Building upon [2308.02636], this article investigates the potential constraining power of persistent homology for cosmological parameters and primordial non-Gaussianity amplitudes in a likelihood-free inference pipeline. We evaluate the ability of persistence images (PIs) to infer parameters, compared to the combined Power Spectrum and Bispectrum (PS/BS), and we compare two types of models: neural-based, and tree-based. PIs consistently lead to better predictions compared to the combined PS/BS when the parameters can be constrained (i.e., for $\{\Omega_{\rm m}, \sigma_8, n_{\rm s}, f_{\rm NL}^{\rm loc}\}$). PIs perform particularly well for $f_{\rm NL}^{\rm loc}$, showing the promise of persistent homology in constraining primordial non-Gaussianity. Our results show that combining PIs with PS/BS provides only marginal gains, indicating that the PS/BS contains little extra or complementary information to the PIs. Finally, we provide a visualization of the most important topological features for $f_{\rm NL}^{\rm loc}$ and for $\Omega_{\rm m}$. This reveals that clusters and voids (0-cycles and 2-cycles) are most informative for $\Omega_{\rm m}$, while $f_{\rm NL}^{\rm loc}$ uses the filaments (1-cycles) in addition to the other two types of topological features.

This paper presents an innovative method for predicting shape errors in 5-axis machining using graph neural networks. The graph structure is defined with nodes representing workpiece surface points and edges denoting the neighboring relationships. The dataset encompasses data from a material removal simulation, process data, and post-machining quality information. Experimental results show that the presented approach can generalize the shape error prediction for the investigated workpiece geometry. Moreover, by modelling spatial and temporal connections within the workpiece, the approach handles a low number of labels compared to non-graphical methods such as Support Vector Machines.

Dealing with missing data poses significant challenges in predictive analysis, often leading to biased conclusions when oversimplified assumptions about the missing data process are made. In cases where the data are missing not at random (MNAR), jointly modeling the data and missing data indicators is essential. Motivated by a real data application with partially missing multivariate outcomes related to leaf photosynthetic traits and several environmental covariates, we propose two methods under a selection model framework for handling data with missingness in the response variables suitable for recovering various missingness mechanisms. Both approaches use a multivariate extension of Bayesian additive regression trees (BART) to flexibly model the outcomes. The first approach simultaneously uses a probit regression model to jointly model the missingness. In scenarios where the relationship between the missingness and the data is more complex or non-linear, we propose a second approach using a probit BART model to characterize the missing data process, thereby employing two BART models simultaneously. Both models also effectively handle ignorable covariate missingness. The efficacy of both models compared to existing missing data approaches is demonstrated through extensive simulations, in both univariate and multivariate settings, and through the aforementioned application to the leaf photosynthetic trait data.

URIEL is a knowledge base offering geographical, phylogenetic, and typological vector representations for 7970 languages. It includes distance measures between these vectors for 4005 languages, which are accessible via the lang2vec tool. Despite being frequently cited, URIEL is limited in terms of linguistic inclusion and overall usability. To tackle these challenges, we introduce URIEL+, an enhanced version of URIEL and lang2vec that addresses these limitations. In addition to expanding typological feature coverage for 2898 languages, URIEL+ improves the user experience with robust, customizable distance calculations to better suit the needs of users. These upgrades also offer competitive performance on downstream tasks and provide distances that better align with linguistic distance studies.

Self-supervision is often used for pre-training to foster performance on a downstream task by constructing meaningful representations of samples. Self-supervised learning (SSL) generally involves generating different views of the same sample and thus requires data augmentations that are challenging to construct for tabular data. This constitutes one of the main challenges of self-supervision for structured data. In the present work, we propose a novel augmentation-free SSL method for tabular data. Our approach, T-JEPA, relies on a Joint Embedding Predictive Architecture (JEPA) and is akin to mask reconstruction in the latent space. It involves predicting the latent representation of one subset of features from the latent representation of a different subset within the same sample, thereby learning rich representations without augmentations. We use our method as a pre-training technique and train several deep classifiers on the obtained representation. Our experimental results demonstrate a substantial improvement in both classification and regression tasks, outperforming models trained directly on samples in their original data space. Moreover, T-JEPA enables some methods to consistently outperform or match the performance of traditional methods likes Gradient Boosted Decision Trees. To understand why, we extensively characterize the obtained representations and show that T-JEPA effectively identifies relevant features for downstream tasks without access to the labels. Additionally, we introduce regularization tokens, a novel regularization method critical for training of JEPA-based models on structured data. Self-supervised learning has caught increasing attention in recent years due to its significant success in many applications. Self-supervision is often used for pre-training to improve models' performance on downstream tasks. In short, the objective of self-supervision for representation learning is to generate meaningful representations from unlabeled data by using pseudo-label. By pushing dissimilar samples farther away while reducing the distance between samples that are alike, self-supervised learning can facilitate learning for both supervised and unsupervised tasks.

Optimization techniques are pivotal in neural network training, shaping both predictive performance and convergence efficiency. This study introduces Foxtsage, a novel hybrid optimisation approach that integrates the Hybrid FOX-TSA with Stochastic Gradient Descent for training Multi-Layer Perceptron models. The proposed Foxtsage method is benchmarked against the widely adopted Adam optimizer across multiple standard datasets, focusing on key performance metrics such as training loss, accuracy, precision, recall, F1-score, and computational time. Experimental results demonstrate that Foxtsage achieves a 42.03% reduction in loss mean (Foxtsage: 9.508, Adam: 16.402) and a 42.19% improvement in loss standard deviation (Foxtsage: 20.86, Adam: 36.085), reflecting enhanced consistency and robustness. Modest improvements in accuracy mean (0.78%), precision mean (0.91%), recall mean (1.02%), and F1-score mean (0.89%) further underscore its predictive performance. However, these gains are accompanied by an increased computational cost, with a 330.87% rise in time mean (Foxtsage: 39.541 seconds, Adam: 9.177 seconds). By effectively combining the global search capabilities of FOX-TSA with the stability and adaptability of SGD, Foxtsage presents itself as a robust and viable alternative for neural network optimization tasks.

Discovering causal relationships in time series data is central in many scientific areas, ranging from economics to climate science. Granger causality is a powerful tool for causality detection. However, its original formulation is limited by its linear form and only recently nonlinear machine-learning generalizations have been introduced. This study contributes to the definition of neural Granger causality models by investigating the application of Kolmogorov-Arnold networks (KANs) in Granger causality detection and comparing their capabilities against multilayer perceptrons (MLP). In this work, we develop a framework called Granger Causality KAN (GC-KAN) along with a tailored training approach designed specifically for Granger causality detection. We test this framework on both Vector Autoregressive (VAR) models and chaotic Lorenz-96 systems, analysing the ability of KANs to sparsify input features by identifying Granger causal relationships, providing a concise yet accurate model for Granger causality detection. Our findings show the potential of KANs to outperform MLPs in discerning interpretable Granger causal relationships, particularly for the ability of identifying sparse Granger causality patterns in high-dimensional settings, and more generally, the potential of AI in causality discovery for the dynamical laws in physical systems.

Efficient training of large-scale heterogeneous graphs is of paramount importance in real-world applications. However, existing approaches typically explore simplified models to mitigate resource and time overhead, neglecting the crucial aspect of simplifying large-scale heterogeneous graphs from the data-centric perspective. Addressing this gap, HGCond introduces graph condensation (GC) in heterogeneous graphs and generates a small condensed graph for efficient model training. Despite its efficacy in graph generation, HGCond encounters two significant limitations. The first is low effectiveness, HGCond excessively relies on the simplest relay model for the condensation procedure, which restricts the ability to exert powerful Heterogeneous Graph Neural Networks (HGNNs) with flexible condensation ratio and limits the generalization ability. The second is low efficiency, HGCond follows the existing GC methods designed for homogeneous graphs and leverages the sophisticated optimization paradigm, resulting in a time-consuming condensing procedure. In light of these challenges, we present the first Training \underline{Free} Heterogeneous Graph Condensation method, termed FreeHGC, facilitating both efficient and high-quality generation of heterogeneous condensed graphs. Specifically, we reformulate the heterogeneous graph condensation problem as a data selection issue, offering a new perspective for assessing and condensing representative nodes and edges in the heterogeneous graphs. By leveraging rich meta-paths, we introduce a new, high-quality heterogeneous data selection criterion to select target-type nodes. Furthermore, two training-free condensation strategies for heterogeneous graphs are designed to condense and synthesize other-types nodes effectively.

As data volumes expand rapidly, distributed machine learning has become essential for addressing the growing computational demands of modern AI systems. However, training models in distributed environments is challenging with participants hold skew, Non-Independent-Identically distributed (Non-IID) data. Low-Rank Adaptation (LoRA) offers a promising solution to this problem by personalizing low-rank updates rather than optimizing the entire model, LoRA-enabled distributed learning minimizes computational and maximize personalization for each participant. Enabling more robust and efficient training in distributed learning settings, especially in large-scale, heterogeneous systems. Despite the strengths of current state-of-the-art methods, they often require manual configuration of the initial rank, which is increasingly impractical as the number of participants grows. This manual tuning is not only time-consuming but also prone to suboptimal configurations. To address this limitation, we propose AutoRank, an adaptive rank-setting algorithm inspired by the bias-variance trade-off. AutoRank leverages the MCDA method TOPSIS to dynamically assign local ranks based on the complexity of each participant's data. By evaluating data distribution and complexity through our proposed data complexity metrics, AutoRank provides fine-grained adjustments to the rank of each participant's local LoRA model. This adaptive approach effectively mitigates the challenges of double-imbalanced, non-IID data. Experimental results demonstrate that AutoRank significantly reduces computational overhead, enhances model performance, and accelerates convergence in highly heterogeneous federated learning environments. Through its strong adaptability, AutoRank offers a scalable and flexible solution for distributed machine learning.

Prototype-based classification learning methods are known to be inherently interpretable. However, this paradigm suffers from major limitations compared to deep models, such as lower performance. This led to the development of the so-called deep Prototype-Based Networks (PBNs), also known as prototypical parts models. In this work, we analyze these models with respect to different properties, including interpretability. In particular, we focus on the Classification-by-Components (CBC) approach, which uses a probabilistic model to ensure interpretability and can be used as a shallow or deep architecture. We show that this model has several shortcomings, like creating contradicting explanations. Based on these findings, we propose an extension of CBC that solves these issues. Moreover, we prove that this extension has robustness guarantees and derive a loss that optimizes robustness. Additionally, our analysis shows that most (deep) PBNs are related to (deep) RBF classifiers, which implies that our robustness guarantees generalize to shallow RBF classifiers. The empirical evaluation demonstrates that our deep PBN yields state-of-the-art classification accuracy on different benchmarks while resolving the interpretability shortcomings of other approaches. Further, our shallow PBN variant outperforms other shallow PBNs while being inherently interpretable and exhibiting provable robustness guarantees.