Representing and processing data in spherical domains presents unique challenges, primarily due to the curvature of the domain, which complicates the application of classical Euclidean techniques. Implicit neural representations (INRs) have emerged as a promising alternative for high-fidelity data representation; however, to effectively handle spherical domains, these methods must be adapted to the inherent geometry of the sphere to maintain both accuracy and stability. In this context, we propose Herglotz-NET (HNET), a novel INR architecture that employs a harmonic positional encoding based on complex Herglotz mappings. This encoding yields a well-posed representation on the sphere with interpretable and robust spectral properties. Moreover, we present a unified expressivity analysis showing that any spherical-based INR satisfying a mild condition exhibits a predictable spectral expansion that scales with network depth. Our results establish HNET as a scalable and flexible framework for accurate modeling of spherical data.

Box-free model watermarking is an emerging technique to safeguard the intellectual property of deep learning models, particularly those for low-level image processing tasks. Existing works have verified and improved its effectiveness in several aspects. However, in this paper, we reveal that box-free model watermarking is prone to removal attacks, even under the real-world threat model such that the protected model and the watermark extractor are in black boxes. Under this setting, we carry out three studies. 1) We develop an extractor-gradient-guided (EGG) remover and show its effectiveness when the extractor uses ReLU activation only. 2) More generally, for an unknown extractor, we leverage adversarial attacks and design the EGG remover based on the estimated gradients. 3) Under the most stringent condition that the extractor is inaccessible, we design a transferable remover based on a set of private proxy models. In all cases, the proposed removers can successfully remove embedded watermarks while preserving the quality of the processed images, and we also demonstrate that the EGG remover can even replace the watermarks. Extensive experimental results verify the effectiveness and generalizability of the proposed attacks, revealing the vulnerabilities of the existing box-free methods and calling for further research.

Motivation: Real-world data often contain measurements with both continuous and discrete values. Despite the availability of many libraries, data sets with mixed data types require intensive pre-processing steps, and it remains a challenge to describe the relationships between variables. The data understanding phase is an important step in the data mining process, however, without making any assumptions on the data, the search space is super-exponential in the number of variables. Methods: We propose graphical hypergeometric networks (HNet), a method to test associations across variables for significance using statistical inference. The aim is to determine a network using only the significant associations in order to shed light on the complex relationships across variables. HNet processes raw unstructured data sets and outputs a network that consists of (partially) directed or undirected edges between the nodes (i.e., variables). To evaluate the accuracy of HNet, we used well known data sets and in addition generated data sets with known ground truth. The performance of HNet is compared to Bayesian structure learning. Results: We demonstrate that HNet showed high accuracy and performance in the detection of node links. In the case of the Alarm data set we can demonstrate on average an MCC score of 0.33 + 0.0002 (P<1x10-6), whereas Bayesian structure learning resulted in an average MCC score of 0.52 + 0.006 (P<1x10-11), and randomly assigning edges resulted in a MCC score of 0.004 + 0.0003 (P=0.49). Conclusions: HNet can process raw unstructured data sets, allows analysis of mixed data types, it easily scales up in number of variables, and allows detailed examination of the detected associations. Availability: https://erdogant.github.io/hnet/

Automated multi-document extractive text summarization is a widely studied research problem in the field of natural language understanding. Such extractive mechanisms compute in some form the worthiness of a sentence to be included into the summary. While the conventional approaches rely on human crafted document-independent features to generate a summary, we develop a data-driven novel summary system called HNet, which exploits the various semantic and compositional aspects latent in a sentence to capture document independent features. The network learns sentence representation in a way that, salient sentences are closer in the vector space than non-salient sentences. This semantic and compositional feature vector is then concatenated with the document-dependent features for sentence ranking. Experiments on the DUC benchmark datasets (DUC-2001, DUC-2002 and DUC-2004) indicate that our model shows significant performance gain of around 1.5-2 points in terms of ROUGE score compared with the state-of-the-art baselines.