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The recent introduction of geometric partition entropy brought a new viewpoint to non-parametric entropy quantification that incorporated the impacts of informative outliers, but its original formulation was limited to the context of a one-dimensional state space. A generalized definition of geometric partition entropy is now provided for samples within a bounded (finite measure) region of a d-dimensional vector space. The basic definition invokes the concept of a Voronoi diagram, but the computational complexity and reliability of Voronoi diagrams in high dimension make estimation by direct theoretical computation unreasonable. This leads to the development of approximation schemes that enable estimation that is faster than current methods by orders of magnitude. The partition intersection ($\pi$) approximation, in particular, enables direct estimates of marginal entropy in any context resulting in an efficient and versatile mutual information estimator. This new measure-based paradigm for data driven information theory allows flexibility in the incorporation of geometry to vary the representation of outlier impact, which leads to a significant broadening in the applicability of established entropy-based concepts. The incorporation of informative outliers is illustrated through analysis of transient dynamics in the synchronization of coupled chaotic dynamical systems.

Simplicity bias, the propensity of deep models to over-rely on simple features, has been identified as a potential reason for limited out-of-distribution generalization of neural networks (Shah et al., 2020). Despite the important implications, this phenomenon has been theoretically confirmed and characterized only under strong dataset assumptions, such as linear separability (Lyu et al., 2021). In this work, we characterize simplicity bias for general datasets in the context of two-layer neural networks initialized with small weights and trained with gradient flow. Specifically, we prove that in the early training phases, network features cluster around a few directions that do not depend on the size of the hidden layer. Furthermore, for datasets with an XOR-like pattern, we precisely identify the learned features and demonstrate that simplicity bias intensifies during later training stages. These results indicate that features learned in the middle stages of training may be more useful for OOD transfer. We support this hypothesis with experiments on image data.

Robustness is a fundamental aspect for developing safe and trustworthy models, particularly when they are deployed in the open world. In this work we analyze the inherent capability of one-stage object detectors to robustly operate in the presence of out-of-distribution (OoD) data. Specifically, we propose a novel detection algorithm for detecting unknown objects in image data, which leverages the features extracted by the model from each sample. Differently from other recent approaches in the literature, our proposal does not require retraining the object detector, thereby allowing for the use of pretrained models. Our proposed OoD detector exploits the application of supervised dimensionality reduction techniques to mitigate the effects of the curse of dimensionality on the features extracted by the model. Furthermore, it utilizes high-resolution feature maps to identify potential unknown objects in an unsupervised fashion. Our experiments analyze the Pareto trade-off between the performance detecting known and unknown objects resulting from different algorithmic configurations and inference confidence thresholds. We also compare the performance of our proposed algorithm to that of logits-based post-hoc OoD methods, as well as possible fusion strategies. Finally, we discuss on the competitiveness of all tested methods against state-of-the-art OoD approaches for object detection models over the recently published Unknown Object Detection benchmark. The obtained results verify that the performance of avant-garde post-hoc OoD detectors can be further improved when combined with our proposed algorithm.

Algorithms that use derivatives of governing equations have accelerated rigid robot simulations and improved their accuracy, enabling the modeling of complex, real-world capabilities. However, extending these methods to soft and hybrid soft-rigid robots is significantly more challenging due to the complexities in modeling continuous deformations inherent in soft bodies. A considerable number of soft robots and the deformable links of hybrid robots can be effectively modeled as slender rods. The Geometric Variable Strain (GVS) model, which employs the screw theory and the strain parameterization of the Cosserat rod, extends the rod theory to model hybrid soft-rigid robots within the same mathematical framework. Using the Recursive Newton-Euler Algorithm, we developed the analytical derivatives of the governing equations of the GVS model. These derivatives facilitate the implicit integration of dynamics and provide the analytical Jacobian of the statics residue, ensuring fast and accurate computations. We applied these derivatives to the mechanical simulations of six common robotic systems: a soft cable-driven manipulator, a hybrid serial robot, a fin-ray finger, a hybrid parallel robot, a contact scenario, and an underwater hybrid mobile robot. Simulation results demonstrate substantial improvements in computational efficiency, with speed-ups of up to three orders of magnitude. We validate the model by comparing simulations done with and without analytical derivatives. Beyond static and dynamic simulations, the techniques discussed in this paper hold the potential to revolutionize the analysis, control, and optimization of hybrid robotic systems for real-world applications.

We consider the problem of estimating a high-dimensional covariance matrix from a small number of observations when covariates on pairs of variables are available and the variables can have spatial structure. This is motivated by the problem arising in demography of estimating the covariance matrix of the total fertility rate (TFR) of 195 different countries when only 11 observations are available. We construct an estimator for high-dimensional covariance matrices by exploiting information about pairwise covariates, such as whether pairs of variables belong to the same cluster, or spatial structure of the variables, and interactions between the covariates. We reformulate the problem in terms of a mixed effects model. This requires the estimation of only a small number of parameters, which are easy to interpret and which can be selected using standard procedures. The estimator is consistent under general conditions, and asymptotically normal. It works if the mean and variance structure of the data is already specified or if some of the data are missing. We assess its performance under our model assumptions, as well as under model misspecification, using simulations. We find that it outperforms several popular alternatives. We apply it to the TFR dataset and draw some conclusions.

We present a computational formulation for the approximate version of several variational inequality problems, investigating their computational complexity and establishing PPAD-completeness. Examining applications in computational game theory, we specifically focus on two key concepts: resilient Nash equilibrium, and multi-leader-follower games -- domains traditionally known for the absence of general solutions. In the presence of standard assumptions and relaxation techniques, we formulate problem versions for such games that are expressible in terms of variational inequalities, ultimately leading to proofs of PPAD-completeness.

Artificial Intelligence (AI) research often aims to develop models that can generalize reliably across complex datasets, yet this remains challenging in fields where data is scarce, intricate, or inaccessible. This paper introduces a novel approach that leverages three generative models of varying complexity to synthesize one of the most demanding structured datasets: Malicious Network Traffic. Our approach uniquely transforms numerical data into text, re-framing data generation as a language modeling task, which not only enhances data regularization but also significantly improves generalization and the quality of the synthetic data. Extensive statistical analyses demonstrate that our method surpasses state-of-the-art generative models in producing high-fidelity synthetic data. Additionally, we conduct a comprehensive study on synthetic data applications, effectiveness, and evaluation strategies, offering valuable insights into its role across various domains. Our code and pre-trained models are openly accessible at Github, enabling further exploration and application of our methodology. Index Terms: Data synthesis, machine learning, traffic generation, privacy preserving data, generative models.

This study is focused on enhancing the Haar Cascade Algorithm to decrease the false positive and false negative rate in face matching and face detection to increase the accuracy rate even under challenging conditions. The face recognition library was implemented with Haar Cascade Algorithm in which the 128-dimensional vectors representing the unique features of a face are encoded. A subprocess was applied where the grayscale image from Haar Cascade was converted to RGB to improve the face encoding. Logical process and face filtering are also used to decrease non-face detection. The Enhanced Haar Cascade Algorithm produced a 98.39% accuracy rate (21.39% increase), 63.59% precision rate, 98.30% recall rate, and 72.23% in F1 Score. In comparison, the Haar Cascade Algorithm achieved a 46.70% to 77.00% accuracy rate, 44.15% precision rate, 98.61% recall rate, and 47.01% in F1 Score. Both algorithms used the Confusion Matrix Test with 301,950 comparisons using the same dataset of 550 images. The 98.39% accuracy rate shows a significant decrease in false positive and false negative rates in facial recognition. Face matching and face detection are more accurate in images with complex backgrounds, lighting variations, and occlusions, or even those with similar attributes.

The success of AI models relies on the availability of large, diverse, and high-quality datasets, which can be challenging to obtain due to data scarcity, privacy concerns, and high costs. Synthetic data has emerged as a promising solution by generating artificial data that mimics real-world patterns. This paper provides an overview of synthetic data research, discussing its applications, challenges, and future directions. We present empirical evidence from prior art to demonstrate its effectiveness and highlight the importance of ensuring its factuality, fidelity, and unbiasedness. We emphasize the need for responsible use of synthetic data to build more powerful, inclusive, and trustworthy language models.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.