.
Quantile feature selection over correlated multivariate time series data has always been a methodological challenge and is an open problem. In this paper, we propose a general Bayesian dimension reduction methodology for feature selection in high-dimensional joint quantile time series analysis, under the name of the quantile feature selection time series (QFSTS) model. The QFSTS model is a general structural time series model, where each component yields an additive contribution to the time series modeling with direct interpretations. Its flexibility is compound in the sense that users can add/deduct components for each time series and each time series can have its own specific valued components of different sizes. Feature selection is conducted in the quantile regression component, where each time series has its own pool of contemporaneous external predictors allowing nowcasting. Bayesian methodology in extending feature selection to the quantile time series research area is developed using multivariate asymmetric Laplace distribution, spike-and-slab prior setup, the Metropolis-Hastings algorithm, and the Bayesian model averaging technique, all implemented consistently in the Bayesian paradigm. The QFSTS model requires small datasets to train and converges fast. Extensive examinations confirmed that the QFSTS model has superior performance in feature selection, parameter estimation, and forecast.
Stochastic variational inference algorithms are derived for fitting various heteroskedastic time series models. We examine Gaussian, t, and skew-t response GARCH models and fit these using Gaussian variational approximating densities. We implement efficient stochastic gradient ascent procedures based on the use of control variates or the reparameterization trick and demonstrate that the proposed implementations provide a fast and accurate alternative to Markov chain Monte Carlo sampling. Additionally, we present sequential updating versions of our variational algorithms, which are suitable for efficient portfolio construction and dynamic asset allocation.
Evolutionary change over time in the context of data pipelines is certain, especially with regard to the structure and semantics of data as well as to the pipeline operators. Dealing with these changes, i.e. providing long-term maintenance, is costly. The present work explores the need for evolution capabilities within pipeline frameworks. In this context dealing with evolution is defined as a two-step process consisting of self-awareness and self-adaption. Furthermore, a conceptual requirements model is provided, which encompasses criteria for self-awareness and self-adaption as well as covering the dimensions data, operator, pipeline and environment. A lack of said capabilities in existing frameworks exposes a major gap. Filling this gap will be a significant contribution for practitioners and scientists alike. The present work envisions and lays the foundation for a framework which can handle evolutionary change.
Math word problems (MWPs) require analyzing text descriptions and generating mathematical equations to derive solutions. Existing works focus on solving MWPs with two types of solvers: tree-based solver and large language model (LLM) solver. However, these approaches always solve MWPs by a single solver, which will bring the following problems: (1) Single type of solver is hard to solve all types of MWPs well. (2) A single solver will result in poor performance due to over-fitting. To address these challenges, this paper utilizes multiple ensemble approaches to improve MWP-solving ability. Firstly, We propose a problem type classifier that combines the strengths of the tree-based solver and the LLM solver. This ensemble approach leverages their respective advantages and broadens the range of MWPs that can be solved. Furthermore, we also apply ensemble techniques to both tree-based solver and LLM solver to improve their performance. For the tree-based solver, we propose an ensemble learning framework based on ten-fold cross-validation and voting mechanism. In the LLM solver, we adopt self-consistency (SC) method to improve answer selection. Experimental results demonstrate the effectiveness of these ensemble approaches in enhancing MWP-solving ability. The comprehensive evaluation showcases improved performance, validating the advantages of our proposed approach. Our code is available at this url: //github.com/zhouzihao501/NLPCC2023-Shared-Task3-ChineseMWP.
The rehearsal strategy is widely used to alleviate the catastrophic forgetting problem in class incremental learning (CIL) by preserving limited exemplars from previous tasks. With imbalanced sample numbers between old and new classes, the classifier learning can be biased. Existing CIL methods exploit the long-tailed (LT) recognition techniques, e.g., the adjusted losses and the data re-sampling methods, to handle the data imbalance issue within each increment task. In this work, the dynamic nature of data imbalance in CIL is shown and a novel Dynamic Residual Classifier (DRC) is proposed to handle this challenging scenario. Specifically, DRC is built upon a recent advance residual classifier with the branch layer merging to handle the model-growing problem. Moreover, DRC is compatible with different CIL pipelines and substantially improves them. Combining DRC with the model adaptation and fusion (MAF) pipeline, this method achieves state-of-the-art results on both the conventional CIL and the LT-CIL benchmarks. Extensive experiments are also conducted for a detailed analysis. The code is publicly available.
Clustering methods are popular for revealing structure in data, particularly in the high-dimensional setting common to contemporary data science. A central statistical question is, "are the clusters really there?" One pioneering method in statistical cluster validation is SigClust, but it is severely underpowered in the important setting where the candidate clusters have unbalanced sizes, such as in rare subtypes of disease. We show why this is the case, and propose a remedy that is powerful in both the unbalanced and balanced settings, using a novel generalization of k-means clustering. We illustrate the value of our method using a high-dimensional dataset of gene expression in kidney cancer patients. A Python implementation is available at //github.com/thomaskeefe/sigclust.
The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model that combines three components: a pseudo-Riemannian metric structure, a non-trivial global topology, and a unique likelihood function that explicitly incorporates a preferred direction in embedding space. We demonstrate the representational capabilities of this method by applying it to the task of link prediction on a series of synthetic and real directed graphs from natural language applications and biology. In particular, we show that low-dimensional cylindrical Minkowski and anti-de Sitter spacetimes can produce equal or better graph representations than curved Riemannian manifolds of higher dimensions.
The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.
The notion of "in-domain data" in NLP is often over-simplistic and vague, as textual data varies in many nuanced linguistic aspects such as topic, style or level of formality. In addition, domain labels are many times unavailable, making it challenging to build domain-specific systems. We show that massive pre-trained language models implicitly learn sentence representations that cluster by domains without supervision -- suggesting a simple data-driven definition of domains in textual data. We harness this property and propose domain data selection methods based on such models, which require only a small set of in-domain monolingual data. We evaluate our data selection methods for neural machine translation across five diverse domains, where they outperform an established approach as measured by both BLEU and by precision and recall of sentence selection with respect to an oracle.
小貼士
登錄享
相關主題
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191