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.

Knowledge distillation transfers knowledge from large models into small models, and has recently made remarkable achievements. However, few studies has investigated the mechanism of knowledge distillation against distribution shift. Distribution shift refers to the data distribution drifts between training and testing phases. In this paper, we reconsider the paradigm of knowledge distillation by reformulating the objective function in shift situations. Under the real scenarios, we propose a unified and systematic framework to benchmark knowledge distillation against two general distributional shifts including diversity and correlation shift. The evaluation benchmark covers more than 30 methods from algorithmic, data-driven, and optimization perspectives for five benchmark datasets. Overall, we conduct extensive experiments on the student model. We reveal intriguing observations of poor teaching performance under distribution shifts; in particular, complex algorithms and data augmentation offer limited gains in many cases.

We reformulate the problem of supervised learning as learning to learn with two nested loops (i.e. The inner loop learns on each individual instance with self-supervision before final prediction. The outer loop learns the self-supervised task used by the inner loop, such that its final prediction improves. Our inner loop turns out to be equivalent to linear attention when the inner-loop learner is only a linear model, and to self-attention when it is a kernel estimator. For practical comparison with linear or self-attention layers, we replace each of them in a transformer with an inner loop, so our outer loop is equivalent to training the architecture. When each inner-loop learner is a neural network, our approach vastly outperforms transformers with linear attention on ImageNet from 224 224 raw pixels in both accuracy and FLOPs, while (regular) transformers cannot run. Test-time training (TTT) is an algorithmic framework for machine learning. The core idea is that each test instance defines its own learning problem, with its own target of generalization (Sun et al., 2020). Since the test instance comes without its label, TTT is performed with a self-supervised task such as reconstruction. Performance should improve on this particular instance for the selfsupervised task, because that is the objective optimized by TTT. But will such a process lead to better performance for the main task we actually care about? If improvement for a self-supervised task transfers to a given main task, we say the two tasks are aligned (Sun et al., 2020). In prior work, task alignment has been an art, combining ingenuity with trial and error (Gandelsman et al., 2022; Wang et al., 2023). Crucially, the amount of ingenuity in task design does not scale with more data and compute.

Planning for many manipulation tasks, such as using tools or assembling parts, often requires both symbolic and geometric reasoning. Task and Motion Planning (TAMP) algorithms typically solve these problems by conducting a tree search over high-level task sequences while checking for kinematic and dynamic feasibility. This can be inefficient as the width of the tree can grow exponentially with the number of possible actions and objects. In this paper, we propose a novel approach to TAMP that relaxes discrete-and-continuous TAMP problems into inference problems on a continuous domain. Our method, Stein Task and Motion Planning (STAMP) subsequently solves this new problem using a gradient-based variational inference algorithm called Stein Variational Gradient Descent, by obtaining gradients from a parallelized differentiable physics simulator. By introducing relaxations to the discrete variables, leveraging parallelization, and approaching TAMP as an Bayesian inference problem, our method is able to efficiently find multiple diverse plans in a single optimization run. We demonstrate our method on two TAMP problems and benchmark them against existing TAMP baselines.

We study monotone submodular maximization under general matroid constraints in the online setting. We prove that online optimization of a large class of submodular functions, namely, weighted threshold potential functions, reduces to online convex optimization (OCO). This is precisely because functions in this class admit a concave relaxation; as a result, OCO policies, coupled with an appropriate rounding scheme, can be used to achieve sublinear regret in the combinatorial setting. We show that our reduction extends to many different versions of the online learning problem, including the dynamic regret, bandit, and optimistic-learning settings.

Scientific machine learning for inferring dynamical systems combines data-driven modeling, physics-based modeling, and empirical knowledge. It plays an essential role in engineering design and digital twinning. In this work, we primarily focus on an operator inference methodology that builds dynamical models, preferably in low-dimension, with a prior hypothesis on the model structure, often determined by known physics or given by experts. Then, for inference, we aim to learn the operators of a model by setting up an appropriate optimization problem. One of the critical properties of dynamical systems is stability. However, this property is not guaranteed by the inferred models. In this work, we propose inference formulations to learn quadratic models, which are stable by design. Precisely, we discuss the parameterization of quadratic systems that are locally and globally stable. Moreover, for quadratic systems with no stable point yet bounded (e.g., chaotic Lorenz model), we discuss how to parameterize such bounded behaviors in the learning process. Using those parameterizations, we set up inference problems, which are then solved using a gradient-based optimization method. Furthermore, to avoid numerical derivatives and still learn continuous systems, we make use of an integral form of differential equations. We present several numerical examples, illustrating the preservation of stability and discussing its comparison with the existing state-of-the-art approach to infer operators. By means of numerical examples, we also demonstrate how the proposed methods are employed to discover governing equations and energy-preserving models.

In many medical image classification problems, labeled data is scarce while unlabeled data is more available. Semi-supervised learning and self-supervised learning are two different research directions that can improve accuracy by learning from extra unlabeled data. Recent methods from both directions have reported significant gains on traditional benchmarks. Yet past benchmarks do not focus on medical tasks and rarely compare self- and semi- methods together on equal footing. Furthermore, past benchmarks often handle hyperparameter tuning suboptimally. First, they may not tune hyperparameters at all, leading to underfitting. Second, when tuning does occur, it often unrealistically uses a labeled validation set much larger than the train set. Both cases make previously published rankings of methods difficult to translate to practical settings. This study contributes a systematic evaluation of self- and semi- methods with a unified experimental protocol intended to guide a practitioner with scarce overall labeled data and a limited compute budget. We answer two key questions: Can hyperparameter tuning be effective with realistic-sized validation sets? If so, when all methods are tuned well, which self- or semi-supervised methods reach the best accuracy? Our study compares 13 representative semi- and self-supervised methods to strong labeled-set-only baselines on 4 medical datasets. From 20000+ total GPU hours of computation, we provide valuable best practices to resource-constrained, results-focused practitioners.

The streaming model is an abstraction of computing over massive data streams, which is a popular way of dealing with large-scale modern data analysis. In this model, there is a stream of data points, one after the other. A streaming algorithm is only allowed one pass over the data stream, and the goal is to perform some analysis during the stream while using as small space as possible. Clustering problems (such as $k$-means and $k$-median) are fundamental unsupervised machine learning primitives, and streaming clustering algorithms have been extensively studied in the past. However, since data privacy becomes a central concern in many real-world applications, non-private clustering algorithms are not applicable in many scenarios. In this work, we provide the first differentially private streaming algorithms for $k$-means and $k$-median clustering of $d$-dimensional Euclidean data points over a stream with length at most $T$ using $poly(k,d,\log(T))$ space to achieve a constant multiplicative error and a $poly(k,d,\log(T))$ additive error. In particular, we present a differentially private streaming clustering framework which only requires an offline DP coreset or clustering algorithm as a blackbox. By plugging in existing results from DP clustering Ghazi, Kumar, Manurangsi 2020 and Kaplan, Stemmer 2018, we achieve (1) a $(1+\gamma)$-multiplicative approximation with $\tilde{O}_\gamma(poly(k,d,\log(T)))$ space for any $\gamma>0$, and the additive error is $poly(k,d,\log(T))$ or (2) an $O(1)$-multiplicative approximation with $\tilde{O}(k^{1.5} \cdot poly(d,\log(T)))$ space and $poly(k,d,\log(T))$ additive error. In addition, our algorithmic framework is also differentially private under the continual release setting, i.e., the union of outputs of our algorithms at every timestamp is always differentially private.

In a landscape characterized by heightened connectivity and mobility, coupled with a surge in cardiovascular ailments, the imperative to curtail healthcare expenses through remote monitoring of cardiovascular health has become more pronounced. The accurate detection and classification of cardiac arrhythmias are pivotal for diagnosing individuals with heart irregularities. This study underscores the feasibility of employing electrocardiograms (ECG) measurements in the home environment for real-time arrhythmia detection. Presenting a fresh application for arrhythmia detection, this paper leverages the cutting-edge You-Only-Look-Once (YOLO)v8 algorithm to categorize single-lead ECG signals. We introduce a novel loss-modified YOLOv8 model, fine-tuned on the MIT-BIH arrhythmia dataset, enabling real-time continuous monitoring. The obtained results substantiate the efficacy of our approach, with the model attaining an average accuracy of 99.5% and 0.992 mAP@50, and a rapid detection time of 0.002 seconds on an NVIDIA Tesla V100. Our investigation exemplifies the potential of real-time arrhythmia detection, enabling users to visually interpret the model output within the comfort of their homes. Furthermore, this study lays the groundwork for an extension into a real-time explainable AI (XAI) model capable of deployment in the healthcare sector, thereby significantly advancing the realm of healthcare solutions.

Recent advances in self-supervised learning and neural network scaling have enabled the creation of large models, known as foundation models, which can be easily adapted to a wide range of downstream tasks. The current paradigm for comparing foundation models involves evaluating them with aggregate metrics on various benchmark datasets. This method of model comparison is heavily dependent on the chosen evaluation metric, which makes it unsuitable for situations where the ideal metric is either not obvious or unavailable. In this work, we present a methodology for directly comparing the embedding space geometry of foundation models, which facilitates model comparison without the need for an explicit evaluation metric. Our methodology is grounded in random graph theory and enables valid hypothesis testing of embedding similarity on a per-datum basis. Further, we demonstrate how our methodology can be extended to facilitate population level model comparison. In particular, we show how our framework can induce a manifold of models equipped with a distance function that correlates strongly with several downstream metrics. We remark on the utility of this population level model comparison as a first step towards a taxonomic science of foundation models.