OSR: Output Space Redistribution for Adaptive Label Removal in Classification Models

Label removal occurs frequently in classification systems with evolving taxonomies, where categories must be dynamically updated or eliminated. To accommodate such changes, classification models must adapt accordingly. Existing solutions, broadly categorized as retraining-based and feature-space-adjustment-based, share common limitations despite their variations, including reliance on access to original data, substantial computational and storage costs, inconsistent results, poor scalability, and degradation of model utility. To address this, we propose a novel approach that leverages statistical redistribution in the output space to approximate the post-removal confidence vectors of a retrained model. Applicable as a modular output filter, our method bypasses the burden of feature-space adjustments or loss-function convergence, alleviating scalability limitations. Furthermore, by requiring only existing labels and prior output confidences, the method potentially mitigates privacy concerns inherent to data-dependent solutions. Extensive experiments demonstrate competitive performance against full retraining, with improvements in computational efficiency and privacy preservation across several classification tasks.

IFW-BLS: Dual-Robust Broad Learning System with Intuitionistic Fuzzy Wave Loss

Broad Learning System is an efficient randomized learning model that expands network width through feature and enhancement nodes and estimates the output weights without deep backpropagation. Its standard least-squares training, however, is vulnerable in two different ways: (i) large residuals caused by noise, outliers, or corrupted labels can dominate the objective, and (ii) all samples are treated as equally reliable even when some lie in ambiguous or locally conflicting regions. This paper proposes IFW-BLS, an Intuitionistic Fuzzy Wave Broad Learning System that addresses these two sources of fragility within one optimization model. The first robustness mechanism is residual-level protection, obtained by replacing the squared loss with the bounded, smooth, and asymmetric wave loss. Boundedness prevents extreme residuals from receiving unbounded influence, while asymmetry allows positive and negative deviations to be penalized differently when the dominant error direction varies. The second mechanism is sample-level credibility control, obtained through intuitionistic fuzzy scores that combine global class-center consistency with local neighborhood conflict. The resulting model evaluates the wave loss on credibility-weighted residuals, so unreliable samples are down-weighted before the bounded loss further limits the effect of extreme errors. A Nesterov accelerated gradient based optimizer is used to solve the proposed objective, avoiding the explicit matrix inversion used in conventional BLS. Experiments on UCI benchmark datasets validate the superiority of the proposed IFW-BLS model over the baseline models; additional corruption experiments also show more stable performance than BLS under noise and outlier contamination.

RecKAN: Kolmogorov-Arnold Networks with a Learnable Recursive Polynomial Basis

Kolmogorov--Arnold Networks (KANs) replace the fixed scalar weights of a standard network with learnable univariate functions on each edge, but existing variants still fix the \emph{basis} that those functions are built from: B-splines, Chebyshev polynomials, wavelets, or Jacobi polynomials, and learn only the combination weights over it. We introduce RecKAN, which instead defines the basis itself by a second order polynomial recurrence, $R_{n+1}(x) = (ax^2+bx+c)R_n(x) + (dx+e)R_{n-1}(x)$, whose five coefficients are learned jointly with the network. We show this recurrence recovers several classical polynomial families including both kinds of Chebyshev polynomials, Fibonacci, Pell, and Jacobsthal polynomials as special cases, and prove that its degree grows linearly in $n$ exactly on the sub-family containing all of them, giving a concrete sense in which the learned basis can move beyond any fixed classical choice. Across multiple benchmark datasets spanning image, text, biomedical time series classification, and time series forecasting, RecKAN outperforms three parameter-matched KAN baselines (Chebyshev, Jacobi, and spline based) on all classification tasks and achieves the lowest MSE on the ETTh1 forecasting benchmark. Additionally, when used as a classifier head with a convolutional backbone, RecKAN achieves higher accuracy than standard MLP heads on Fashion MNIST, CIFAR-10, and SVHN. On a synthetic function fitting benchmark it tracks a sharply oscillatory target that a parameter comparable MLP under fits. We further show that the learned recurrence coefficients are interpretable: on the task requiring the most local structure, training moves the basis away from the linear degree growth regime that contains every classical family we identify, consistent with our theoretical analysis of what that structural shift enables.

Semi-Supervised Classification with Informative Missing Labels in Weibull Mixture Models

We consider semi-supervised classification from a partially classified sample arising from a two-component Weibull mixture. The feature is observed for all data, whereas some class labels are missing. The probability of a missing label is modelled as a function of classification uncertainty, giving a feature-dependent missing-at-random (MAR) mechanism that shares parameters with the Weibull-mixture classifier. The missing-label indicators can therefore provide information about the classifier in addition to the observed features and available class labels. Under a common Weibull shape, a Bayes' rule has at most one positive decision boundary, which is unique when the rule is nonconstant; under unequal shapes, it can have two. We characterise these decision regions, derive the Fisher information for the classifier after adjustment for nuisance parameters in the missingness model, and obtain a decision-boundary expansion of the expected error rate of the plug-in sample rule relative to the Bayes error. The expansion yields classification-specific asymptotic relative efficiency formulas for the one- and two-boundary cases and shows that a positive-definite increase in Fisher information is sufficient, but not necessary, for a smaller first-order expected error rate. Numerical studies and a semi-synthetic analysis based on hard-drive failure data illustrate potential reductions in expected error rate and improvements in decision-boundary estimation from modelling feature-dependent label missingness.

A convolutional framework for detecting event-driven dynamics in energy price series

This paper develops a general convolutional neural network (CNN) framework for detecting heterogeneous event-driven dynamics in univariate time series windows. We show that the induced CNN class exactly represents classifiers based on range, maximum drawup, maximum drawdown and slope change, and uniformly approximates realised volatility and autoregressive explosiveness on compact domains. We further establish error bounds for representative rules in finite samples and an oracle inequality for learning across them. Simulations show that the proposed model can match or outperform classifiers based on individual statistics as the training sample grows. In an application to six daily energy price series, a hierarchical CNN distinguishes event windows and event families. Applied without retraining to observations withheld after 20 February 2026, the fitted model identifies predominantly geopolitical dynamics in several oil and refined product series around the outbreak of the 2026 Iran war, while distinguishing a contemporaneous natural gas spike associated with weather.

Residual-Guided Randomized Neural Networks

Randomized neural networks enable fast and analytically tractable training by fixing the input to hidden layer parameters at random and learning the output weights in closed form; however, their performance critically depends on a single uninformed draw of hidden units. This one shot and task uninformed feature construction often leads to redundant representations and suboptimal utilization of model capacity. To address this limitation, we propose a simple and broadly applicable residual guided procedure that greedily constructs the hidden layer using a closed form residual decrease criterion. At each stage, we (i) generate a pool of random candidate units, (ii) score each candidate by the exact reduction it induces in the ridge regularized objective, (iii) select the top k units, and (iv) refit the readout in closed form using the standard design with direct input links. This procedure yields a progressive training process with a guaranteed monotonic decrease of the training objective. The method is model agnostic: only the candidate generation is architecture specific, while the scoring selection refitting loop is shared across models. Extensive experiments on 71 benchmark datasets from the UCI repository, covering both binary and multiclass classification tasks, demonstrate that the proposed residual-guided models consistently outperform their baseline counterparts in terms of accuracy, stability, and overall ranking performance.

Curvature-Aware Radius Shrinkage for Adaptive Nearest Neighbor Classification

Nearest neighbor classification relies fundamentally on how locality is defined, yet conventional $k$-NN imposes the same neighborhood cardinality throughout the feature space. This assumption can be inadequate for data whose local geometry varies substantially across the underlying manifold. We introduce Curvature-Aware Radius Shrinkage for Adaptive Nearest Neighbor Classification (CARSANN), a geometry-driven framework that adapts the spatial support of each neighborhood according to local geometric complexity. CARSANN first estimates intrinsic dimensionality using TwoNN and constructs an intrinsic representation through principal component analysis. Local mean curvature is then estimated using a shape-operator-based formulation and controls neighborhood scale: highly curved regions receive stronger radius shrinkage, whereas approximately flat regions retain broader spatial support. Unlike methods that modify only the number of neighbors or the local metric, CARSANN explicitly adapts the spatial extent of local evidence. Experiments on more than 70 real-world OpenML datasets show that CARSANN consistently improves upon standard $k$-NN and is competitive with adaptive nearest-neighbor methods. In a controlled comparison using the same base neighborhood size, CARSANN achieves higher balanced accuracy on 40 of 45 datasets, increasing mean balanced accuracy from 0.6506 to 0.7528. The advantage also persists against $k$-NN with fixed $k=5$. Friedman and Nemenyi tests confirm that the improvements are statistically significant. These results indicate that local manifold curvature can serve as an effective geometric control variable for adapting neighborhood support, providing a complementary paradigm to cardinality-based nearest-neighbor adaptation.

EXAONE Tabular 1.0 : Technical Report

EXAONE Tabular is a compact tabular foundation model family for classification and regression via in-context learning, producing predictions without dataset-specific gradient updates. Pretrained exclusively on a synthetic structural-causal-model (SCM) prior, its central contribution is an architecture-centered redesign of tabular in-context learning. Rather than compressing features into a fixed row embedding before a separate row-level learner, EXAONE Tabular interleaves feature-axis attention within each item with support-conditioned item-axis attention within each feature at every Transformer layer, mediated by item-summary and feature-summary tokens. Across four public benchmarks, EXAONE Tabular combines strong predictive performance with high efficiency. On TabArena, its 20.81M-parameter classification model ranks first overall, surpassing tuned ensembles and 4-hour AutoML pipelines, while regression reaches the performance regime of the 1.64B-parameter TabFM at roughly 1/11 the inference cost. On BCCO and TALENT, EXAONE Tabular ranks second in classification and first in regression. On ScoringBench, it achieves the best mean rank for both point-estimation and predictive-distribution quality, leading the $R^2$, RMSE, and CRPS evaluations. Together, these results establish EXAONE Tabular as a state-of-the-art compact tabular foundation model family, combining strong predictive performance across classification, point regression, and probabilistic regression with an efficient model design.

A Heterogeneous Mixture of Experts Framework for Interpretable Machine Learning

Mixture-of-Experts (MoE) models provide a flexible framework for partitioning complex prediction problems into simpler local learning tasks through an input-dependent gating mechanism. Existing interpretable MoE approaches, such as Mixture of Decision Trees (MoDT), achieve transparency by employing homogeneous decision-tree experts, but this restricts the model to a single inductive bias across all regions of the feature space. We extend the MoDT framework by introducing heterogeneous expert families comprising decision trees, linear support vector machines, and quadratic discriminant analysis under a common probabilistic gating mechanism. To ensure coherent likelihood-based inference, non-probabilistic experts are calibrated to produce conditional class probabilities, allowing parameter estimation within the generalized Expectation-Maximization framework of MoDT. We further establish theoretical monotone ascent guarantees for the proposed heterogeneous gating updates, providing a justification for the optimization procedure. Experiments on a diverse collection of synthetic and real-world benchmark datasets demonstrate that the proposed framework adaptively specializes experts according to local data geometry, yielding interpretable expert assignments while achieving predictive performance competitive with homogeneous MoDT and Random Forests. The proposed approach combines interpretability, adaptive inductive bias selection, and probabilistic coherence within a unified mixture-of-experts framework.

Learning from Uncertainty-dependent Missing Labels for Semi-supervised Classification

Missing labels are usually regarded as a source of information loss in classification. We study a semi-supervised setting in which the probability of label missingness depends on the observed features through posterior classification uncertainty. In this setting, the missingness indicator is not only a record of an unobserved label, but also an observable signal generated by a mechanism linked to the classifier. We develop a likelihood-based information theory for such uncertainty-dependent missing labels. Under correct specification, we derive a Fisher-information decomposition that separates a partial-labeling component from a nonnegative mechanism-curvature term. Under joint misspecification of the label model and the missingness mechanism, we obtain the corresponding Godambe--Eicker--Huber--White sensitivity and sandwich-covariance partitions. We also clarify the relevant complete-data benchmark: favorable missingness can increase information relative to ordinary fully labeled or budget-matched non-informative labeling baselines, but cannot exceed the information in the augmented experiment in which labels and mechanism indicators are both observed. For plug-in classifiers, we connect the information decomposition to margin-based excess-risk bounds. In regular two-component mixture settings this yields the parametric \(n^{-1}\) excess-risk rate, with constants determined by the nuisance-adjusted information in discriminant directions. Gaussian-mixture calculations and a medical diagnosis example illustrate how uncertainty-dependent labeling mechanisms can improve estimation and classification under a fixed labeling budget.

DICS: Data-Informed Centroid Splitting for Decision Tree Classifiers

Decision tree-based models are widely used in machine learning due to their interpretability and strong empirical performance. However, training decision trees can be computationally expensive, particularly for large and high-dimensional datasets, largely due to the exhaustive search over candidate splits at each node. To improve computational efficiency, we propose Data-Informed Centroid Splitting (DICS), a clustering-based framework that constructs a compact and informative set of candidate splits using data-driven priors. By incorporating class-aware structure, DICS significantly reduces the split search space for classification tasks while preserving predictive performance. We further provide theoretical analysis showing that under the stated assumptions, DICS does not degrade the performance of classification trees compared to exhaustive split search. DICS can be incorporated into classification trees, random forests, and gradient-boosting models. Extensive experiments demonstrate that DICS achieves comparable accuracy while substantially reducing training time across synthetic and benchmark datasets, highlighting the benefit of integrating data-informed priors into split selection for scalable classification tree learning.

Sparse Prototype Code Underlies Classification and Prediction Across Modalities

Neural representations have become a central tool for studying the internal mechanisms of modern AI models, yet their complex high-dimensional structure makes them difficult to interpret. We show that classification tasks give rise to a universal representational geometry, shared across state-of-the-art models in vision, audio, and language processing. The key structure is that within-class variability is not random in representation space. Instead, its classifier-relevant component has strong and structured correlations with the class's own centroid and with the centroids of its competing classes. Building on this observation, we derive an analytical mean-field theory governed mainly by the variability along true-class and rival-class centroid coordinates, together with a global renormalization of the class radius that compensates for the non-Gaussian statistics of real representations. The theory accurately predicts classification accuracy across architectures and modalities. The relevant geometric quantities improve systematically with model scale, mirroring the observed gains in accuracy. A striking feature of the theory is its sparsity: accurate prediction requires only a small set of centroid coordinates associated with the true class and its strongest rivals - connecting our framework to sparse-feature extraction approaches such as sparse autoencoders. Together, these results provide a parsimonious predictive theory of neural representations and suggest that classification in deep networks is governed by a sparse, centroid-aligned structure embedded within the full high-dimensional representation space.

Robust Dempster-Shafer Evidence Fusion with Chaos-Conflict Measurement and Historical-Experience Weighting

Multi-source evidence fusion under Dempster-Shafer theory faces two persistent challenges: existing conflict measures assess inter-evidence inconsistency and intra-evidence uncertainty independently, yielding incomplete evaluations, and current fusion methods evaluate evidence sources exclusively through instantaneous comparisns without exploiting their long-term reliability across diverse decision contexts. This paper proposes a unified evidence reasoning framework that addresses both limitations. Specifically, a chaos-conflict measurement is introduced to jointly quantify cross-evidence conflict and intra-evidence non-specificity, with five formally proven properties ensuring consistent assessment. A historical experience driven weighting scheme partitions the decision space via spectral clustering and applies regret theory to compute context-specific reliability profiles from past fusion outcomes. These mechanisms feed into a hybrid combination rule that adaptively balances uncertainty preservation against weighted consensus, controlled by the global conflict level, followed by a belief-interval decision strategy that enables robust classification without discarding epistemic uncertainty. Experiments on 16 real-world benchmark datasets demonstrate that the proposed framework achieves an average F1 score of 85.78 and a mean AUC of 93.30, outperforming eight DST-based baselines and three gradient boosting methods. Ablation analysis confirms the contribution of each component we proposed. The framework offers an effective approach for adaptive evidence fusion in multi-source decision making.

Adaptive $k$ Nearest Neighbors Classifier via Granular Ball Computing

The $k$-Nearest Neighbor~(KNN) algorithm is widely used across various tasks. The selection of the $k$ value is a key issue because it significantly impacts performance. In this paper, an adaptive and efficient KNN approach via granular-ball computing is proposed. The method consists of two stages. \textcolor{black}{In the training stage, the dataset is first coarsely partitioned to reduce the complexity of data distributions within a granular ball, and then the Fisher criterion is introduced to control ball splitting and stopping, yielding a multi-granularity granular ball representation. In the prediction stage, the nearest granular ball is first located through a weighted distance mechanism, and an adaptive neighborhood is then constructed around the test sample. The effective $k$ value is dynamically determined by the actual number of samples contained in this neighborhood. The neighborhood induced by the nearest granular ball provides more stable local group information, thereby improving robustness against noise and local perturbations.} Experimental results demonstrate that the proposed method outperforms existing KNN variants across multiple datasets in terms of both accuracy and efficiency. The code has been open-sourced for reproducibility: https://github.com/lianxiaoyu724/Adaptive-GBKNN.

Robust Dual-Model Collaborative Random Vector Functional Link Network

Random vector functional link (RVFL) networks are lightweight and fast neural models that offer efficient training and strong generalization through randomized hidden-layer weights and direct input-output connections. However, conventional RVFL models are sensitive to noisy labels, outliers, and imbalanced data, which limits their performance in real-world applications. To address these challenges, we propose the kernel risk-sensitive mean p-power based RVFL (KRPRVFL) model, which integrates the computational efficiency of RVFL with the robustness of the kernel risk-sensitive mean p-power (KRP) criterion. By replacing the standard least-squares objective with a KRP-based loss, KRPRVFL adaptively reduces the influence of corrupted or unreliable samples during training, resulting in improved stability and generalization. Additionally, a collaborative learning mechanism is introduced to enable adaptive interaction among model components, further enhancing robustness in complex and noisy environments. The proposed framework also leverages kernel-induced feature mapping to capture nonlinear relationships without requiring explicit hidden-layer selection, maintaining both efficiency and scalability. Extensive experiments on UCI and KEEL benchmark datasets demonstrate that KRPRVFL consistently outperforms baseline models in terms of accuracy, robustness, and statistical significance, highlighting its effectiveness as a fast, scalable, and reliable solution for challenging classification tasks.

Sparse and robust geometric twin support vector machine via asymmetric RoBoSS loss function

In real-world scenarios, the training data usually contains redundant features, label noise and feature noise, which provide severe challenges for the efficiency of machine learning methods. Since standard support vector machine (SVM) adopts $l_2$-norm penalty and hinge loss function, it lacks the ability of selecting significant features and is sensitive to noise. To address these issues, this paper proposes a novel asymmetric, robust, bounded, sparse and smooth (aR) loss function for $l_1$-norm penalized geometric twin SVM (aRSGTSVM) to handle classification and regression tasks. The $l_1$-norm penalty can achieve the feature selection. The proposed aR loss function can not only effectively mitigate the impact of label noise, but also significantly enhance the stability to resampling noise, i.e., the zero-mean feature noise around the boundary hyperplanes. Furthermore, a statistical analysis of the robustness of aRSGTSVM was also conducted using the influence function. Since aRSGTSVM involves nonconvex and nonsmooth optimization, we develop a fast and stable proximal gradient descent based solving algorithm. Compared with related state-of-the-art methods, experimental results demonstrate the superiority of the proposed aRSGTSVM on both synthetic and UCI datasets. Furthermore, we apply aRSGTSVM to index tracking tasks, where results for tracking the different indices in the China stock market show that it can achieve satisfactory performance.

Recent advances in weakly supervised learning: New supervision paradigms, assumption relaxations, and practical solutions

Deep learning has achieved great success in recent years thanks to the availability of high-quality, well-annotated training data. However, this requirement is often not met in real-world applications. Weakly supervised learning aims to train an accurate model with incomplete, inexact, or inaccurate supervision. In this chapter, we will discuss recent advances in this field, including new supervision paradigms, relaxed assumptions, and practical solutions. First, we introduce a new weakly supervised binary classification problem called confidence-difference classification and propose consistent approaches to solve it. Next, we investigate complementary-label learning, a weakly supervised multi-class classification problem. Our proposed approaches are based on more relaxed assumptions about the data generation process than existing consistent approaches. Lastly, we present an evaluation framework for partial-label learning, another popular multi-class weakly supervised learning problem, in order to promote fair and realistic evaluation of algorithms in this field.

Bridging the Gap Between Hyperdimensional Computing and Kernel Methods via the Nyström Method

Hyperdimensional computing (HDC) is an approach from the cognitive science literature for solving information processing tasks using data represented as high-dimensional random vectors. The technique has a rigorous mathematical backing, and is easy to implement in energy-efficient and highly parallel hardware like FPGAs and "processing-in-memory" architectures. The effectiveness of HDC in machine learning largely depends on how raw data is mapped to high-dimensional space. In this work, we propose NysHD, a new method for constructing this mapping that is based on the Nyström method from the literature on kernel approximation. Our approach provides a simple recipe to turn any user-defined positive-semidefinite similarity function into an equivalent mapping in HDC. There is a vast literature on the design of such functions for learning problems. Our approach provides a mechanism to import them into the HDC setting, expanding the types of problems that can be tackled using HDC. Empirical evaluation against existing HDC encoding methods shows that NysHD can achieve, on average, 11% and 17% better classification accuracy on graph and string datasets respectively.

Minimax Optimal Early-Stopped Gradient Descent for Gaussian Mixture Classification

In overparameterised classification, training data can be linearly separable even when the underlying distribution is not. In this setting, gradient descent (GD) on the logistic loss diverges in norm while converging in direction to a max-margin interpolating classifier, whose implicit bias can be statistically suboptimal. In this work, we show that early stopping can overcome this suboptimality: in a Gaussian mixture model with label-flipping noise, GD stopped at an appropriate oracle time achieves minimax-optimal excess zero-one risk for covariance spectra with fast and continuous decay, including polynomial and exponential spectral decays. Our analysis combines a sharp upper bound for the early-stopped iterate with a matching statistical lower bound over arbitrary classifiers, yielding optimal rates that are validated by experiments. A central technical contribution is a new calibration result that converts excess logistic risk into excess zero-one risk; it handles the model misspecification induced by the label-flipping noise, and removes the square-root rate in standard bounds. We also establish a lower bound for linear interpolators, showing that interpolation can require exponentially more samples than early stopping to achieve the same excess risk.

Statistical comparisons of time-series feature sets on classification tasks

In recent years, numerous open-source software libraries have been developed for computing sets of features from univariate time series. The type and number of features vary across these feature sets, which have been constructed with varying disciplinary perspectives on quantifying structure in time-series data. To date, the relative strengths and weaknesses of these feature sets on time-series classification problems remains largely unexplored. Here we aimed to understand the relative performance of six open-source feature sets and three baseline feature sets (based on distributional and/or basic spectral structure) across 124 univariate time-series classification problems using a normalization-based approach to problem-level benchmarking that better indexes the relative strengths and weaknesses of different algorithms compared to prior rank-based approaches. Despite their dramatic differences in size, composition, and computation time, we found that feature sets performed relatively similarly overall (85.3% of pairwise comparisons resulted in ties), with the largest feature set, tsfresh, exhibiting the strongest overall performance (29.03% wins across all pairwise comparisons against other feature sets). We also highlighted specific problems on which the specific composition of a given feature set gave it a substantial performance advantage or disadvantage, and problems where simple baselines comprised of Fourier coefficients and quantiles were sufficient to achieve strong performance. Our results demonstrate the need to consider problem-level performance when benchmarking time-series feature sets, and highlight the importance of feature make-up in driving relative classification performance.

Search Strategies for Optimal Classification and Regression Trees

Optimal decision trees (ODTs) are compact, interpretable machine learning models that globally optimize a given objective, but their scalability remains challenging. While recent work has proposed a variety of search strategies to improve scalability, the precise contribution of each strategy remains unclear. To address this gap, we introduce a general algorithmic framework for ODTs that instantiates previously used search strategies and enables the definition of new ones. This provides a common lens through which to understand and compare different strategies, which we use to empirically investigate the effect of 18 search strategies. Compared to the state of the art, the best strategy in our evaluation achieves significantly better anytime performance for classification, and improves runtime by more than an order of magnitude for regression.

Voronoi Histograms for Adaptive Vectorization of Expected Persistence Diagrams

Persistence Diagram (PD) is known to capture point cloud topology effectively, but its computation has high time complexity. Expected Persistence Diagram (EPD) has been developed to reduce the time cost by studying the topology of multiple subsets of a point cloud and it serves as a distribution of topological features. Existing EPD vectorizations often rely on predefined point transformations, such as Gaussian or landscape functions. We study an alternative discretization based on Voronoi histograms, which trades smooth functional approximation for adaptive partition-based counting. We propose to use Voronoi Diagram-based histogram as the vectorization of EPD, without imposing an explicit smooth point transformation model. Under stated separation and normalization conditions, we establish stability bounds and characterize when the histogram representation preserves Wasserstein-scale variation. We demonstrate the effectiveness of our proposed representation on real-world datasets which have significant topological features for classification and dimensionality reduction tasks.

Understanding Context Sampling in TabPFN on Small Tabular Datasets

TabPFN performs classification through in-context learning: it conditions on a set of labeled training rows (the context, or prototypes) and predicts test labels without gradient updates. On small tabular datasets, practitioners must still choose the context size and which rows constitute the context. We study how these choices affect prediction stability, accuracy, and selection cost using repeated context sampling on 15 OpenML datasets. Specifically, we investigate (i) whether larger contexts reduce prediction variability across random draws, (ii) whether accuracy depends on preserving the training distribution or on feature-space coverage, and (iii) whether expensive selection methods such as K-Means and farthest-point sampling provide benefits over uniform random sampling. We find that larger contexts are both more accurate and substantially more stable, with AUC coefficient of variation decreasing from roughly 6 to 18% at k=16 to 1 to 4% at larger context sizes on datasets with room for improvement. Although accuracy correlates with distribution representativeness in random contexts, controlled experiments show that matching feature means alone can reduce accuracy by up to 0.5 AUC because it reduces context diversity. Mixed-effects analysis identifies diversity and coverage, rather than feature-mean matching, as the stronger predictor of accuracy (diversity beta=+0.23, p=3x10^-12; feature-mean shift beta=-0.01, p=0.71). K-Means and farthest-point sampling achieve similar accuracy to random selection while requiring two to three orders of magnitude more selection cost. These results show that random sampling succeeds because it provides feature-space coverage in expectation, not because it reproduces the underlying data distribution.

Multiclass Classification without Labels via Posterior Simplex Geometry

In many classification problems, reliable instance-level labels are unavailable. However, it is often possible to construct weakly enriched unlabeled samples: datasets selected by different cuts, sources, populations, or experimental conditions that change latent class proportions without revealing them. Classification without Labels (CWoLa) shows that, in the binary case ($K=2$), a classifier trained to distinguish two impure mixtures with different class proportions can recover an optimal class discriminator without knowing the mixture proportions. We extend this principle to multiclass learning from several unlabeled mixtures ($K>2$), where the learner observes only mixture identity and neither latent class labels nor class-prior matrices. We prove that, for a multiclass mixture model, the Bayes-optimal mixture classifier $g^\star$ maps data points into a $(K-1)$-simplex embedded in mixture-posterior space. The $K$ vertices of this simplex are induced by the latent classes through the unknown mixing matrix. Leveraging this geometry, we propose prior-free procedures that train a standard classifier to distinguish mixture identities and then extract latent class structure using either post-hoc simplex fitting or a bottleneck architecture. Experiments on MNIST, CIFAR-10, and Galaxy10 DECaLS show that mixture identity alone can recover latent classes and their fractions in the mixture. By narrowing the gap between weakly supervised and fully supervised performance, we provide a mathematically grounded, scalable tool for multiclass discovery in label-scarce domains.

Joint Flow Matching for Generator-Consistent Classification

We introduce Joint Flow Matching (JFM), a training framework for continuous normalising flows over multiple variables. Standard flow matching transports variables from noise to data simultaneously, offering no natural mechanism for forward and reverse conditional inference from a shared joint model. JFM resolves this by assigning opposite roles to each variable at the temporal endpoints. We prove that JFM produces a consistent joint distribution where that forward or reverse integration are conditionals of the same joint. We explore this consistency in the context of joint classification and generation as the basis for interpretability in discriminative-generative models. We validate JFM on conditional datasets producing competitive accuracy with inherently well-calibrated confidence scores without post-hoc calibration, and classifier-consistent image generation.

XGRVFL-MV: Residual-Coupled Graph-Embedded Multi-View Random Vector Functional Link Network with FleXi Guardian Loss

Random Vector Functional Link (RVFL) networks provide an efficient randomized learning framework for classification. Existing multi-view RVFL methods utilize complementary information from multiple views. However, preserving view-specific geometric structure, limiting the influence of large prediction residuals, and modeling relationships between multiple views remain challenging. This paper proposes a Residual-Coupled Graph-Embedded Multi-View RVFL model with fleXi guardian loss (XGRVFL-MV) for multi-view classification. The proposed model constructs RVFL representation for each view, incorporates graph embedding with intrinsic and penalty graphs constructed using the Local Fisher Discriminant Analysis weighting scheme. It also uses the bounded and asymmetric FleXi Guardian (XG) loss for residual learning. A residual-coupling term is introduced to encourage consistency among view-specific prediction residuals while preserving view-specific representations. The resulting optimization problem is solved using an inversion-free first-order optimization procedure based on Nesterov accelerated gradient descent. We evaluate the proposed model on UCI, KEEL, AwA, and Corel5k benchmark datasets. Experimental results, together with statistical analyses and hyperparameter sensitivity analyses, show that XGRVFL-MV achieves competitive classification performance compared with the baseline methods across the evaluated benchmark datasets.

Robust Multi-View Classification under Noisy Supervision via Global Anchor Consensus

In recent years, multi-view learning has attracted increasing attention, as it integrates the complementary information of heterogeneous views. Most existing multi-view classification methods rely on accurate annotations to guarantee performance. However, noisy labels are ubiquitous in practice due to imperfect annotation, and the refinement signals that existing methods derive from models trained on such noisy supervision can gradually lose their reliability. To deal with this problem, we propose a novel Global Anchor-based Label Auditing method (GALA) for multi-view classification to resist the negative impact of noisy labels. Specifically, we construct a global anchor for each class in every view, which aggregates the samples of the whole class and thus offers a stable reference insensitive to individual predictions. Then, each view measures how close an instance is to the anchor of its observed label relative to the nearest competing anchor, and the per-view evaluations are fused with the classifier confidence into a cross-view audit score. Based on the audit scores, suspicious samples are assigned small weights, and an adaptive correction strategy rewrites a label only when the anchor-based candidate agrees with the classifier prediction. Finally, the corrected labels in turn refine the anchors and supervise noise-robust representation learning. Extensive experiments on six datasets demonstrate that GALA outperforms eight state-of-the-art methods, especially under high noise rates.

Robust Losses from Univariate Base Functions for Noisy-Label Learning

Learning with noisy labels is a fundamental problem in training reliable deep neural networks. Robust loss functions provide a direct and effective way to mitigate the adverse effects of label noise. However, most existing robust losses are designed directly at the level of the final multiclass objective, which makes it difficult to systematically characterize and extend their robustness properties. In this paper, we propose a general framework that constructs robust multiclass losses from univariate base functions. By defining mapping operators from base functions to multiclass losses, the robustness of the induced losses can be characterized through simple properties of the base functions. We develop two complementary construction schemes, Target Separation and Binary Reduction, corresponding to inter-class independent and inter-class dependent formulations, respectively. For both schemes, we analyze their symmetry and asymmetry properties and derive corresponding sufficient conditions, which provide theoretical criteria for noise-robust loss design. The proposed framework also provides a new route to constructing symmetric losses, serving as a complement to normalization-based symmetric loss designs. Extensive experiments on synthetic and real-world noisy-label benchmarks demonstrate that the proposed losses achieve competitive or superior performance under various noise settings.

Graph-Embedded Intuitionistic Fuzzy Broad Learning System: A Multi-view Framework

The Broad Learning System (BLS) has been widely used for data classification and is based on a layer-by-layer feed-forward structure. However, it gives the same importance to all data points, which reduces its effectiveness on real-world datasets with noise and outliers. In addition, it does not consider the geometric structure of the data and has limitations in handling data from multiple sources. To address these challenges, we propose a Multi-View Graph-Embedded Intuitionistic Fuzzy Broad Learning System (MVGIFBLS) that integrates multi-view learning, graph embedding, and intuitionistic fuzzy theory into the BLS framework. This design enables the model to combine information from multiple sources and learn more discriminative representations. Graph embedding captures the geometric relationships among samples and improves class separation through intrinsic and penalty subspaces based on local Fisher discriminant analysis. Intuitionistic fuzzy theory enhances robustness to noise, while kernel-based neighborhood analysis captures local data structures. We evaluate the proposed framework on several UCI, KEEL, and AwA benchmark datasets using comparative evaluation, Gaussian feature noise analysis, ablation studies, and statistical analysis. The results demonstrate that each component contributes positively to the overall framework and that the proposed MVGIFBLS consistently achieves higher Area Under the Curve (AUC) scores and maintains robust performance under Gaussian feature noise.

Is the Statistical Advantage Worth the Cost? An Empirical Comparison of KANs and MLPs for Structured Data Classification

This study presents an empirical benchmarking comparison between Kolmogorov-Arnold Networks (KANs) and Multi-Layer Perceptrons (MLPs) on structured tabular classification tasks. Motivated by the growing interest in KANs as an alternative function-approximating architecture, we evaluate their out-of-the-box performance on twelve publicly available datasets spanning binary, multiclass, multilabel, and ordinal problems. Both models were trained under standardized preprocessing, architecture, and fixed hyperparameter settings, with performance assessed using test accuracy and F1-Score, paired hypothesis testing, and effect size analysis. Results show that KANs statistically outperform MLPs in binary and multiclass domains and achieve a significant aggregate advantage across all datasets. However, the observed medium effect size (d = -0.46) raises an important cost-benefit consideration: while KANs offer superior generalization through adaptive spline-based mappings, this advantage comes with substantially higher parameter and computational complexity relative to the MLP baseline. These findings suggest KANs are the preferred choice for high-precision applications, while MLPs remain a robust and efficient option for resource-constrained environments. Future work should extend this analysis to additional data modalities to further refine these architectural selection criteria.