Feature selection is a key step in many tabular prediction problems, where multiple candidate variables may be redundant, noisy, or weakly informative. We investigate feature selection based on Kolmogorov-Arnold Networks (KANs), which parameterize feature transformations with splines and expose per-feature importance scores in a natural way. From this idea we derive four KAN-based selection criteria (coefficient norms, gradient-based saliency, and knockout scores) and compare them with standard methods such as LASSO, Random Forest feature importance, Mutual Information, and SVM-RFE on a suite of real and synthetic classification and regression datasets. Using average F1 and $R^2$ scores across three feature-retention levels (20%, 40%, 60%), we find that KAN-based selectors are generally competitive with, and sometimes superior to, classical baselines. In classification, KAN criteria often match or exceed existing methods on multi-class tasks by removing redundant features and capturing nonlinear interactions. In regression, KAN-based scores provide robust performance on noisy and heterogeneous datasets, closely tracking strong ensemble predictors; we also observe characteristic failure modes, such as overly aggressive pruning with an $\ell_1$ criterion. Stability and redundancy analyses further show that KAN-based selectors yield reproducible feature subsets across folds while avoiding unnecessary correlation inflation, ensuring reliable and non-redundant variable selection. Overall, our findings demonstrate that KAN-based feature selection provides a powerful and interpretable alternative to traditional methods, capable of uncovering nonlinear and multivariate feature relevance beyond sparsity or impurity-based measures.

Personalized object detection aims to adapt a general-purpose detector to recognize user-specific instances from only a few examples. Lightweight models often struggle in this setting due to their weak semantic priors, while large vision-language models (VLMs) offer strong object-level understanding but are too computationally demanding for real-time or on-device applications. We introduce MOCHA (Multi-modal Objects-aware Cross-arcHitecture Alignment), a distillation framework that transfers multimodal region-level knowledge from a frozen VLM teacher into a lightweight vision-only detector. MOCHA extracts fused visual and textual teacher's embeddings and uses them to guide student training through a dual-objective loss that enforces accurate local alignment and global relational consistency across regions. This process enables efficient transfer of semantics without the need for teacher modifications or textual input at inference. MOCHA consistently outperforms prior baselines across four personalized detection benchmarks under strict few-shot regimes, yielding a +10.1 average improvement, with minimal inference cost.

Adversarial attacks on tabular data present unique challenges due to the heterogeneous nature of mixed categorical and numerical features. Unlike images where pixel perturbations maintain visual similarity, tabular data lacks intuitive similarity metrics, making it difficult to define imperceptible modifications. Additionally, traditional gradient-based methods prioritise $\ell_p$-norm constraints, often producing adversarial examples that deviate from the original data distributions. To address this, we propose a latent-space perturbation framework using a mixed-input Variational Autoencoder (VAE) to generate statistically consistent adversarial examples. The proposed VAE integrates categorical embeddings and numerical features into a unified latent manifold, enabling perturbations that preserve statistical consistency. We introduce In-Distribution Success Rate (IDSR) to jointly evaluate attack effectiveness and distributional alignment. Evaluation across six publicly available datasets and three model architectures demonstrates that our method achieves substantially lower outlier rates and more consistent performance compared to traditional input-space attacks and other VAE-based methods adapted from image domain approaches, achieving substantially lower outlier rates and higher IDSR across six datasets and three model architectures. Our comprehensive analyses of hyperparameter sensitivity, sparsity control, and generative architecture demonstrate that the effectiveness of VAE-based attacks depends strongly on reconstruction quality and the availability of sufficient training data. When these conditions are met, the proposed framework achieves superior practical utility and stability compared with input-space methods. This work underscores the importance of maintaining on-manifold perturbations for generating realistic and robust adversarial examples in tabular domains.

Decision trees are popular in survival analysis for their interpretability and ability to model complex relationships. Survival trees, which predict the timing of singular events using censored historical data, are typically built through heuristic approaches. Recently, there has been growing interest in globally optimized trees, where the overall tree is trained by minimizing the error function over all its parameters. We propose a new soft survival tree model (SST), with a soft splitting rule at each branch node, trained via a nonlinear optimization formulation amenable to decomposition. Since SSTs provide for every input vector a specific survival function associated to a single leaf node, they satisfy the conditional computation property and inherit the related benefits. SST and the training formulation combine flexibility with interpretability: any smooth survival function (parametric, semiparametric, or nonparametric) estimated through maximum likelihood can be used, and each leaf node of an SST yields a cluster of distinct survival functions which are associated to the data points routed to it. Numerical experiments on 15 well-known datasets show that SSTs, with parametric and spline-based semiparametric survival functions, trained using an adaptation of the node-based decomposition algorithm proposed by Consolo et al. (2024) for soft regression trees, outperform three benchmark survival trees in terms of four widely-used discrimination and calibration measures. SSTs can also be extended to consider group fairness.

Continual learning under adversarial conditions remains an open problem, as existing methods often compromise either robustness, scalability, or both. We propose a novel framework that integrates Interval Bound Propagation (IBP) with a hypernetwork-based architecture to enable certifiably robust continual learning across sequential tasks. Our method, SHIELD, generates task-specific model parameters via a shared hypernetwork conditioned solely on compact task embeddings, eliminating the need for replay buffers or full model copies and enabling efficient over time. To further enhance robustness, we introduce Interval MixUp, a novel training strategy that blends virtual examples represented as $\ell_{\infty}$ balls centered around MixUp points. Leveraging interval arithmetic, this technique guarantees certified robustness while mitigating the wrapping effect, resulting in smoother decision boundaries. We evaluate SHIELD under strong white-box adversarial attacks, including PGD and AutoAttack, across multiple benchmarks. It consistently outperforms existing robust continual learning methods, achieving state-of-the-art average accuracy while maintaining both scalability and certification. These results represent a significant step toward practical and theoretically grounded continual learning in adversarial settings.

Federated learning (FL) remains highly vulnerable to adaptive backdoor attacks that preserve stealth by closely imitating benign update statistics. Existing defenses predominantly rely on anomaly detection in parameter or gradient space, overlooking behavioral constraints that backdoor attacks must satisfy to ensure reliable trigger activation. These anomaly-centric methods fail against adaptive attacks that normalize update magnitudes and mimic benign statistical patterns while preserving backdoor functionality, creating a fundamental detection gap. To address this limitation, this paper introduces FeRA (Federated Representative Attention) -- a novel attention-driven defense that shifts the detection paradigm from anomaly-centric to consistency-centric analysis. FeRA exploits the intrinsic need for backdoor persistence across training rounds, identifying malicious clients through suppressed representation-space variance, an orthogonal property to traditional magnitude-based statistics. The framework conducts multi-dimensional behavioral analysis combining spectral and spatial attention, directional alignment, mutual similarity, and norm inflation across two complementary detection mechanisms: consistency analysis and norm-inflation detection. Through this mechanism, FeRA isolates malicious clients that exhibit low-variance consistency or magnitude amplification. Extensive evaluation across six datasets, nine attacks, and three model architectures under both Independent and Identically Distributed (IID) and non-IID settings confirm FeRA achieves superior backdoor mitigation. Under different non-IID settings, FeRA achieved the lowest average Backdoor Accuracy (BA), about 1.67% while maintaining high clean accuracy compared to other state-of-the-art defenses. The code is available at https://github.com/Peatech/FeRA_defense.git.

Self-supervised learning (SSL) has recently advanced through non-contrastive methods that couple an invariance term with variance, covariance, or redundancy-reduction penalties. While such objectives shape first- and second-order statistics of the representation, they largely ignore the local geometry of the underlying data manifold. In this paper, we introduce CurvSSL, a curvature-regularized self-supervised learning framework, and its RKHS extension, kernel CurvSSL. Our approach retains a standard two-view encoder-projector architecture with a Barlow Twins-style redundancy-reduction loss on projected features, but augments it with a curvature-based regularizer. Each embedding is treated as a vertex whose $k$ nearest neighbors define a discrete curvature score via cosine interactions on the unit hypersphere; in the kernel variant, curvature is computed from a normalized local Gram matrix in an RKHS. These scores are aligned and decorrelated across augmentations by a Barlow-style loss on a curvature-derived matrix, encouraging both view invariance and consistency of local manifold bending. Experiments on MNIST and CIFAR-10 datasets with a ResNet-18 backbone show that curvature-regularized SSL yields competitive or improved linear evaluation performance compared to Barlow Twins and VICReg. Our results indicate that explicitly shaping local geometry is a simple and effective complement to purely statistical SSL regularizers.

Penalty-based methods have become popular for solving bilevel optimization (BLO) problems, thanks to their effective first-order nature. However, they often require inner-loop iterations to solve the lower-level (LL) problem and small outer-loop step sizes to handle the increased smoothness induced by large penalty terms, leading to suboptimal complexity. This work considers the general BLO problems with coupled constraints (CCs) and leverages a novel penalty reformulation that decouples the upper- and lower-level variables. This yields an improved analysis of the smoothness constant, enabling larger step sizes and reduced iteration complexity for Penalty-Based Gradient Descent algorithms in ALTernating fashion (ALT-PBGD). Building on the insight of reduced smoothness, we propose PBGD-Free, a novel fully single-loop algorithm that avoids inner loops for the uncoupled constraint BLO. For BLO with CCs, PBGD-Free employs an efficient inner-loop with substantially reduced iteration complexity. Furthermore, we propose a novel curvature condition describing the "flatness" of the upper-level objective with respect to the LL variable. This condition relaxes the traditional upper-level Lipschitz requirement, enables smaller penalty constant choices, and results in a negligible penalty gradient term during upper-level variable updates. We provide rigorous convergence analysis and validate the method's efficacy through hyperparameter optimization for support vector machines and fine-tuning of large language models.

We study a matrix completion problem where both the ground truth $R$ matrix and the unknown sampling distribution $P$ over observed entries are low-rank matrices, and \textit{share a common subspace}. We assume that a large amount $M$ of \textit{unlabeled} data drawn from the sampling distribution $P$ is available, together with a small amount $N$ of labeled data drawn from the same distribution and noisy estimates of the corresponding ground truth entries. This setting is inspired by recommender systems scenarios where the unlabeled data corresponds to `implicit feedback' (consisting in interactions such as purchase, click, etc. ) and the labeled data corresponds to the `explicit feedback', consisting of interactions where the user has given an explicit rating to the item. Leveraging powerful results from the theory of low-rank subspace recovery, together with classic generalization bounds for matrix completion models, we show error bounds consisting of a sum of two error terms scaling as $\widetilde{O}\left(\sqrt{\frac{nd}{M}}\right)$ and $\widetilde{O}\left(\sqrt{\frac{dr}{N}}\right)$ respectively, where $d$ is the rank of $P$ and $r$ is the rank of $M$. In synthetic experiments, we confirm that the true generalization error naturally splits into independent error terms corresponding to the estimations of $P$ and and the ground truth matrix $\ground$ respectively. In real-life experiments on Douban and MovieLens with most explicit ratings removed, we demonstrate that the method can outperform baselines relying only on the explicit ratings, demonstrating that our assumptions provide a valid toy theoretical setting to study the interaction between explicit and implicit feedbacks in recommender systems.

In this study, a scalable online kernel learning framework is proposed for estimating bidirectional causal effects in systems characterized by mutual dependence and heteroskedasticity. Traditional causal inference often focuses on unidirectional effects, overlooking the common bidirectional relationships in real-world phenomena. Building on heteroskedasticity-based identification, the proposed method integrates a quasi-maximum likelihood estimator for simultaneous equation models with large scale online kernel learning. It employs random Fourier feature approximations to flexibly model nonlinear conditional means and variances, while an adaptive online gradient descent algorithm ensures computational efficiency for streaming and high-dimensional data. Results from extensive simulations demonstrate that the proposed method achieves superior accuracy and stability than single equation and polynomial approximation baselines, exhibiting lower bias and root mean squared error across various data-generating processes. These results confirm that the proposed approach effectively captures complex bidirectional causal effects with near-linear computational scaling. By combining econometric identification with modern machine learning techniques, the proposed framework offers a practical, scalable, and theoretically grounded solution for large scale causal inference in natural/social science, policy making, business, and industrial applications.