In this work, we study the problem of finding the maximum value of a non-negative submodular function subject to a limit on the number of items selected, a ubiquitous problem that appears in many applications, such as data summarization and nonlinear regression. We provide the first deterministic, linear-time approximation algorithms for this problem that do not assume the objective is monotone. We present three deterministic, linear-time algorithms: a single-pass streaming algorithm with a ratio of $23.313 + \epsilon$, which is the first linear-time streaming algorithm; a simpler deterministic linear-time algorithm with a ratio of $11.657$; and a $(4 + O(\epsilon ))$-approximation algorithm. Finally, we present a deterministic algorithm that obtains ratio of $e + \epsilon$ in $O_{\epsilon}(n \log(n))$ time, close to the best known expected ratio of $e - 0.121$ in polynomial time.
Adversarial examples in machine learning has emerged as a focal point of research due to their remarkable ability to deceive models with seemingly inconspicuous input perturbations, potentially resulting in severe consequences. In this study, we embark on a comprehensive exploration of adversarial machine learning models, shedding light on their intrinsic complexity and interpretability. Our investigation reveals intriguing links between machine learning model complexity and Einstein's theory of special relativity, through the concept of entanglement. More specific, we define entanglement computationally and demonstrate that distant feature samples can exhibit strong correlations, akin to entanglement in quantum realm. This revelation challenges conventional perspectives in describing the phenomenon of adversarial transferability observed in contemporary machine learning models. By drawing parallels with the relativistic effects of time dilation and length contraction during computation, we gain deeper insights into adversarial machine learning, paving the way for more robust and interpretable models in this rapidly evolving field.
Despite having the same basic prophet inequality setup and model of loss aversion, conclusions in our multi-dimensional model differs considerably from the one-dimensional model of Kleinberg et al. For example, Kleinberg et al. gives a tight closed-form on the competitive ratio that an online decision-maker can achieve as a function of $\lambda$, for any $\lambda \geq 0$. In our multi-dimensional model, there is a sharp phase transition: if $k$ denotes the number of dimensions, then when $\lambda \cdot (k-1) \geq 1$, no non-trivial competitive ratio is possible. On the other hand, when $\lambda \cdot (k-1) < 1$, we give a tight bound on the achievable competitive ratio (similar to Kleinberg et al.). As another example, Kleinberg et al. uncovers an exponential improvement in their competitive ratio for the random-order vs. worst-case prophet inequality problem. In our model with $k\geq 2$ dimensions, the gap is at most a constant-factor. We uncover several additional key differences in the multi- and single-dimensional models.
In this study, we propose a non-coherent over-the-air computation (OAC) scheme to calculate the majority vote (MV) reliably in fading channels. The proposed approach relies on modulating the amplitude of the elements of complementary sequences (CSs) based on the sign of the parameters to be aggregated. Since it does not use channel state information at the nodes, it is compatible with time-varying channels. To demonstrate the efficacy of our method, we employ it in a scenario where an unmanned aerial vehicle (UAV) is guided by distributed sensors, relying on the MV computed using our proposed scheme. We show that the proposed scheme reduces the computation error rate notably with a longer sequence length in fading channels while maintaining the peak-to-mean-envelope power ratio of the transmitted orthogonal frequency division multiplexing signals to be less than or equal to 3 dB.
With the advent of advanced multi-sensor fusion models, there has been a notable enhancement in the performance of perception tasks within in terms of autonomous driving. Despite these advancements, the challenges persist, particularly in the fusion of data from cameras and LiDAR sensors. A critial concern is the accurate alignment of data from these disparate sensors. Our observations indicate that the projected positions of LiDAR points often misalign on the corresponding image. Furthermore, fusion models appear to struggle in accurately segmenting these misaligned points. In this paper, we would like to address this problem carefully, with a specific focus on the nuScenes dataset and the SOTA of fusion models 2DPASS, and providing the possible solutions or potential improvements.
In continual learning, many classifiers use softmax function to learn confidence. However, numerous studies have pointed out its inability to accurately determine confidence distributions for outliers, often referred to as epistemic uncertainty. This inherent limitation also curtails the accurate decisions for selecting what to forget and keep in previously trained confidence distributions over continual learning process. To address the issue, we revisit the effects of masking softmax function. While this method is both simple and prevalent in literature, its implication for retaining confidence distribution during continual learning, also known as stability, has been under-investigated. In this paper, we revisit the impact of softmax masking, and introduce a methodology to utilize its confidence preservation effects. In class- and task-incremental learning benchmarks with and without memory replay, our approach significantly increases stability while maintaining sufficiently large plasticity. In the end, our methodology shows better overall performance than state-of-the-art methods, particularly in the use with zero or small memory. This lays a simple and effective foundation of strongly stable replay-based continual learning.
In this paper, we study the design and analysis of experiments conducted on a set of units over multiple time periods where the starting time of the treatment may vary by unit. The design problem involves selecting an initial treatment time for each unit in order to most precisely estimate both the instantaneous and cumulative effects of the treatment. We first consider non-adaptive experiments, where all treatment assignment decisions are made prior to the start of the experiment. For this case, we show that the optimization problem is generally NP-hard, and we propose a near-optimal solution. Under this solution, the fraction entering treatment each period is initially low, then high, and finally low again. Next, we study an adaptive experimental design problem, where both the decision to continue the experiment and treatment assignment decisions are updated after each period's data is collected. For the adaptive case, we propose a new algorithm, the Precision-Guided Adaptive Experiment (PGAE) algorithm, that addresses the challenges at both the design stage and at the stage of estimating treatment effects, ensuring valid post-experiment inference accounting for the adaptive nature of the design. Using realistic settings, we demonstrate that our proposed solutions can reduce the opportunity cost of the experiments by over 50%, compared to static design benchmarks.
In this work we consider the problem of estimating the principal subspace (span of the top r singular vectors) of a symmetric matrix in a federated setting, when each node has access to estimates of this matrix. We study how to make this problem Byzantine resilient. We introduce a novel provably Byzantine-resilient, communication-efficient, and private algorithm, called Subspace-Median, to solve it. We also study the most natural solution for this problem, a geometric median based modification of the federated power method, and explain why it is not useful. We consider two special cases of the resilient subspace estimation meta-problem - federated principal components analysis (PCA) and the spectral initialization step of horizontally federated low rank column-wise sensing (LRCCS) in this work. For both these problems we show how Subspace Median provides a resilient solution that is also communication-efficient. Median of Means extensions are developed for both problems. Extensive simulation experiments are used to corroborate our theoretical guarantees. Our second contribution is a complete AltGDmin based algorithm for Byzantine-resilient horizontally federated LRCCS and guarantees for it. We do this by developing a geometric median of means estimator for aggregating the partial gradients computed at each node, and using Subspace Median for initialization.
In this study, we propose to evaluate the use of deep learning methods for semantic classification at the sentence level to accelerate the process of corpus building in the field of humanities and linguistics, a traditional and time-consuming task. We introduce a novel corpus comprising around 2500 sentences spanning from 300 BCE to 900 CE including sexual semantics (medical, erotica, etc.). We evaluate various sentence classification approaches and different input embedding layers, and show that all consistently outperform simple token-based searches. We explore the integration of idiolectal and sociolectal metadata embeddings (centuries, author, type of writing), but find that it leads to overfitting. Our results demonstrate the effectiveness of this approach, achieving high precision and true positive rates (TPR) of respectively 70.60% and 86.33% using HAN. We evaluate the impact of the dataset size on the model performances (420 instead of 2013), and show that, while our models perform worse, they still offer a high enough precision and TPR, even without MLM, respectively 69% and 51%. Given the result, we provide an analysis of the attention mechanism as a supporting added value for humanists in order to produce more data.
In this work, the problem of shape optimization, subject to PDE constraints, is reformulated as an $L^p$ best approximation problem under divergence constraints to the shape tensor introduced in Laurain and Sturm: ESAIM Math. Model. Numer. Anal. 50 (2016). More precisely, the main result of this paper states that the $L^p$ distance of the above approximation problem is equal to the dual norm of the shape derivative considered as a functional on $W^{1,p^\ast}$ (where $1/p + 1/p^\ast = 1$). This implies that for any given shape, one can evaluate its distance from being a stationary one with respect to the shape derivative by simply solving the associated $L^p$-type least mean approximation problem. Moreover, the Lagrange multiplier for the divergence constraint turns out to be the shape deformation of steepest descent. This provides a way, as an alternative to the approach by Deckelnick, Herbert and Hinze: ESAIM Control Optim. Calc. Var. 28 (2022), for computing shape gradients in $W^{1,p^\ast}$ for $p^\ast \in ( 2 , \infty )$. The discretization of the least mean approximation problem is done with (lowest-order) matrix-valued Raviart-Thomas finite element spaces leading to piecewise constant approximations of the shape deformation acting as Lagrange multiplier. Admissible deformations in $W^{1,p^\ast}$ to be used in a shape gradient iteration are reconstructed locally. Our computational results confirm that the $L^p$ distance of the best approximation does indeed measure the distance of the considered shape to optimality. Also confirmed by our computational tests are the observations that choosing $p^\ast$ (much) larger than 2 (which means that $p$ must be close to 1 in our best approximation problem) decreases the chance of encountering mesh degeneracy during the shape gradient iteration.
In this work, we tackle the problem of bandwidth estimation (BWE) for real-time communication systems; however, in contrast to previous works, we leverage the vast efforts of prior heuristic-based BWE methods and synergize these approaches with deep learning-based techniques. Our work addresses challenges in generalizing to unseen network dynamics and extracting rich representations from prior experience, two key challenges in integrating data-driven bandwidth estimators into real-time systems. To that end, we propose Merlin, the first purely offline, data-driven solution to BWE that harnesses prior heuristic-based methods to extract an expert BWE policy. Through a series of experiments, we demonstrate that Merlin surpasses state-of-the-art heuristic-based and deep learning-based bandwidth estimators in terms of objective quality of experience metrics while generalizing beyond the offline world to in-the-wild network deployments where Merlin achieves a 42.85% and 12.8% reduction in packet loss and delay, respectively, when compared against WebRTC in inter-continental videoconferencing calls. We hope that Merlin's offline-oriented design fosters new strategies for real-time network control.