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.
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This paper delves into the analysis of nonlinear deformation induced by dielectric actuation in pre-stressed ideal dielectric elastomers. It formulates a nonlinear ordinary differential equation governing this deformation based on the hyperelastic model under dielectric stress. Through numerical integration and neural network approximations, the relationship between voltage and stretch is established. Neural networks are employed to approximate solutions for voltage-to-stretch and stretch-to-voltage transformations obtained via an explicit Runge-Kutta method. The effectiveness of these approximations is demonstrated by leveraging them for compensating nonlinearity through the waveshaping of the input signal. The comparative analysis highlights the superior accuracy of the approximated solutions over baseline methods, resulting in minimized harmonic distortions when utilizing dielectric elastomers as acoustic actuators. This study underscores the efficacy of the proposed approach in mitigating nonlinearities and enhancing the performance of dielectric elastomers in acoustic actuation applications.
Lately, propelled by the phenomenal advances around the transformer architecture, the legal NLP field has enjoyed spectacular growth. To measure progress, well curated and challenging benchmarks are crucial. However, most benchmarks are English only and in legal NLP specifically there is no multilingual benchmark available yet. Additionally, many benchmarks are saturated, with the best models clearly outperforming the best humans and achieving near perfect scores. We survey the legal NLP literature and select 11 datasets covering 24 languages, creating LEXTREME. To provide a fair comparison, we propose two aggregate scores, one based on the datasets and one on the languages. The best baseline (XLM-R large) achieves both a dataset aggregate score a language aggregate score of 61.3. This indicates that LEXTREME is still very challenging and leaves ample room for improvement. To make it easy for researchers and practitioners to use, we release LEXTREME on huggingface together with all the code required to evaluate models and a public Weights and Biases project with all the runs.
The ability to derive useful information by asking clarifying questions (ACQ) is an important element of real life collaboration on reasoning tasks, such as question answering (QA). Existing natural language ACQ challenges, however, evaluate generations based on word overlap rather than the value of the information itself. Word overlap is often an inappropriate metric for question generation since many different questions could be useful in a given situation, and a single question can be phrased many different ways. Instead, we propose evaluating questions pragmatically based on the value of the information they retrieve. Here we present a definition and framework for natural language pragmatic asking of clarifying questions (PACQ), the problem of generating questions that result in answers useful for a reasoning task. We also present fact-level masking (FLM), a procedure for converting natural language datasets into self-supervised PACQ datasets by omitting particular critical facts. Finally, we generate a PACQ dataset from the HotpotQA dataset using FLM and evaluate several zero-shot language models on it. Our experiments show that current zero-shot models struggle to ask questions that retrieve useful information, as compared to human annotators. These results demonstrate an opportunity to use FLM datasets and the PACQ framework to objectively evaluate and improve question generation and other language models.
The main computational challenge in Bayesian inference is to compute integrals against a high-dimensional posterior distribution. In the past decades, variational inference (VI) has emerged as a tractable approximation to these integrals, and a viable alternative to the more established paradigm of Markov Chain Monte Carlo. However, little is known about the approximation accuracy of VI. In this work, we bound the TV error and the mean and covariance approximation error of Gaussian VI in terms of dimension and sample size. Our error analysis relies on a Hermite series expansion of the log posterior whose first terms are precisely cancelled out by the first order optimality conditions associated to the Gaussian VI optimization problem.
The characteristics of data like distribution and heterogeneity, become more complex and counterintuitive as the dimensionality increases. This phenomenon is known as curse of dimensionality, where common patterns and relationships (e.g., internal and boundary pattern) that hold in low-dimensional space may be invalid in higher-dimensional space. It leads to a decreasing performance for the regression, classification or clustering models or algorithms. Curse of dimensionality can be attributed to many causes. In this paper, we first summarize five challenges associated with manipulating high-dimensional data, and explains the potential causes for the failure of regression, classification or clustering tasks. Subsequently, we delve into two major causes of the curse of dimensionality, distance concentration and manifold effect, by performing theoretical and empirical analyses. The results demonstrate that nearest neighbor search (NNS) using three typical distance measurements, Minkowski distance, Chebyshev distance, and cosine distance, becomes meaningless as the dimensionality increases. Meanwhile, the data incorporates more redundant features, and the variance contribution of principal component analysis (PCA) is skewed towards a few dimensions. By interpreting the causes of the curse of dimensionality, we can better understand the limitations of current models and algorithms, and drive to improve the performance of data analysis and machine learning tasks in high-dimensional space.
The increased prevalence of online meetings has significantly enhanced the practicality of a model that can automatically generate the summary of a given meeting. This paper introduces a novel and effective approach to automate the generation of meeting summaries. Current approaches to this problem generate general and basic summaries, considering the meeting simply as a long dialogue. However, our novel algorithms can generate abstractive meeting summaries that are driven by the action items contained in the meeting transcript. This is done by recursively generating summaries and employing our action-item extraction algorithm for each section of the meeting in parallel. All of these sectional summaries are then combined and summarized together to create a coherent and action-item-driven summary. In addition, this paper introduces three novel methods for dividing up long transcripts into topic-based sections to improve the time efficiency of our algorithm, as well as to resolve the issue of large language models (LLMs) forgetting long-term dependencies. Our pipeline achieved a BERTScore of 64.98 across the AMI corpus, which is an approximately 4.98% increase from the current state-of-the-art result produced by a fine-tuned BART (Bidirectional and Auto-Regressive Transformers) model.
The Kaczmarz algorithm is an iterative method that solves linear systems of equations. It stands out among iterative algorithms when dealing with large systems for two reasons. First, at each iteration, the Kaczmarz algorithm uses a single equation, resulting in minimal computational work per iteration. Second, solving the entire system may only require the use of a small subset of the equations. These characteristics have attracted significant attention to the Kaczmarz algorithm. Researchers have observed that randomly choosing equations can improve the convergence rate of the algorithm. This insight led to the development of the Randomized Kaczmarz algorithm and, subsequently, several other variations emerged. In this paper, we extensively analyze the native Kaczmarz algorithm and many of its variations using large-scale dense random systems as benchmarks. Through our investigation, we have verified that, for consistent systems, various row sampling schemes can outperform both the original and Randomized Kaczmarz method. Specifically, sampling without replacement and using quasirandom numbers are the fastest techniques. However, for inconsistent systems, the Conjugate Gradient method for Least-Squares problems overcomes all variations of the Kaczmarz method for these types of systems.
Harmonic potentials provide globally convergent potential fields that are provably free of local minima. Due to its analytical format, it is particularly suitable for generating safe and reliable robot navigation policies. However, for complex environments that consist of a large number of overlapping non-sphere obstacles, the computation of associated transformation functions can be tedious. This becomes more apparent when: (i) the workspace is initially unknown and the underlying potential fields are updated constantly as the robot explores it; (ii) the high-level mission consists of sequential navigation tasks among numerous regions, requiring the robot to switch between different potentials. Thus, this work proposes an efficient and automated scheme to construct harmonic potentials incrementally online as guided by the task automaton. A novel two-layer harmonic tree (HT) structure is introduced that facilitates the hybrid combination of oriented search algorithms for task planning and harmonic-based navigation controllers for non-holonomic robots. Both layers are adapted efficiently and jointly during online execution to reflect the actual feasibility and cost of navigation within the updated workspace. Global safety and convergence are ensured both for the high-level task plan and the low-level robot trajectory. Known issues such as oscillation or long-detours for purely potential-based methods and sharp-turns or high computation complexity for purely search-based methods are prevented. Extensive numerical simulation and hardware experiments are conducted against several strong baselines.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
We propose a novel approach to multimodal sentiment analysis using deep neural networks combining visual analysis and natural language processing. Our goal is different than the standard sentiment analysis goal of predicting whether a sentence expresses positive or negative sentiment; instead, we aim to infer the latent emotional state of the user. Thus, we focus on predicting the emotion word tags attached by users to their Tumblr posts, treating these as "self-reported emotions." We demonstrate that our multimodal model combining both text and image features outperforms separate models based solely on either images or text. Our model's results are interpretable, automatically yielding sensible word lists associated with emotions. We explore the structure of emotions implied by our model and compare it to what has been posited in the psychology literature, and validate our model on a set of images that have been used in psychology studies. Finally, our work also provides a useful tool for the growing academic study of images - both photographs and memes - on social networks.
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