We present a novel optimization algorithm, element-wise relaxed scalar auxiliary variable (E-RSAV), that satisfies an unconditional energy dissipation law and exhibits improved alignment between the modified and the original energy. Our algorithm features rigorous proofs of linear convergence in the convex setting. Furthermore, we present a simple accelerated algorithm that improves the linear convergence rate to super-linear in the univariate case. We also propose an adaptive version of E-RSAV with Steffensen step size. We validate the robustness and fast convergence of our algorithm through ample numerical experiments.
We present Dolphin, a novel benchmark that addresses the need for a natural language generation (NLG) evaluation framework dedicated to the wide collection of Arabic languages and varieties. The proposed benchmark encompasses a broad range of 13 different NLG tasks, including dialogue generation, question answering, machine translation, summarization, among others. Dolphin comprises a substantial corpus of 40 diverse and representative public datasets across 50 test splits, carefully curated to reflect real-world scenarios and the linguistic richness of Arabic. It sets a new standard for evaluating the performance and generalization capabilities of Arabic and multilingual models, promising to enable researchers to push the boundaries of current methodologies. We provide an extensive analysis of Dolphin, highlighting its diversity and identifying gaps in current Arabic NLG research. We also offer a public leaderboard that is both interactive and modular and evaluate several models on our benchmark, allowing us to set strong baselines against which researchers can compare.
signSGD is popular in nonconvex optimization due to its communication efficiency. Yet, existing analyses of signSGD rely on assuming that data are sampled with replacement in each iteration, contradicting the practical implementation where data are randomly reshuffled and sequentially fed into the algorithm. We bridge this gap by proving the first convergence result of signSGD with random reshuffling (SignRR) for nonconvex optimization. Given the dataset size $n$, the number of epochs of data passes $T$, and the variance bound of a stochastic gradient $\sigma^2$, we show that SignRR has the same convergence rate $O(\log(nT)/\sqrt{nT} + \|\sigma\|_1)$ as signSGD \citep{bernstein2018signsgd}. We then present SignRVR and SignRVM, which leverage variance-reduced gradients and momentum updates respectively, both converging at $O(\log(nT)/\sqrt{nT})$. In contrast with the analysis of signSGD, our results do not require an extremely large batch size in each iteration to be of the same order as the total number of iterations \citep{bernstein2018signsgd} or the signs of stochastic and true gradients match element-wise with a minimum probability of 1/2 \citep{safaryan2021stochastic}. We also extend our algorithms to cases where data are distributed across different machines, yielding dist-SignRVR and dist-SignRVM, both converging at $O(\log(n_0T)/\sqrt{n_0T})$, where $n_0$ is the dataset size of a single machine. We back up our theoretical findings through experiments on simulated and real-world problems, verifying that randomly reshuffled sign methods match or surpass existing baselines.
A cost-effective alternative to manual data labeling is weak supervision (WS), where data samples are automatically annotated using a predefined set of labeling functions (LFs), rule-based mechanisms that generate artificial labels for the associated classes. In this work, we investigate noise reduction techniques for WS based on the principle of k-fold cross-validation. We introduce a new algorithm ULF for Unsupervised Labeling Function correction, which denoises WS data by leveraging models trained on all but some LFs to identify and correct biases specific to the held-out LFs. Specifically, ULF refines the allocation of LFs to classes by re-estimating this assignment on highly reliable cross-validated samples. Evaluation on multiple datasets confirms ULF's effectiveness in enhancing WS learning without the need for manual labeling.
Fourier feature approximations have been successfully applied in the literature for scalable Gaussian Process (GP) regression. In particular, Quadrature Fourier Features (QFF) derived from Gaussian quadrature rules have gained popularity in recent years due to their improved approximation accuracy and better calibrated uncertainty estimates compared to Random Fourier Feature (RFF) methods. However, a key limitation of QFF is that its performance can suffer from well-known pathologies related to highly oscillatory quadrature, resulting in mediocre approximation with limited features. We address this critical issue via a new Trigonometric Quadrature Fourier Feature (TQFF) method, which uses a novel non-Gaussian quadrature rule specifically tailored for the desired Fourier transform. We derive an exact quadrature rule for TQFF, along with kernel approximation error bounds for the resulting feature map. We then demonstrate the improved performance of our method over RFF and Gaussian QFF in a suite of numerical experiments and applications, and show the TQFF enjoys accurate GP approximations over a broad range of length-scales using fewer features.
Low-distortional metric embeddings are a crucial component in the modern algorithmic toolkit. In an online metric embedding, points arrive sequentially and the goal is to embed them into a simple space irrevocably, while minimizing the distortion. Our first result is a deterministic online embedding of a general metric into Euclidean space with distortion $O(\log n)\cdot\min\{\sqrt{\log\Phi},\sqrt{n}\}$ (or, $O(d)\cdot\min\{\sqrt{\log\Phi},\sqrt{n}\}$ if the metric has doubling dimension $d$), solving a conjecture by Newman and Rabinovich (2020), and quadratically improving the dependence on the aspect ratio $\Phi$ from Indyk et al.\ (2010). Our second result is a stochastic embedding of a metric space into trees with expected distortion $O(d\cdot \log\Phi)$, generalizing previous results (Indyk et al.\ (2010), Bartal et al.\ (2020)). Next, we study the \emph{online minimum-weight perfect matching} problem, where a sequence of $2n$ metric points arrive in pairs, and one has to maintain a perfect matching at all times. We allow recourse (as otherwise the order of arrival determines the matching). The goal is to return a perfect matching that approximates the \emph{minimum-weight} perfect matching at all times, while minimizing the recourse. Our third result is a randomized algorithm with competitive ratio $O(d\cdot \log \Phi)$ and recourse $O(\log \Phi)$ against an oblivious adversary, this result is obtained via our new stochastic online embedding. Our fourth result is a deterministic algorithm against an adaptive adversary, using $O(\log^2 n)$ recourse, that maintains a matching of weight at most $O(\log n)$ times the weight of the MST, i.e., a matching of lightness $O(\log n)$. We complement our upper bounds with a strategy for an oblivious adversary that, with recourse $r$, establishes a lower bound of $\Omega(\frac{\log n}{r \log r})$ for both competitive ratio and lightness.
We present an implementation of a Web3 platform that leverages the Groth16 Zero-Knowledge Proof schema to verify the validity of questionnaire results within Smart Contracts. Our approach ensures that the answer key of the questionnaire remains undisclosed throughout the verification process, while ensuring that the evaluation is done fairly. To accomplish this, users respond to a series of questions, and their answers are encoded and securely transmitted to a hidden backend. The backend then performs an evaluation of the user's answers, generating the overall result of the questionnaire. Additionally, it generates a Zero-Knowledge Proof, attesting that the answers were appropriately evaluated against a valid set of constraints. Next, the user submits their result along with the proof to a Smart Contract, which verifies their validity and issues a non-fungible token (NFT) as an attestation of the user's test result. In this research, we implemented the Zero-Knowledge functionality using Circom 2 and deployed the Smart Contract using Solidity, thereby showcasing a practical and secure solution for questionnaire validity verification in the context of Smart Contracts.
Text Classification is the most essential and fundamental problem in Natural Language Processing. While numerous recent text classification models applied the sequential deep learning technique, graph neural network-based models can directly deal with complex structured text data and exploit global information. Many real text classification applications can be naturally cast into a graph, which captures words, documents, and corpus global features. In this survey, we bring the coverage of methods up to 2023, including corpus-level and document-level graph neural networks. We discuss each of these methods in detail, dealing with the graph construction mechanisms and the graph-based learning process. As well as the technological survey, we look at issues behind and future directions addressed in text classification using graph neural networks. We also cover datasets, evaluation metrics, and experiment design and present a summary of published performance on the publicly available benchmarks. Note that we present a comprehensive comparison between different techniques and identify the pros and cons of various evaluation metrics in this survey.
In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.
Graph Convolutional Network (GCN) has been widely applied in transportation demand prediction due to its excellent ability to capture non-Euclidean spatial dependence among station-level or regional transportation demands. However, in most of the existing research, the graph convolution was implemented on a heuristically generated adjacency matrix, which could neither reflect the real spatial relationships of stations accurately, nor capture the multi-level spatial dependence of demands adaptively. To cope with the above problems, this paper provides a novel graph convolutional network for transportation demand prediction. Firstly, a novel graph convolution architecture is proposed, which has different adjacency matrices in different layers and all the adjacency matrices are self-learned during the training process. Secondly, a layer-wise coupling mechanism is provided, which associates the upper-level adjacency matrix with the lower-level one. It also reduces the scale of parameters in our model. Lastly, a unitary network is constructed to give the final prediction result by integrating the hidden spatial states with gated recurrent unit, which could capture the multi-level spatial dependence and temporal dynamics simultaneously. Experiments have been conducted on two real-world datasets, NYC Citi Bike and NYC Taxi, and the results demonstrate the superiority of our model over the state-of-the-art ones.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.