A growing body of work in economics and computation focuses on the trade-off between implementability and simplicity in mechanism design. The goal is to develop a theory that not only allows to design an incentive structure easy to grasp for imperfectly rational agents, but also understand the ensuing limitations on the class of mechanisms that enforce it. In this context, the concept of OSP mechanisms has assumed a prominent role since they provably account for the absence of contingent reasoning skills, a specific cognitive limitation. For single-dimensional agents, it is known that OSP mechanisms need to use certain greedy algorithms. In this work, we introduce a notion that interpolates between OSP and SOSP, a more stringent notion where agents only plan a subset of their own future moves. We provide an algorithmic characterization of this novel class of mechanisms for single-dimensional domains and binary allocation problems, that precisely measures the interplay between simplicity and implementability. We build on this to show how mechanisms based on reverse greedy algorithms (a.k.a., deferred acceptance auctions) are algorithmically more robust to imperfectly rationality than those adopting greedy algorithms.
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Interpretability and explainability have gained more and more attention in the field of machine learning as they are crucial when it comes to high-stakes decisions and troubleshooting. Since both provide information about predictors and their decision process, they are often seen as two independent means for one single end. This view has led to a dichotomous literature: explainability techniques designed for complex black-box models, or interpretable approaches ignoring the many explainability tools. In this position paper, we challenge the common idea that interpretability and explainability are substitutes for one another by listing their principal shortcomings and discussing how both of them mitigate the drawbacks of the other. In doing so, we call for a new perspective on interpretability and explainability, and works targeting both topics simultaneously, leveraging each of their respective assets.
In deep learning applications, robustness measures the ability of neural models that handle slight changes in input data, which could lead to potential safety hazards, especially in safety-critical applications. Pre-deployment assessment of model robustness is essential, but existing methods often suffer from either high costs or imprecise results. To enhance safety in real-world scenarios, metrics that effectively capture the model's robustness are needed. To address this issue, we compare the rigour and usage conditions of various assessment methods based on different definitions. Then, we propose a straightforward and practical metric utilizing hypothesis testing for probabilistic robustness and have integrated it into the TorchAttacks library. Through a comparative analysis of diverse robustness assessment methods, our approach contributes to a deeper understanding of model robustness in safety-critical applications.
Face recognition applications have grown in parallel with the size of datasets, complexity of deep learning models and computational power. However, while deep learning models evolve to become more capable and computational power keeps increasing, the datasets available are being retracted and removed from public access. Privacy and ethical concerns are relevant topics within these domains. Through generative artificial intelligence, researchers have put efforts into the development of completely synthetic datasets that can be used to train face recognition systems. Nonetheless, the recent advances have not been sufficient to achieve performance comparable to the state-of-the-art models trained on real data. To study the drift between the performance of models trained on real and synthetic datasets, we leverage a massive attribute classifier (MAC) to create annotations for four datasets: two real and two synthetic. From these annotations, we conduct studies on the distribution of each attribute within all four datasets. Additionally, we further inspect the differences between real and synthetic datasets on the attribute set. When comparing through the Kullback-Leibler divergence we have found differences between real and synthetic samples. Interestingly enough, we have verified that while real samples suffice to explain the synthetic distribution, the opposite could not be further from being true.
To analyze the worst-case running time of branching algorithms, the majority of work in exponential time algorithms focuses on designing complicated branching rules over developing better analysis methods for simple algorithms. In the mid-$2000$s, Fomin et al. [2005] introduced measure & conquer, an advanced general analysis method, sparking widespread adoption for obtaining tighter worst-case running time upper bounds for many fundamental NP-complete problems. Yet, much potential in this direction remains untapped, as most subsequent work applied it without further advancement. Motivated by this, we present piecewise analysis, a new general method that analyzes the running time of branching algorithms. Our approach is to define a similarity ratio that divides instances into groups and then analyze the running time within each group separately. The similarity ratio is a scale between two parameters of an instance I. Instead of relying on a single measure and a single analysis for the whole instance space, our method allows to take advantage of different intrinsic properties of instances with different similarity ratios. To showcase its potential, we reanalyze two $17$-year-old algorithms from Fomin et al. [2007] that solve $4$-Coloring and #$3$-Coloring respectively. The original analysis in their paper gave running times of $O(1.7272^n)$ and $O(1.6262^n)$ respectively for these algorithms, our analysis improves these running times to $O(1.7215^n)$ and $O(1.6232^n)$. Among the two improvements, our new running time $O(1.7215^n)$ is the first improvement in the best known running time for the 4-Coloring problem since 2007.
Graph neural networks are becoming increasingly popular in the field of machine learning due to their unique ability to process data structured in graphs. They have also been applied in safety-critical environments where perturbations inherently occur. However, these perturbations require us to formally verify neural networks before their deployment in safety-critical environments as neural networks are prone to adversarial attacks. While there exists research on the formal verification of neural networks, there is no work verifying the robustness of generic graph convolutional network architectures with uncertainty in the node features and in the graph structure over multiple message-passing steps. This work addresses this research gap by explicitly preserving the non-convex dependencies of all elements in the underlying computations through reachability analysis with (matrix) polynomial zonotopes. We demonstrate our approach on three popular benchmark datasets.
We investigate the computational power of particle methods, a well-established class of algorithms with applications in scientific computing and computer simulation. The computational power of a compute model determines the class of problems it can solve. Automata theory allows describing the computational power of abstract machines (automata) and the problems they can solve. At the top of the Chomsky hierarchy of formal languages and grammars are Turing machines, which resemble the concept on which most modern computers are built. Although particle methods can be interpreted as automata based on their formal definition, their computational power has so far not been studied. We address this by analyzing Turing completeness of particle methods. In particular, we prove two sets of restrictions under which a particle method is still Turing powerful, and we show when it loses Turing powerfulness. This contributes to understanding the theoretical foundations of particle methods and provides insight into the powerfulness of computer simulations.
Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.
In pace with developments in the research field of artificial intelligence, knowledge graphs (KGs) have attracted a surge of interest from both academia and industry. As a representation of semantic relations between entities, KGs have proven to be particularly relevant for natural language processing (NLP), experiencing a rapid spread and wide adoption within recent years. Given the increasing amount of research work in this area, several KG-related approaches have been surveyed in the NLP research community. However, a comprehensive study that categorizes established topics and reviews the maturity of individual research streams remains absent to this day. Contributing to closing this gap, we systematically analyzed 507 papers from the literature on KGs in NLP. Our survey encompasses a multifaceted review of tasks, research types, and contributions. As a result, we present a structured overview of the research landscape, provide a taxonomy of tasks, summarize our findings, and highlight directions for future work.
Game theory has by now found numerous applications in various fields, including economics, industry, jurisprudence, and artificial intelligence, where each player only cares about its own interest in a noncooperative or cooperative manner, but without obvious malice to other players. However, in many practical applications, such as poker, chess, evader pursuing, drug interdiction, coast guard, cyber-security, and national defense, players often have apparently adversarial stances, that is, selfish actions of each player inevitably or intentionally inflict loss or wreak havoc on other players. Along this line, this paper provides a systematic survey on three main game models widely employed in adversarial games, i.e., zero-sum normal-form and extensive-form games, Stackelberg (security) games, zero-sum differential games, from an array of perspectives, including basic knowledge of game models, (approximate) equilibrium concepts, problem classifications, research frontiers, (approximate) optimal strategy seeking techniques, prevailing algorithms, and practical applications. Finally, promising future research directions are also discussed for relevant adversarial games.
Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.
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