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Event-based sensors, distinguished by their high temporal resolution of 1$\mathrm{\mu s}$ and a dynamic range of 120$\mathrm{dB}$, stand out as ideal tools for deployment in fast-paced settings like vehicles and drones. Traditional object detection techniques that utilize Artificial Neural Networks (ANNs) face challenges due to the sparse and asynchronous nature of the events these sensors capture. In contrast, Spiking Neural Networks (SNNs) offer a promising alternative, providing a temporal representation that is inherently aligned with event-based data. This paper explores the unique membrane potential dynamics of SNNs and their ability to modulate sparse events. We introduce an innovative spike-triggered adaptive threshold mechanism designed for stable training. Building on these insights, we present a specialized spiking feature pyramid network (SpikeFPN) optimized for automotive event-based object detection. Comprehensive evaluations demonstrate that SpikeFPN surpasses both traditional SNNs and advanced ANNs enhanced with attention mechanisms. Evidently, SpikeFPN achieves a mean Average Precision (mAP) of 0.477 on the {GEN1 Automotive Detection (GAD)} benchmark dataset, marking a significant increase of 9.7\% over the previous best SNN. Moreover, the efficient design of SpikeFPN ensures robust performance while optimizing computational resources, attributed to its innate sparse computation capabilities.

We introduce two new classes of measures of information for statistical experiments which generalise and subsume $\phi$-divergences, integral probability metrics, $\mathfrak{N}$-distances (MMD), and $(f,\Gamma)$ divergences between two or more distributions. This enables us to derive a simple geometrical relationship between measures of information and the Bayes risk of a statistical decision problem, thus extending the variational $\phi$-divergence representation to multiple distributions in an entirely symmetric manner. The new families of divergence are closed under the action of Markov operators which yields an information processing equality which is a refinement and generalisation of the classical data processing inequality. This equality gives insight into the significance of the choice of the hypothesis class in classical risk minimization.

The combined universal probability $\mathbf{m}(D)$ of strings $x$ in sets $D$ is close to max $\m(x)$ over $x$ in $D$: their logs differ by at most $D$'s information $\mathbf{I}(D:\mathcal{H})$ about the halting sequence $\mathcal{H}$.

An adjacency sketching or implicit labeling scheme for a family $\cal F$ of graphs is a method that defines for any $n$ vertex $G \in \cal F$ an assignment of labels to each vertex in $G$, so that the labels of two vertices tell you whether or not they are adjacent. The goal is to come up with labeling schemes that use as few bits as possible to represent the labels. By using randomness when assigning labels, it is sometimes possible to produce adjacency sketches with much smaller label sizes, but this comes at the cost of introducing some probability of error. Both deterministic and randomized labeling schemes have been extensively studied, as they have applications for distributed data structures and deeper connections to universal graphs and communication complexity. The main question of interest is which graph families have schemes using short labels, usually $O(\log n)$ in the deterministic case or constant for randomized sketches. In this work we consider the resilience of probabilistic adjacency sketches against an adversary making adaptive queries to the labels. This differs from the previously analyzed probabilistic setting which is ``one shot". We show that in the adaptive adversarial case the size of the labels is tightly related to the maximal degree of the graphs in $\cal F$. This results in a stronger characterization compared to what is known in the non-adversarial setting. In more detail, we construct sketches that fail with probability $\varepsilon$ for graphs with maximal degree $d$ using $2d\log (1/\varepsilon)$ bit labels and show that this is roughly the best that can be done for any specific graph of maximal degree $d$, e.g.\ a $d$-ary tree.

Given a set $P$ of $n$ points and a set $S$ of $m$ disks in the plane, the disk coverage problem asks for a smallest subset of disks that together cover all points of $P$. The problem is NP-hard. In this paper, we consider a line-separable unit-disk version of the problem where all disks have the same radius and their centers are separated from the points of $P$ by a line $\ell$. We present an $m^{2/3}n^{2/3}2^{O(\log^*(m+n))} + O((n+m)\log (n+m))$ time algorithm for the problem. This improves the previously best result of $O(nm+ n\log n)$ time. Our techniques also solve the line-constrained version of the problem, where centers of all disks of $S$ are located on a line $\ell$ while points of $P$ can be anywhere in the plane. Our algorithm runs in $O(m\sqrt{n} + (n+m)\log(n+m))$ time, which improves the previously best result of $O(nm\log(m+n))$ time. In addition, our results lead to an algorithm of $n^{10/3}2^{O(\log^*n)}$ time for a half-plane coverage problem (given $n$ half-planes and $n$ points, find a smallest subset of half-planes covering all points); this improves the previously best algorithm of $O(n^4\log n)$ time. Further, if all half-planes are lower ones, our algorithm runs in $n^{4/3}2^{O(\log^*n)}$ time while the previously best algorithm takes $O(n^2\log n)$ time.

Given a continuous definable function $f: S \to \mathbb{R}$ on a definable set $S$, we study sublevel sets of the form $S^f_t = \{x \in S: f(x) \leq t\}$ for all $t \in \mathbb{R}$. Using o-minimal structures, we prove that the Euler characteristic of $S^f_t$ is right continuous with respect to $t$. Furthermore, when $S$ is compact, we show that $S^f_{t+\delta}$ deformation retracts to $S^f_t$ for all sufficiently small $\delta > 0$. Applying these results, we also characterize the relationship between the concepts of Euler characteristic transform and smooth Euler characteristic transform in topological data analysis.

Recent work demonstrated the existence of Boolean functions for which Shapley values provide misleading information about the relative importance of features in rule-based explanations. Such misleading information was broadly categorized into a number of possible issues. Each of those issues relates with features being relevant or irrelevant for a prediction, and all are significant regarding the inadequacy of Shapley values for rule-based explainability. This earlier work devised a brute-force approach to identify Boolean functions, defined on small numbers of features, and also associated instances, which displayed such inadequacy-revealing issues, and so served as evidence to the inadequacy of Shapley values for rule-based explainability. However, an outstanding question is how frequently such inadequacy-revealing issues can occur for Boolean functions with arbitrary large numbers of features. It is plain that a brute-force approach would be unlikely to provide insights on how to tackle this question. This paper answers the above question by proving that, for any number of features, there exist Boolean functions that exhibit one or more inadequacy-revealing issues, thereby contributing decisive arguments against the use of Shapley values as the theoretical underpinning of feature-attribution methods in explainability.

We propose and analyze exact and inexact regularized Newton-type methods for finding a global saddle point of \emph{convex-concave} unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order methods for min-max optimization is relatively limited, as obtaining global rates of convergence with second-order information is much more involved. In this paper, we examine how second-order information can be used to speed up extra-gradient methods, even under inexactness. Specifically, we show that the proposed algorithms generate iterates that remain within a bounded set and the averaged iterates converge to an $\epsilon$-saddle point within $O(\epsilon^{-2/3})$ iterations in terms of a restricted gap function. Our algorithms match the theoretically established lower bound in this context and our analysis provides a simple and intuitive convergence analysis for second-order methods without any boundedness requirements. Finally, we present a series of numerical experiments on synthetic and real data that demonstrate the efficiency of the proposed algorithms.

It is important to detect anomalous inputs when deploying machine learning systems. The use of larger and more complex inputs in deep learning magnifies the difficulty of distinguishing between anomalous and in-distribution examples. At the same time, diverse image and text data are available in enormous quantities. We propose leveraging these data to improve deep anomaly detection by training anomaly detectors against an auxiliary dataset of outliers, an approach we call Outlier Exposure (OE). This enables anomaly detectors to generalize and detect unseen anomalies. In extensive experiments on natural language processing and small- and large-scale vision tasks, we find that Outlier Exposure significantly improves detection performance. We also observe that cutting-edge generative models trained on CIFAR-10 may assign higher likelihoods to SVHN images than to CIFAR-10 images; we use OE to mitigate this issue. We also analyze the flexibility and robustness of Outlier Exposure, and identify characteristics of the auxiliary dataset that improve performance.

Neural machine translation (NMT) is a deep learning based approach for machine translation, which yields the state-of-the-art translation performance in scenarios where large-scale parallel corpora are available. Although the high-quality and domain-specific translation is crucial in the real world, domain-specific corpora are usually scarce or nonexistent, and thus vanilla NMT performs poorly in such scenarios. Domain adaptation that leverages both out-of-domain parallel corpora as well as monolingual corpora for in-domain translation, is very important for domain-specific translation. In this paper, we give a comprehensive survey of the state-of-the-art domain adaptation techniques for NMT.