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We consider variants of the classic Multiway Cut problem. Multiway Cut asks to partition a graph $G$ into $k$ parts so as to separate $k$ given terminals. Recently, Chandrasekaran and Wang (ESA 2021) introduced $\ell_p$-norm Multiway, a generalization of the problem, in which the goal is to minimize the $\ell_p$ norm of the edge boundaries of $k$ parts. We provide an $O(\log^{1/2} n\log^{1/2+1/p} k)$ approximation algorithm for this problem, improving upon the approximation guarantee of $O(\log^{3/2} n \log^{1/2} k)$ due to Chandrasekaran and Wang. We also introduce and study Norm Multiway Cut, a further generalization of Multiway Cut. We assume that we are given access to an oracle, which answers certain queries about the norm. We present an $O(\log^{1/2} n \log^{7/2} k)$ approximation algorithm with a weaker oracle and an $O(\log^{1/2} n \log^{5/2} k)$ approximation algorithm with a stronger oracle. Additionally, we show that without any oracle access, there is no $n^{1/4-\varepsilon}$ approximation algorithm for every $\varepsilon > 0$ assuming the Hypergraph Dense-vs-Random Conjecture.

In this paper, we perform a time-domain analysis of the higher-order Allan variance for atomic clock models of arbitrary order. Adopting a standard atomic clock model where the time series of the clock reading deviation is expressed as a Wiener or integrated Wiener process, we define the higher-order Allan variance as the mean squared higher-order difference of the clock reading deviation. The main results of this paper are threefold. First, we prove that the higher-order difference operation of the clock reading deviation, which can be interpreted as a linear aggregation with binomial coefficients, is not only sufficient, but also necessary for a resulting aggregated time series to be an independent and identically distributed Gaussian process. Second, we derive a complete analytical expression of the higher-order Allan variance, which consists of both time-dependent and time-independent terms. Third and finally, we prove that the higher-order Allan variance is time-independent if and only if the order of difference operation is greater than or equal to the order of the atomic clock model.

We present Self-Driven Strategy Learning ($\textit{sdsl}$), a lightweight online learning methodology for automated reasoning tasks that involve solving a set of related problems. $\textit{sdsl}$ does not require offline training, but instead automatically constructs a dataset while solving earlier problems. It fits a machine learning model to this data which is then used to adjust the solving strategy for later problems. We formally define the approach as a set of abstract transition rules. We describe a concrete instance of the sdsl calculus which uses conditional sampling for generating data and random forests as the underlying machine learning model. We implement the approach on top of the Kissat solver and show that the combination of Kissat+$\textit{sdsl}$ certifies larger bounds and finds more counter-examples than other state-of-the-art bounded model checking approaches on benchmarks obtained from the latest Hardware Model Checking Competition.

We present an evaluation of text simplification (TS) in Spanish for a production system, by means of two corpora focused in both complex-sentence and complex-word identification. We compare the most prevalent Spanish-specific readability scores with neural networks, and show that the latter are consistently better at predicting user preferences regarding TS. As part of our analysis, we find that multilingual models underperform against equivalent Spanish-only models on the same task, yet all models focus too often on spurious statistical features, such as sentence length. We release the corpora in our evaluation to the broader community with the hopes of pushing forward the state-of-the-art in Spanish natural language processing.

This paper presents an improved loss function for neural source code summarization. Code summarization is the task of writing natural language descriptions of source code. Neural code summarization refers to automated techniques for generating these descriptions using neural networks. Almost all current approaches involve neural networks as either standalone models or as part of a pretrained large language models e.g., GPT, Codex, LLaMA. Yet almost all also use a categorical cross-entropy (CCE) loss function for network optimization. Two problems with CCE are that 1) it computes loss over each word prediction one-at-a-time, rather than evaluating a whole sentence, and 2) it requires a perfect prediction, leaving no room for partial credit for synonyms. We propose and evaluate a loss function to alleviate this problem. In essence, we propose to use a semantic similarity metric to calculate loss over the whole output sentence prediction per training batch, rather than just loss for each word. We also propose to combine our loss with traditional CCE for each word, which streamlines the training process compared to baselines. We evaluate our approach over several baselines and report an improvement in the vast majority of conditions.

Self-supervised learning, dubbed the dark matter of intelligence, is a promising path to advance machine learning. Yet, much like cooking, training SSL methods is a delicate art with a high barrier to entry. While many components are familiar, successfully training a SSL method involves a dizzying set of choices from the pretext tasks to training hyper-parameters. Our goal is to lower the barrier to entry into SSL research by laying the foundations and latest SSL recipes in the style of a cookbook. We hope to empower the curious researcher to navigate the terrain of methods, understand the role of the various knobs, and gain the know-how required to explore how delicious SSL can be.

Learning on big data brings success for artificial intelligence (AI), but the annotation and training costs are expensive. In future, learning on small data is one of the ultimate purposes of AI, which requires machines to recognize objectives and scenarios relying on small data as humans. A series of machine learning models is going on this way such as active learning, few-shot learning, deep clustering. However, there are few theoretical guarantees for their generalization performance. Moreover, most of their settings are passive, that is, the label distribution is explicitly controlled by one specified sampling scenario. This survey follows the agnostic active sampling under a PAC (Probably Approximately Correct) framework to analyze the generalization error and label complexity of learning on small data using a supervised and unsupervised fashion. With these theoretical analyses, we categorize the small data learning models from two geometric perspectives: the Euclidean and non-Euclidean (hyperbolic) mean representation, where their optimization solutions are also presented and discussed. Later, some potential learning scenarios that may benefit from small data learning are then summarized, and their potential learning scenarios are also analyzed. Finally, some challenging applications such as computer vision, natural language processing that may benefit from learning on small data are also surveyed.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

Co-evolving time series appears in a multitude of applications such as environmental monitoring, financial analysis, and smart transportation. This paper aims to address the following challenges, including (C1) how to incorporate explicit relationship networks of the time series; (C2) how to model the implicit relationship of the temporal dynamics. We propose a novel model called Network of Tensor Time Series, which is comprised of two modules, including Tensor Graph Convolutional Network (TGCN) and Tensor Recurrent Neural Network (TRNN). TGCN tackles the first challenge by generalizing Graph Convolutional Network (GCN) for flat graphs to tensor graphs, which captures the synergy between multiple graphs associated with the tensors. TRNN leverages tensor decomposition to model the implicit relationships among co-evolving time series. The experimental results on five real-world datasets demonstrate the efficacy of the proposed method.

The potential of graph convolutional neural networks for the task of zero-shot learning has been demonstrated recently. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, knowledge from distant nodes can get diluted when propagating through intermediate nodes, because current approaches to zero-shot learning use graph propagation schemes that perform Laplacian smoothing at each layer. We show that extensive smoothing does not help the task of regressing classifier weights in zero-shot learning. In order to still incorporate information from distant nodes and utilize the graph structure, we propose an Attentive Dense Graph Propagation Module (ADGPM). ADGPM allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants and an attention scheme is further used to weigh their contribution depending on the distance to the node. Finally, we illustrate that finetuning of the feature representation after training the ADGPM leads to considerable improvements. Our method achieves competitive results, outperforming previous zero-shot learning approaches.