Uncertainty estimation for unlabeled data is crucial to active learning. With a deep neural network employed as the backbone model, the data selection process is highly challenging due to the potential over-confidence of the model inference. Existing methods resort to special learning fashions (e.g. adversarial) or auxiliary models to address this challenge. This tends to result in complex and inefficient pipelines, which would render the methods impractical. In this work, we propose a novel algorithm that leverages noise stability to estimate data uncertainty. The key idea is to measure the output derivation from the original observation when the model parameters are randomly perturbed by noise. We provide theoretical analyses by leveraging the small Gaussian noise theory and demonstrate that our method favors a subset with large and diverse gradients. Our method is generally applicable in various tasks, including computer vision, natural language processing, and structural data analysis. It achieves competitive performance compared against state-of-the-art active learning baselines.

Robotic detection of people in crowded and/or cluttered human-centered environments including hospitals, long-term care, stores and airports is challenging as people can become occluded by other people or objects, and deform due to variations in clothing or pose. There can also be loss of discriminative visual features due to poor lighting. In this paper, we present a novel multimodal person detection architecture to address the mobile robot problem of person detection under intraclass variations. We present a two-stage training approach using 1) a unique pretraining method we define as Temporal Invariant Multimodal Contrastive Learning (TimCLR), and 2) a Multimodal Faster R-CNN (MFRCNN) detector. TimCLR learns person representations that are invariant under intraclass variations through unsupervised learning. Our approach is unique in that it generates image pairs from natural variations within multimodal image sequences, in addition to synthetic data augmentation, and contrasts crossmodal features to transfer invariances between different modalities. These pretrained features are used by the MFRCNN detector for finetuning and person detection from RGB-D images. Extensive experiments validate the performance of our DL architecture in both human-centered crowded and cluttered environments. Results show that our method outperforms existing unimodal and multimodal person detection approaches in terms of detection accuracy in detecting people with body occlusions and pose deformations in different lighting conditions.

Bandit convex optimization (BCO) is a general framework for online decision making under uncertainty. While tight regret bounds for general convex losses have been established, existing algorithms achieving these bounds have prohibitive computational costs for high dimensional data. In this paper, we propose a simple and practical BCO algorithm inspired by the online Newton step algorithm. We show that our algorithm achieves optimal (in terms of horizon) regret bounds for a large class of convex functions that we call $\kappa$-convex. This class contains a wide range of practically relevant loss functions including linear, quadratic, and generalized linear models. In addition to optimal regret, this method is the most efficient known algorithm for several well-studied applications including bandit logistic regression. Furthermore, we investigate the adaptation of our second-order bandit algorithm to online convex optimization with memory. We show that for loss functions with a certain affine structure, the extended algorithm attains optimal regret. This leads to an algorithm with optimal regret for bandit LQR/LQG problems under a fully adversarial noise model, thereby resolving an open question posed in \citep{gradu2020non} and \citep{sun2023optimal}. Finally, we show that the more general problem of BCO with (non-affine) memory is harder. We derive a $\tilde{\Omega}(T^{2/3})$ regret lower bound, even under the assumption of smooth and quadratic losses.

Large-scale black-box models have become ubiquitous across numerous applications. Understanding the influence of individual training data sources on predictions made by these models is crucial for improving their trustworthiness. Current influence estimation techniques involve computing gradients for every training point or repeated training on different subsets. These approaches face obvious computational challenges when scaled up to large datasets and models. In this paper, we introduce and explore the Mirrored Influence Hypothesis, highlighting a reciprocal nature of influence between training and test data. Specifically, it suggests that evaluating the influence of training data on test predictions can be reformulated as an equivalent, yet inverse problem: assessing how the predictions for training samples would be altered if the model were trained on specific test samples. Through both empirical and theoretical validations, we demonstrate the wide applicability of our hypothesis. Inspired by this, we introduce a new method for estimating the influence of training data, which requires calculating gradients for specific test samples, paired with a forward pass for each training point. This approach can capitalize on the common asymmetry in scenarios where the number of test samples under concurrent examination is much smaller than the scale of the training dataset, thus gaining a significant improvement in efficiency compared to existing approaches. We demonstrate the applicability of our method across a range of scenarios, including data attribution in diffusion models, data leakage detection, analysis of memorization, mislabeled data detection, and tracing behavior in language models. Our code will be made available at https://github.com/ruoxi-jia-group/Forward-INF.

Traditional machine learning often assumes that the observed data of interest are supported on a linear vector space Topological deep learning (TDL) is a rapidly and can be described by a set of feature vectors. However, evolving field that uses topological features to understand there is growing awareness that, in many cases, this viewpoint and design deep learning models. This is insufficient to describe several data within the real paper posits that TDL may complement graph representation world. For example, molecules may be described more appropriately learning and geometric deep learning by graphs than feature vectors. Other examples by incorporating topological concepts, and can include three-dimensional objects represented by meshes, thus provide a natural choice for various machine as encountered in computer graphics and geometry processing, learning settings. To this end, this paper discusses or data supported on top of a complex social network open problems in TDL, ranging from practical of interrelated actors. Hence, there has been an increased benefits to theoretical foundations. For each problem, interest in importing concepts from geometry and topology it outlines potential solutions and future research into the usual machine learning pipelines to gain further opportunities.

We characterize regions of a loss surface as corridors when the continuous curves of steepest descent -- the solutions of the gradient flow -- become straight lines. We show that corridors provide insights into gradient-based optimization, since corridors are exactly the regions where gradient descent and the gradient flow follow the same trajectory, while the loss decreases linearly. As a result, inside corridors there are no implicit regularization effects or training instabilities that have been shown to occur due to the drift between gradient descent and the gradient flow. Using the loss linear decrease on corridors, we devise a learning rate adaptation scheme for gradient descent; we call this scheme Corridor Learning Rate (CLR). The CLR formulation coincides with a special case of Polyak step-size, discovered in the context of convex optimization. The Polyak step-size has been shown recently to have also good convergence properties for neural networks; we further confirm this here with results on CIFAR-10 and ImageNet.

Training Deep Neural Networks (DNNs) with small batches using Stochastic Gradient Descent (SGD) yields superior test performance compared to larger batches. The specific noise structure inherent to SGD is known to be responsible for this implicit bias. DP-SGD, used to ensure differential privacy (DP) in DNNs' training, adds Gaussian noise to the clipped gradients. Surprisingly, large-batch training still results in a significant decrease in performance, which poses an important challenge because strong DP guarantees necessitate the use of massive batches. We first show that the phenomenon extends to Noisy-SGD (DP-SGD without clipping), suggesting that the stochasticity (and not the clipping) is the cause of this implicit bias, even with additional isotropic Gaussian noise. We theoretically analyse the solutions obtained with continuous versions of Noisy-SGD for the Linear Least Square and Diagonal Linear Network settings, and reveal that the implicit bias is indeed amplified by the additional noise. Thus, the performance issues of large-batch DP-SGD training are rooted in the same underlying principles as SGD, offering hope for potential improvements in large batch training strategies.

In supervised learning of neural networks and regression models, understanding the dynamics of optimization algorithms, and in particular stochastic gradient descent (SGD), is of utmost importance. However, despite much progress in a number of directions, this still remains a highly challenging theoretical problem. A fruitful approach that allows making analytical progress consists of suitably approximating SGD by a continuous time approximation, henceforth called stochastic gradient flow (SGF). In this contribution, we build up on this approach, to develop a general formalism characterizing the dynamics of the stochastic process, and apply it to the investigation of the test risk (or generalization error) as a function of time. As is well known, the classical bias-variance trade-off has been challenged in a number of models displaying the double descent phenomenon [1, 2, 3]. Analytical derivations of double descent curves have been achieved for relatively simple models, but are limited to the use of least squares estimators (no dynamics) and pure gradient flow (GF) approximations of gradient descent (GD). The present work goes one step further by investigating the effects of stochasticity on the double descent curve. Our main contributions are summarized as follows: C1 We consider a general Itô stochastic differential equation (SDE) and represent the Markovian transition probability as a path integral, Eq. (12). A general'explicit' formula for the transition probability, Eq. (18), is derived in the limit of a small learning rate by using a Laplace approximation.

Bayesian optimization has been successfully applied to optimize black-box functions where the number of evaluations is severely limited. However, in many real-world applications, it is hard or impossible to know in advance which designs are feasible due to some physical or system limitations. These issues lead to an even more challenging problem of optimizing an unknown function with unknown constraints. In this paper, we observe that in such scenarios optimal solution typically lies on the boundary between feasible and infeasible regions of the design space, making it considerably more difficult than that with interior optima. Inspired by this observation, we propose BE-CBO, a new Bayesian optimization method that efficiently explores the boundary between feasible and infeasible designs. To identify the boundary, we learn the constraints with an ensemble of neural networks that outperform the standard Gaussian Processes for capturing complex boundaries. Our method demonstrates superior performance against state-of-the-art methods through comprehensive experiments on synthetic and real-world benchmarks.

We propose a novel neural pipeline, MSGazeNet, that learns gaze representations by taking advantage of the eye anatomy information through a multistream framework. Our proposed solution comprises two components, first a network for isolating anatomical eye regions, and a second network for multistream gaze estimation. The eye region isolation is performed with a U-Net style network which we train using a synthetic dataset that contains eye region masks for the visible eyeball and the iris region. The synthetic dataset used in this stage is procured using the UnityEyes simulator, and consists of 80,000 eye images. Successive to training, the eye region isolation network is then transferred to the real domain for generating masks for the real-world eye images. In order to successfully make the transfer, we exploit domain randomization in the training process, which allows for the synthetic images to benefit from a larger variance with the help of augmentations that resemble artifacts. The generated eye region masks along with the raw eye images are then used together as a multistream input to our gaze estimation network, which consists of wide residual blocks. The output embeddings from these encoders are fused in the channel dimension before feeding into the gaze regression layers. We evaluate our framework on three gaze estimation datasets and achieve strong performances. Our method surpasses the state-of-the-art by 7.57% and 1.85% on two datasets, and obtains competitive results on the other. We also study the robustness of our method with respect to the noise in the data and demonstrate that our model is less sensitive to noisy data. Lastly, we perform a variety of experiments including ablation studies to evaluate the contribution of different components and design choices in our solution.