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We challenge the idea that edge insertions are local improvement operations and show that the edge-insertion algorithm must sometimes insert an edge between vertices that are at the farthest combinatorial distance apart, and that this edge must also cross linearly many edges of the triangulation for the algorithm to escape a local optimum and return the optimal triangulation.

Hyperparameters of Deep Learning (DL) pipelines are crucial for their downstream performance. While a large number of methods for Hyperparameter Optimization (HPO) have been developed, their incurred costs are often untenable for modern DL. Consequently, manual experimentation is still the most prevalent approach to optimize hyperparameters, relying on the researcher's intuition, domain knowledge, and cheap preliminary explorations. To resolve this misalignment between HPO algorithms and DL researchers, we propose PriorBand, an HPO algorithm tailored to DL, able to utilize both expert beliefs and cheap proxy tasks. Empirically, we demonstrate PriorBand's efficiency across a range of DL benchmarks and show its gains under informative expert input and robustness against poor expert beliefs

Large Language Models (LLMs) employing Chain-of-Thought (CoT) prompting have broadened the scope for improving multi-step reasoning capabilities. Usually, answer calibration strategies such as step-level or path-level calibration play a vital role in multi-step reasoning. While effective, there remains a significant gap in our understanding of the key factors that drive their success. In this paper, we break down the design of recent answer calibration strategies and present a unified view which establishes connections between them. We then conduct a thorough evaluation on these strategies from a unified view, systematically scrutinizing step-level and path-level answer calibration across multiple paths. Our study holds the potential to illuminate key insights for optimizing multi-step reasoning with answer calibration.

Computational argumentation has become an essential tool in various fields, including artificial intelligence, law, and public policy. It is an emerging research field in natural language processing (NLP) that attracts increasing attention. Research on computational argumentation mainly involves two types of tasks: argument mining and argument generation. As large language models (LLMs) have demonstrated strong abilities in understanding context and generating natural language, it is worthwhile to evaluate the performance of LLMs on various computational argumentation tasks. This work aims to embark on an assessment of LLMs, such as ChatGPT, Flan models and LLaMA2 models, under zero-shot and few-shot settings within the realm of computational argumentation. We organize existing tasks into 6 main classes and standardise the format of 14 open-sourced datasets. In addition, we present a new benchmark dataset on counter speech generation, that aims to holistically evaluate the end-to-end performance of LLMs on argument mining and argument generation. Extensive experiments show that LLMs exhibit commendable performance across most of these datasets, demonstrating their capabilities in the field of argumentation. We also highlight the limitations in evaluating computational argumentation and provide suggestions for future research directions in this field.

Existing bounds on the generalization error of deep networks assume some form of smooth or bounded dependence on the input variable, falling short of investigating the mechanisms controlling such factors in practice. In this work, we present an extensive experimental study of the empirical Lipschitz constant of deep networks undergoing double descent, and highlight non-monotonic trends strongly correlating with the test error. Building a connection between parameter-space and input-space gradients for SGD around a critical point, we isolate two important factors -- namely loss landscape curvature and distance of parameters from initialization -- respectively controlling optimization dynamics around a critical point and bounding model function complexity, even beyond the training data. Our study presents novels insights on implicit regularization via overparameterization, and effective model complexity for networks trained in practice.

We derive and study time-uniform confidence spheres - termed confidence sphere sequences (CSSs) - which contain the mean of random vectors with high probability simultaneously across all sample sizes. Inspired by the original work of Catoni and Giulini, we unify and extend their analysis to cover both the sequential setting and to handle a variety of distributional assumptions. More concretely, our results include an empirical-Bernstein CSS for bounded random vectors (resulting in a novel empirical-Bernstein confidence interval), a CSS for sub-$\psi$ random vectors, and a CSS for heavy-tailed random vectors based on a sequentially valid Catoni-Giulini estimator. Finally, we provide a version of our empirical-Bernstein CSS that is robust to contamination by Huber noise.

EHR audit logs are a highly granular stream of events that capture clinician activities, and is a significant area of interest for research in characterizing clinician workflow on the electronic health record (EHR). Existing techniques to measure the complexity of workflow through EHR audit logs (audit logs) involve time- or frequency-based cross-sectional aggregations that are unable to capture the full complexity of a EHR session. We briefly evaluate the usage of transformer-based tabular language model (tabular LM) in measuring the entropy or disorderedness of action sequences within workflow and release the evaluated models publicly.

The problem of optimizing discrete phases in a reconfigurable intelligent surface (RIS) to maximize the received power at a user equipment is addressed. Necessary and sufficient conditions to achieve this maximization are given. These conditions are employed in an algorithm to achieve the maximization. New versions of the algorithm are given that are proven to achieve convergence in N or fewer steps whether the direct link is completely blocked or not, where N is the number of the RIS elements, whereas previously published results achieve this in KN or 2N number of steps where K is the number of discrete phases, e.g., [1], [2]. Thus, for a discrete-phase RIS, the techniques presented in this paper achieve the optimum received power in the smallest number of steps published in the literature. In addition, in each of those N steps, the techniques presented in this paper determine only one or a small number of phase shifts with a simple elementwise update rule, which result in a substantial reduction of computation time, as compared to the algorithms in the literature, e.g., [2], [3].

While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.