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In this study, we establish that deep neural networks employing ReLU and ReLU$^2$ activation functions are capable of representing Lagrange finite element functions of any order on simplicial meshes across arbitrary dimensions. We introduce a novel global formulation of the basis functions for Lagrange elements, grounded in a geometric decomposition of these elements and leveraging two essential properties of high-dimensional simplicial meshes and barycentric coordinate functions. This representation theory facilitates a natural approximation result for such deep neural networks. Our findings present the first demonstration of how deep neural networks can systematically generate general continuous piecewise polynomial functions.

In this paper, we introduce MVSparse, a novel and efficient framework for cooperative multi-person tracking across multiple synchronized cameras. The MVSparse system is comprised of a carefully orchestrated pipeline, combining edge server-based models with distributed lightweight Reinforcement Learning (RL) agents operating on individual cameras. These RL agents intelligently select informative blocks within each frame based on historical camera data and detection outcomes from neighboring cameras, significantly reducing computational load and communication overhead. The edge server aggregates multiple camera views to perform detection tasks and provides feedback to the individual agents. By projecting inputs from various perspectives onto a common ground plane and applying deep detection models, MVSparse optimally leverages temporal and spatial redundancy in multi-view videos. Notably, our contributions include an empirical analysis of multi-camera pedestrian tracking datasets, the development of a multi-camera, multi-person detection pipeline, and the implementation of MVSparse, yielding impressive results on both open datasets and real-world scenarios. Experimentally, MVSparse accelerates overall inference time by 1.88X and 1.60X compared to a baseline approach while only marginally compromising tracking accuracy by 2.27% and 3.17%, respectively, showcasing its promising potential for efficient multi-camera tracking applications.

Reducing and detecting hallucinations in large language models is an open research problem. In this project, we attempt to leverage recent advances in the field of uncertainty estimation to reduce hallucinations in frozen large language models. Epistemic neural networks have recently been proposed to improve output joint distributions for large pre-trained models. ENNs are small networks attached to large, frozen models to improve the model's joint distributions and uncertainty estimates. In this work, we train an epistemic neural network on top of the Llama-2 7B model combined with a contrastive decoding feature enhancement technique. We are the first to train an ENN for the next token prediction task and explore the efficacy of this method in reducing hallucinations on the TruthfulQA dataset. In essence, we provide a method that leverages a pre-trained model's latent embeddings to reduce hallucinations.

Motivated by the recent empirical success of incorporating public data into differentially private learning, we theoretically investigate how a shared representation learned from public data can improve private learning. We explore two common scenarios of transfer learning for linear regression, both of which assume the public and private tasks (regression vectors) share a low-rank subspace in a high-dimensional space. In the first single-task transfer scenario, the goal is to learn a single model shared across all users, each corresponding to a row in a dataset. We provide matching upper and lower bounds showing that our algorithm achieves the optimal excess risk within a natural class of algorithms that search for the linear model within the given subspace estimate. In the second scenario of multitask model personalization, we show that with sufficient public data, users can avoid private coordination, as purely local learning within the given subspace achieves the same utility. Taken together, our results help to characterize the benefits of public data across common regimes of private transfer learning.

In this study, we present the bicubic Hermite element method (BHEM), a new computational framework devised for the elastodynamic simulation of parametric thin-shell structures. The BHEM is constructed based on parametric quadrilateral Hermite patches, which serve as a unified representation for shell geometry, simulation, collision avoidance, as well as rendering. Compared with the commonly utilized linear FEM, the BHEM offers higher-order solution spaces, enabling the capture of more intricate and smoother geometries while employing significantly fewer finite elements. In comparison to other high-order methods, the BHEM achieves conforming $\mathcal{C}^1$ continuity for Kirchhoff-Love (KL) shells with minimal complexity. Furthermore, by leveraging the subdivision and convex hull properties of Hermite patches, we develop an efficient algorithm for ray-patch intersections, facilitating collision handling in simulations and ray tracing in rendering. This eliminates the need for laborious remodeling of the pre-existing parametric surface as the conventional approaches do. We substantiate our claims with comprehensive experiments, which demonstrate the high accuracy and versatility of the proposed method.

This paper establishes the equivalence between Local Differential Privacy (LDP) and a global limit on learning any knowledge about an object. However, an output from an LDP query is not necessarily required to provide exact amount of knowledge equal to the upper bound of the learning limit. Since the amount of knowledge gain should be proportional to the incurred privacy loss, the traditional approach of using DP guarantee to measure privacy loss can occasionally overestimate the actual privacy loss. This is especially problematic in privacy accounting in LDP, where privacy loss is computed by accumulating the DP guarantees. To address this issue, this paper introduces the concept of \textit{realized privacy loss}, which measures the actual knowledge gained by the analyst after a query, as a more accurate measure of privacy loss. The realized privacy loss is integrated into the privacy accounting of fully adaptive composition, where an adversary adaptively selects queries based on previous results. Bayesian Privacy Filter is implemented to continually accept queries until the realized privacy loss of the composed queries equals the DP guarantee of the composition, allowing the full utilization of the privacy budget. Tracking the realized privacy loss during the composition is achieved through Bayesian Privacy Odometer, and the gap between the privacy budget and the realized privacy loss measures the leeway of the DP guarantee for future queries. A branch-and-bound method is devised to enable the Bayesian Privacy Filter to safeguard objects with continuous values. The Bayesian Privacy Filter is proven to be at least as efficient as the basic composition, and more efficient if the queries are privacy-loss compactible. Experimental results indicate that Bayesian Privacy Filter outperforms the basic composition by a factor of one to four when composing linear and logistic regressions.

Contrastive loss has been increasingly used in learning representations from multiple modalities. In the limit, the nature of the contrastive loss encourages modalities to exactly match each other in the latent space. Yet it remains an open question how the modality alignment affects the downstream task performance. In this paper, based on an information-theoretic argument, we first prove that exact modality alignment is sub-optimal in general for downstream prediction tasks. Hence we advocate that the key of better performance lies in meaningful latent modality structures instead of perfect modality alignment. To this end, we propose three general approaches to construct latent modality structures. Specifically, we design 1) a deep feature separation loss for intra-modality regularization; 2) a Brownian-bridge loss for inter-modality regularization; and 3) a geometric consistency loss for both intra- and inter-modality regularization. Extensive experiments are conducted on two popular multi-modal representation learning frameworks: the CLIP-based two-tower model and the ALBEF-based fusion model. We test our model on a variety of tasks including zero/few-shot image classification, image-text retrieval, visual question answering, visual reasoning, and visual entailment. Our method achieves consistent improvements over existing methods, demonstrating the effectiveness and generalizability of our proposed approach on latent modality structure regularization.

In the era of deep learning, modeling for most NLP tasks has converged to several mainstream paradigms. For example, we usually adopt the sequence labeling paradigm to solve a bundle of tasks such as POS-tagging, NER, Chunking, and adopt the classification paradigm to solve tasks like sentiment analysis. With the rapid progress of pre-trained language models, recent years have observed a rising trend of Paradigm Shift, which is solving one NLP task by reformulating it as another one. Paradigm shift has achieved great success on many tasks, becoming a promising way to improve model performance. Moreover, some of these paradigms have shown great potential to unify a large number of NLP tasks, making it possible to build a single model to handle diverse tasks. In this paper, we review such phenomenon of paradigm shifts in recent years, highlighting several paradigms that have the potential to solve different NLP tasks.

Data augmentation has been widely used to improve generalizability of machine learning models. However, comparatively little work studies data augmentation for graphs. This is largely due to the complex, non-Euclidean structure of graphs, which limits possible manipulation operations. Augmentation operations commonly used in vision and language have no analogs for graphs. Our work studies graph data augmentation for graph neural networks (GNNs) in the context of improving semi-supervised node-classification. We discuss practical and theoretical motivations, considerations and strategies for graph data augmentation. Our work shows that neural edge predictors can effectively encode class-homophilic structure to promote intra-class edges and demote inter-class edges in given graph structure, and our main contribution introduces the GAug graph data augmentation framework, which leverages these insights to improve performance in GNN-based node classification via edge prediction. Extensive experiments on multiple benchmarks show that augmentation via GAug improves performance across GNN architectures and datasets.

Machine learning techniques have deeply rooted in our everyday life. However, since it is knowledge- and labor-intensive to pursue good learning performance, human experts are heavily involved in every aspect of machine learning. In order to make machine learning techniques easier to apply and reduce the demand for experienced human experts, automated machine learning (AutoML) has emerged as a hot topic with both industrial and academic interest. In this paper, we provide an up to date survey on AutoML. First, we introduce and define the AutoML problem, with inspiration from both realms of automation and machine learning. Then, we propose a general AutoML framework that not only covers most existing approaches to date but also can guide the design for new methods. Subsequently, we categorize and review the existing works from two aspects, i.e., the problem setup and the employed techniques. Finally, we provide a detailed analysis of AutoML approaches and explain the reasons underneath their successful applications. We hope this survey can serve as not only an insightful guideline for AutoML beginners but also an inspiration for future research.