We explore algorithmic aspects of a simply transitive commutative group action coming from the class field theory of imaginary hyperelliptic function fields. Namely, the Jacobian of an imaginary hyperelliptic curve defined over $\mathbb F_q$ acts on a subset of isomorphism classes of Drinfeld modules. We describe an algorithm to compute the group action efficiently. This is a function field analog of the Couveignes-Rostovtsev-Stolbunov group action. We report on an explicit computation done with our proof-of-concept C++/NTL implementation; it took a fraction of a second on a standard computer. We prove that the problem of inverting the group action reduces to the problem of finding isogenies of fixed $\tau$-degree between Drinfeld $\mathbb F_q[X]$-modules, which is solvable in polynomial time thanks to an algorithm by Wesolowski. We give asymptotic complexity bounds for all algorithms presented in this paper.
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A set function can be extended to the unit cube in various ways; the correlation gap measures the ratio between two natural extensions. This quantity has been identified as the performance guarantee in a range of approximation algorithms and mechanism design settings. It is known that the correlation gap of a monotone submodular function is at least $1-1/e$, and this is tight for simple matroid rank functions. We initiate a fine-grained study of the correlation gap of matroid rank functions. In particular, we present an improved lower bound on the correlation gap as parametrized by the rank and girth of the matroid. We also show that for any matroid, the correlation gap of its weighted matroid rank function is minimized under uniform weights. Such improved lower bounds have direct applications for submodular maximization under matroid constraints, mechanism design, and contention resolution schemes.
Conducting safety simulations in various simulators, such as the Gazebo simulator, became a very popular means of testing vehicles against potential safety risks (i.e. crashes). However, this was not the case with security testing. Performing security testing in a simulator is very difficult because security attacks are performed on a different abstraction level. In addition, the attacks themselves are becoming more sophisticated, which directly contributes to the difficulty of executing them in a simulator. In this paper, we attempt to tackle the aforementioned gap by investigating possible attacks that can be simulated, and then performing their simulations. The presented approach shows that attacks targeting the LiDAR and GPS components of unmanned aerial vehicles can be simulated. This is achieved by exploiting vulnerabilities of the ROS and MAVLink protocol and injecting malicious processes into an application. As a result, messages with arbitrary values can be spoofed to the corresponding topics, which allows attackers to update relevant parameters and cause a potential crash of a vehicle. This was tested in multiple scenarios, thereby proving that it is indeed possible to simulate certain attack types, such as spoofing and jamming.
The machine learning modeling process conventionally culminates in selecting a single model that maximizes a selected performance metric. However, this approach leads to abandoning a more profound analysis of slightly inferior models. Particularly in medical and healthcare studies, where the objective extends beyond predictions to valuable insight generation, relying solely on a single model can result in misleading or incomplete conclusions. This problem is particularly pertinent when dealing with a set of models known as $\textit{Rashomon set}$, with performance close to maximum one. Such a set can be numerous and may contain models describing the data in a different way, which calls for comprehensive analysis. This paper introduces a novel process to explore models in the Rashomon set, extending the conventional modeling approach. We propose the $\texttt{Rashomon_DETECT}$ algorithm to detect models with different behavior. It is based on recent developments in the eXplainable Artificial Intelligence (XAI) field. To quantify differences in variable effects among models, we introduce the Profile Disparity Index (PDI) based on measures from functional data analysis. To illustrate the effectiveness of our approach, we showcase its application in predicting survival among hemophagocytic lymphohistiocytosis (HLH) patients - a foundational case study. Additionally, we benchmark our approach on other medical data sets, demonstrating its versatility and utility in various contexts. If differently behaving models are detected in the Rashomon set, their combined analysis leads to more trustworthy conclusions, which is of vital importance for high-stakes applications such as medical applications.
Quantum density matrix represents all the information of the entire quantum system, and novel models of meaning employing density matrices naturally model linguistic phenomena such as hyponymy and linguistic ambiguity, among others in quantum question answering tasks. Naturally, we argue that applying the quantum density matrix into classical Question Answering (QA) tasks can show more effective performance. Specifically, we (i) design a new mechanism based on Long Short-Term Memory (LSTM) to accommodate the case when the inputs are matrixes; (ii) apply the new mechanism to QA problems with Convolutional Neural Network (CNN) and gain the LSTM-based QA model with the quantum density matrix. Experiments of our new model on TREC-QA and WIKI-QA data sets show encouraging results. Similarly, we argue that the quantum density matrix can also enhance the image feature information and the relationship between the features for the classical image classification. Thus, we (i) combine density matrices and CNN to design a new mechanism; (ii) apply the new mechanism to some representative classical image classification tasks. A series of experiments show that the application of quantum density matrix in image classification has the generalization and high efficiency on different datasets. The application of quantum density matrix both in classical question answering tasks and classical image classification tasks show more effective performance.
Most of the existing work in one-stage referring expression comprehension (REC) mainly focuses on multi-modal fusion and reasoning, while the influence of other factors in this task lacks in-depth exploration. To fill this gap, we conduct an empirical study in this paper. Concretely, we first build a very simple REC network called SimREC, and ablate 42 candidate designs/settings, which covers the entire process of one-stage REC from network design to model training. Afterwards, we conduct over 100 experimental trials on three benchmark datasets of REC. The extensive experimental results not only show the key factors that affect REC performance in addition to multi-modal fusion, e.g., multi-scale features and data augmentation, but also yield some findings that run counter to conventional understanding. For example, as a vision and language (V&L) task, REC does is less impacted by language prior. In addition, with a proper combination of these findings, we can improve the performance of SimREC by a large margin, e.g., +27.12% on RefCOCO+, which outperforms all existing REC methods. But the most encouraging finding is that with much less training overhead and parameters, SimREC can still achieve better performance than a set of large-scale pre-trained models, e.g., UNITER and VILLA, portraying the special role of REC in existing V&L research.
Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We aim to examine the most likely transition path between equilibrium stable states of the vector field. In the small noise regime, the action functional does not involve the solution of the skeleton equation which describes the unperturbed deterministic flow of the vector field shifted by the interaction at zero distance. As a result, we are led to study the most likely transition path for a stochastic differential equation without distribution dependency. This enables the computation of the most likely transition path for these distribution-dependent stochastic dynamical systems by the adaptive minimum action method and we illustrate our approach in two examples.
Traditional approaches for manipulation planning rely on an explicit geometric model of the environment to formulate a given task as an optimization problem. However, inferring an accurate model from raw sensor input is a hard problem in itself, in particular for articulated objects (e.g., closets, drawers). In this paper, we propose a Neural Field Representation (NFR) of articulated objects that enables manipulation planning directly from images. Specifically, after taking a few pictures of a new articulated object, we can forward simulate its possible movements, and, therefore, use this neural model directly for planning with trajectory optimization. Additionally, this representation can be used for shape reconstruction, semantic segmentation and image rendering, which provides a strong supervision signal during training and generalization. We show that our model, which was trained only on synthetic images, is able to extract a meaningful representation for unseen objects of the same class, both in simulation and with real images. Furthermore, we demonstrate that the representation enables robotic manipulation of an articulated object in the real world directly from images.
We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning problem, being NP-hard in the general case of having edge weights of different signs. We propose a new method of estimating an upper bound of the objective function that we combine with the classical branch-and-bound technique to find the exact solution. We evaluate our approach on a broad range of random graphs and real-world networks. The proposed approach provided tighter upper bounds and achieved significant convergence speed improvements compared to known alternative methods.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
We introduce a generic framework that reduces the computational cost of object detection while retaining accuracy for scenarios where objects with varied sizes appear in high resolution images. Detection progresses in a coarse-to-fine manner, first on a down-sampled version of the image and then on a sequence of higher resolution regions identified as likely to improve the detection accuracy. Built upon reinforcement learning, our approach consists of a model (R-net) that uses coarse detection results to predict the potential accuracy gain for analyzing a region at a higher resolution and another model (Q-net) that sequentially selects regions to zoom in. Experiments on the Caltech Pedestrians dataset show that our approach reduces the number of processed pixels by over 50% without a drop in detection accuracy. The merits of our approach become more significant on a high resolution test set collected from YFCC100M dataset, where our approach maintains high detection performance while reducing the number of processed pixels by about 70% and the detection time by over 50%.
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