Finding saddle points of dynamical systems is an important problem in practical applications such as the study of rare events of molecular systems. Gentlest ascent dynamics (GAD) is one of a number of algorithms in existence that attempt to find saddle points in dynamical systems. It works by deriving a new dynamical system in which saddle points of the original system become stable equilibria. GAD has been recently generalized to the study of dynamical systems on manifolds (differential algebraic equations) described by equality constraints and given in an extrinsic formulation. In this paper, we present an extension of GAD to manifolds defined by point-clouds, formulated using the intrinsic viewpoint. These point-clouds are adaptively sampled during an iterative process that drives the system from the initial conformation (typically in the neighborhood of a stable equilibrium) to a saddle point. Our method requires the reactant (initial conformation), does not require the explicit constraint equations to be specified, and is purely data-driven.
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With the advent of the big model era, the demand for data has become more important. Especially in monocular 3D object detection, expensive manual annotations potentially limit further developments. Existing works have investigated weakly supervised algorithms with the help of LiDAR modality to generate 3D pseudo labels, which cannot be applied to ordinary videos. In this paper, we propose a novel paradigm, termed as BA$^2$-Det, leveraging the idea of global-to-local 3D reconstruction for 2D supervised monocular 3D object detection. Specifically, we recover 3D structures from monocular videos by scene-level global reconstruction with global bundle adjustment (BA) and obtain object clusters by the DoubleClustering algorithm. Learning from completely reconstructed objects in global BA, GBA-Learner predicts pseudo labels for occluded objects. Finally, we train an LBA-Learner with object-centric local BA to generalize the generated 3D pseudo labels to moving objects. Experiments on the large-scale Waymo Open Dataset show that the performance of BA$^2$-Det is on par with the fully-supervised BA-Det trained with 10% videos and even outperforms some pioneer fully-supervised methods. We also show the great potential of BA$^2$-Det for detecting open-set 3D objects in complex scenes. The code will be made available. Project page: //ba2det.site .
In many industrial applications, obtaining labeled observations is not straightforward as it often requires the intervention of human experts or the use of expensive testing equipment. In these circumstances, active learning can be highly beneficial in suggesting the most informative data points to be used when fitting a model. Reducing the number of observations needed for model development alleviates both the computational burden required for training and the operational expenses related to labeling. Online active learning, in particular, is useful in high-volume production processes where the decision about the acquisition of the label for a data point needs to be taken within an extremely short time frame. However, despite the recent efforts to develop online active learning strategies, the behavior of these methods in the presence of outliers has not been thoroughly examined. In this work, we investigate the performance of online active linear regression in contaminated data streams. Our study shows that the currently available query strategies are prone to sample outliers, whose inclusion in the training set eventually degrades the predictive performance of the models. To address this issue, we propose a solution that bounds the search area of a conditional D-optimal algorithm and uses a robust estimator. Our approach strikes a balance between exploring unseen regions of the input space and protecting against outliers. Through numerical simulations, we show that the proposed method is effective in improving the performance of online active learning in the presence of outliers, thus expanding the potential applications of this powerful tool.
Machine Learning-as-a-Service, a pay-as-you-go business pattern, is widely accepted by third-party users and developers. However, the open inference APIs may be utilized by malicious customers to conduct model extraction attacks, i.e., attackers can replicate a cloud-based black-box model merely via querying malicious examples. Existing model extraction attacks mainly depend on the posterior knowledge (i.e., predictions of query samples) from Oracle. Thus, they either require high query overhead to simulate the decision boundary, or suffer from generalization errors and overfitting problems due to query budget limitations. To mitigate it, this work proposes an efficient model extraction attack based on prior knowledge for the first time. The insight is that prior knowledge of unlabeled proxy datasets is conducive to the search for the decision boundary (e.g., informative samples). Specifically, we leverage self-supervised learning including autoencoder and contrastive learning to pre-compile the prior knowledge of the proxy dataset into the feature extractor of the substitute model. Then we adopt entropy to measure and sample the most informative examples to query the target model. Our design leverages both prior and posterior knowledge to extract the model and thus eliminates generalizability errors and overfitting problems. We conduct extensive experiments on open APIs like Traffic Recognition, Flower Recognition, Moderation Recognition, and NSFW Recognition from real-world platforms, Azure and Clarifai. The experimental results demonstrate the effectiveness and efficiency of our attack. For example, our attack achieves 95.1% fidelity with merely 1.8K queries (cost 2.16$) on the NSFW Recognition API. Also, the adversarial examples generated with our substitute model have better transferability than others, which reveals that our scheme is more conducive to downstream attacks.
Privacy noise may negate the benefits of using adaptive optimizers in differentially private model training. Prior works typically address this issue by using auxiliary information (e.g., public data) to boost the effectiveness of adaptive optimization. In this work, we explore techniques to estimate and efficiently adapt to gradient geometry in private adaptive optimization without auxiliary data. Motivated by the observation that adaptive methods can tolerate stale preconditioners, we propose differentially private adaptive training with delayed preconditioners (DP^2), a simple method that constructs delayed but less noisy preconditioners to better realize the benefits of adaptivity. Theoretically, we provide convergence guarantees for our method for both convex and non-convex problems, and analyze trade-offs between delay and privacy noise reduction. Empirically, we explore DP^2 across several real-world datasets, demonstrating that it can improve convergence speed by as much as 4x relative to non-adaptive baselines and match the performance of state-of-the-art optimization methods that require auxiliary data.
We propose a new, computationally efficient, sparsity adaptive changepoint estimator for detecting changes in unknown subsets of a high-dimensional data sequence. Assuming the data sequence is Gaussian, we prove that the new method successfully estimates the number and locations of changepoints with a given error rate and under minimal conditions, for all sparsities of the changing subset. Moreover, our method has computational complexity linear up to logarithmic factors in both the length and number of time series, making it applicable to large data sets. Through extensive numerical studies we show that the new methodology is highly competitive in terms of both estimation accuracy and computational cost. The practical usefulness of the method is illustrated by analysing sensor data from a hydro power plant. An efficient R implementation is available.
Energy-efficient execution of task-based parallel applications is crucial as tasking is a widely supported feature in many parallel programming libraries and runtimes. Currently, state-of-the-art proposals primarily rely on leveraging core asymmetry and CPU DVFS. Additionally, these proposals mostly use heuristics and lack the ability to explore the trade-offs between energy usage and performance. However, our findings demonstrate that focusing solely on CPU energy consumption for energy-efficient scheduling while neglecting memory energy consumption leaves room for further energy savings. We propose JOSS, a runtime scheduling framework that leverages both CPU DVFS and memory DVFS in conjunction with core asymmetry and task characteristics to enable energy-efficient execution of task-based applications. JOSS also enables the exploration of energy and performance trade-offs by supporting user-defined performance constraints. JOSS uses a set of models to predict task execution time, CPU and memory power consumption, and then selects the configuration for the tunable knobs to achieve the desired energy performance trade-off. Our evaluation shows that JOSS achieves 21.2% energy reduction, on average, compared to the state-of-the-art. Moreover, we demonstrate that even in the absence of a memory DVFS knob, taking energy consumption of both CPU and memory into account achieves better energy savings compared to only accounting for CPU energy. Furthermore, JOSS is able to adapt scheduling to reduce energy consumption while satisfying the desired performance constraints.
We propose, analyze and implement a virtual element discretization for an interfacial poroelasticity-elasticity consolidation problem. The formulation of the time-dependent poroelasticity equations uses displacement, fluid pressure, and total pressure, and the elasticity equations are written in the displacement-pressure formulation. The construction of the virtual element scheme does not require Lagrange multipliers to impose the transmission conditions (continuity of displacement and total traction, and no-flux for the fluid) on the interface. We show the stability and convergence of the virtual element method for different polynomial degrees, and the error bounds are robust with respect to delicate model parameters (such as Lame constants, permeability, and storativity coefficient). Finally, we provide numerical examples that illustrate the properties of the scheme.
In many real-world scenarios, Reinforcement Learning (RL) algorithms are trained on data with dynamics shift, i.e., with different underlying environment dynamics. A majority of current methods address such issue by training context encoders to identify environment parameters. Data with dynamics shift are separated according to their environment parameters to train the corresponding policy. However, these methods can be sample inefficient as data are used \textit{ad hoc}, and policies trained for one dynamics cannot benefit from data collected in all other environments with different dynamics. In this paper, we find that in many environments with similar structures and different dynamics, optimal policies have similar stationary state distributions. We exploit such property and learn the stationary state distribution from data with dynamics shift for efficient data reuse. Such distribution is used to regularize the policy trained in a new environment, leading to the SRPO (\textbf{S}tate \textbf{R}egularized \textbf{P}olicy \textbf{O}ptimization) algorithm. To conduct theoretical analyses, the intuition of similar environment structures is characterized by the notion of homomorphous MDPs. We then demonstrate a lower-bound performance guarantee on policies regularized by the stationary state distribution. In practice, SRPO can be an add-on module to context-based algorithms in both online and offline RL settings. Experimental results show that SRPO can make several context-based algorithms far more data efficient and significantly improve their overall performance.
We study the multi-objective minimum weight base problem, an abstraction of classical NP-hard combinatorial problems such as the multi-objective minimum spanning tree problem. We prove some important properties of the convex hull of the non-dominated front, such as its approximation quality and an upper bound on the number of extreme points. Using these properties, we give the first run-time analysis of the MOEA/D algorithm for this problem, an evolutionary algorithm that effectively optimizes by decomposing the objectives into single-objective components. We show that the MOEA/D, given an appropriate decomposition setting, finds all extreme points within expected fixed-parameter polynomial time in the oracle model, the parameter being the number of objectives. Experiments are conducted on random bi-objective minimum spanning tree instances, and the results agree with our theoretical findings. Furthermore, compared with a previously studied evolutionary algorithm for the problem GSEMO, MOEA/D finds all extreme points much faster across all instances.
We investigate a generalized framework for estimating latent low-rank tensors in an online setting, encompassing both linear and generalized linear models. This framework offers a flexible approach for handling continuous or categorical variables. Additionally, we investigate two specific applications: online tensor completion and online binary tensor learning. To address these challenges, we propose the online Riemannian gradient descent algorithm, which demonstrates linear convergence and the ability to recover the low-rank component under appropriate conditions in all applications. Furthermore, we establish a precise entry-wise error bound for online tensor completion. Notably, our work represents the first attempt to incorporate noise in the online low-rank tensor recovery task. Intriguingly, we observe a surprising trade-off between computational and statistical aspects in the presence of noise. Increasing the step size accelerates convergence but leads to higher statistical error, whereas a smaller step size yields a statistically optimal estimator at the expense of slower convergence. Moreover, we conduct regret analysis for online tensor regression. Under the fixed step size regime, a fascinating trilemma concerning the convergence rate, statistical error rate, and regret is observed. With an optimal choice of step size we achieve an optimal regret of $O(\sqrt{T})$. Furthermore, we extend our analysis to the adaptive setting where the horizon T is unknown. In this case, we demonstrate that by employing different step sizes, we can attain a statistically optimal error rate along with a regret of $O(\log T)$. To validate our theoretical claims, we provide numerical results that corroborate our findings and support our assertions.
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