Prototypical self-supervised learning methods consistently suffer from partial prototype collapse, where multiple prototypes converge to nearly identical representations. This undermines their central purpose -- providing diverse and informative targets to guide encoders toward rich representations -- and has led practitioners to over-parameterize prototype sets or add ad-hoc regularizers, which mitigate symptoms rather than address the root cause. We empirically trace the collapse to the joint optimization of encoders and prototypes, which encourages a type of shortcut learning: early in training prototypes drift toward redundant representations that minimize loss without necessarily enhancing representation diversity. To break the joint optimization, we introduce a fully decoupled training strategy that learns prototypes and encoders under separate objectives. Concretely, we model prototypes as a Gaussian mixture updated with an online EM-style procedure, independent of the encoder's loss. This simple yet principled decoupling eliminates prototype collapse without explicit regularization and yields consistently diverse prototypes and stronger downstream performance.

Studies on various facets of pattern classification is often imperative while working with multi - dimensional samples pertaining to diverse application scenarios. In this notion, w eighted dimension - based distance measure has been one of the vital considerat ions in pattern analysis as it reflects the degree of similarity between samples . Though it is often presumed to be settled with the pervasive use of Euclidean distance, plethora of issues often surface. In this paper, we present (a) a detail analysis on t he impact of distance measure norms and weights of dimensions along with visualization, (b) a novel weighting scheme for each dimension, (c) incorporation of this dimensional weighting schema in to a KNN classifier, and (d) pattern classification on a varie ty of synthetic as well as realistic datasets with the developed model . It has perform ed well across diverse experiments in comparison to the traditional KNN under the same experimental setups. Specifically, for gene expression datasets, it yields signific ant and consistent gain in classification accuracy (around 10%) in all cross - validation experiments with different values of k. As such datasets contain limited number of samples of high dimensions, meaningful selection of nearest neighbours is desirable, and this requirement is reasonably met by regulat ing the shape and size of the region enclos ing the k number of reference samples with the developed weighting schema and appropriate norm . I t, therefore, stands as an important generalization of K NN classifier powered by weighted Minkowski distance with the present weighting schema .

Simultaneous recordings from thousands of neurons across multiple brain areas reveal rich mixtures of activity that are shared between regions and dynamics that are unique to each region. Existing alignment or multi-view methods neglect temporal structure, whereas dynamical latent variable models capture temporal dependencies but are usually restricted to a single area, assume linear read-outs, or conflate shared and private signals. We introduce the Coupled Transformer Autoencoder (CTAE) - a sequence model that addresses both (i) non-stationary, non-linear dynamics and (ii) separation of shared versus region-specific structure in a single framework. CTAE employs transformer encoders and decoders to capture long-range neural dynamics and explicitly partitions each region's latent space into orthogonal shared and private subspaces. We demonstrate the effectiveness of CTAE on two high-density electrophysiology datasets with simultaneous recordings from multiple regions, one from motor cortical areas and the other from sensory areas. CTAE extracts meaningful representations that better decode behavioral variables compared to existing approaches.

We study whether liquidity and volatility proxies of a core set of cryptoassets generate spillovers that forecast market-wide risk. Our empirical framework integrates three statistical layers: (A) interactions between core liquidity and returns, (B) principal-component relations linking liquidity and returns, and (C) volatility-factor projections that capture cross-sectional volatility crowding. The analysis is complemented by vector autoregression impulse responses and forecast error variance decompositions (see Granger 1969; Sims 1980), heterogeneous autoregressive models with exogenous regressors (HAR-X, Corsi 2009), and a leakage-safe machine learning protocol using temporal splits, early stopping, validation-only thresholding, and SHAP-based interpretation. Using daily data from 2021 to 2025 (1462 observations across 74 assets), we document statistically significant Granger-causal relationships across layers and moderate out-of-sample predictive accuracy. We report the most informative figures, including the pipeline overview, Layer A heatmap, Layer C robustness analysis, vector autoregression variance decompositions, and the test-set precision-recall curve. Full data and figure outputs are provided in the artifact repository.

Time series forecasting plays a pivotal role in critical domains such as energy management and financial markets. Although deep learning-based approaches (e.g., MLP, RNN, Transformer) have achieved remarkable progress, the prevailing "long-sequence information gain hypothesis" exhibits inherent limitations. Through systematic experimentation, this study reveals a counterintuitive phenomenon: appropriately truncating historical data can paradoxically enhance prediction accuracy, indicating that existing models learn substantial redundant features (e.g., noise or irrelevant fluctuations) during training, thereby compromising effective signal extraction. Building upon information bottleneck theory, we propose an innovative solution termed Adaptive Masking Loss with Representation Consistency (AMRC), which features two core components: 1) Dynamic masking loss, which adaptively identified highly discriminative temporal segments to guide gradient descent during model training; 2) Representation consistency constraint, which stabilized the mapping relationships among inputs, labels, and predictions. Experimental results demonstrate that AMRC effectively suppresses redundant feature learning while significantly improving model performance. This work not only challenges conventional assumptions in temporal modeling but also provides novel theoretical insights and methodological breakthroughs for developing efficient and robust forecasting models.

In this paper, we explore the two-point zeroth-order gradient estimator and identify the distribution of random perturbations that minimizes the estimator's asymptotic variance as the perturbation stepsize tends to zero. We formulate it as a constrained functional optimization problem over the space of perturbation distributions. Our findings reveal that such desired perturbations can align directionally with the true gradient, instead of maintaining a fixed length. While existing research has largely focused on fixed-length perturbations, the potential advantages of directional alignment have been overlooked. To address this gap, we delve into the theoretical and empirical properties of the directionally aligned perturbation (DAP) scheme, which adaptively offers higher accuracy along critical directions. Additionally, we provide a convergence analysis for stochastic gradient descent using δ -unbiased random perturbations, extending existing complexity bounds to a wider range of perturbations. Through empirical evaluations on both synthetic problems and practical tasks, we demonstrate that DAPs outperform traditional methods under specific conditions. Zeroth-order optimization (ZOO) has emerged as a crucial paradigm in machine learning and optimization, particularly in scenarios where gradient information is unavailable or prohibitively expensive to compute. The randomized method (Akhavan et al., 2022) has also emerged as a critical direction. While traditional first-order methods utilize the stochastic gradient f p x; ξ q to update parameters, zeroth-order optimization relies solely on function evaluations.

The study explores the potential of AI technologies in personalized learning, suggesting the prediction of academic success through leadership personality traits and machine learning modelling. The primary data were obtained from 129 master's students in the Environmental Engineering Department, who underwent five leadership personality tests with 23 characteristics. Students used self-assessment tools that included Personality Insight, Workplace Culture, Motivation at Work, Management Skills, and Emotion Control tests. The test results were combined with the average grade obtained from academic reports. The study employed exploratory data analysis and correlation analysis. Feature selection utilized Pearson correlation coefficients of personality traits. The average grades were separated into three categories: fail, pass, and excellent. The modelling process was performed by tuning seven ML algorithms, such as SVM, LR, KNN, DT, GB, RF, XGBoost and LightGBM. The highest predictive performance was achieved with the RF classifier, which yielded an accuracy of 87.50% for the model incorporating 17 personality trait features and the leadership mark feature, and an accuracy of 85.71% for the model excluding this feature. In this way, the study offers an additional opportunity to identify students' strengths and weaknesses at an early stage of their education process and select the most suitable strategies for personalized learning.

Zeroth-order optimization (ZOO) is an important framework for stochastic optimization when gradients are unavailable or expensive to compute. A potential limitation of existing ZOO methods is the bias inherent in most gradient estimators unless the perturbation stepsize vanishes. In this paper, we overcome this biasedness issue by proposing a novel family of unbiased gradient estimators based solely on function evaluations. By reformulating directional derivatives as a telescoping series and sampling from carefully designed distributions, we construct estimators that eliminate bias while maintaining favorable variance. We analyze their theoretical properties, derive optimal scaling distributions and perturbation stepsizes of four specific constructions, and prove that SGD using the proposed estimators achieves optimal complexity for smooth non-convex objectives. Experiments on synthetic tasks and language model fine-tuning confirm the superior accuracy and convergence of our approach compared to standard methods.

We analyze task orderings in continual learning for linear regression, assuming joint realizability of training data. We focus on orderings that greedily maximize dissimilarity between consecutive tasks, a concept briefly explored in prior work but still surrounded by open questions. Using tools from the Kaczmarz method literature, we formalize such orderings and develop geometric and algebraic intuitions around them. Empirically, we demonstrate that greedy orderings converge faster than random ones in terms of the average loss across tasks, both for linear regression with random data and for linear probing on CIFAR-100 classification tasks. Analytically, in a high-rank regression setting, we prove a loss bound for greedy orderings analogous to that of random ones. However, under general rank, we establish a repetition-dependent separation. Specifically, while prior work showed that for random orderings, with or without replacement, the average loss after $k$ iterations is bounded by $\mathcal{O}(1/\sqrt{k})$, we prove that single-pass greedy orderings may fail catastrophically, whereas those allowing repetition converge at rate $\mathcal{O}(1/\sqrt[3]{k})$. Overall, we reveal nuances within and between greedy and random orderings.

''Noisy'' datasets (regimes with low signal to noise ratios, small sample sizes, faulty data collection, etc) remain a key research frontier for classification methods with both theoretical and practical implications. We introduce FINDER, a rigorous framework for analyzing generic classification problems, with tailored algorithms for noisy datasets. FINDER incorporates fundamental stochastic analysis ideas into the feature learning and inference stages to optimally account for the randomness inherent to all empirical datasets. We construct ''stochastic features'' by first viewing empirical datasets as realizations from an underlying random field (without assumptions on its exact distribution) and then mapping them to appropriate Hilbert spaces. The Kosambi-Karhunen-Loéve expansion (KLE) breaks these stochastic features into computable irreducible components, which allow classification over noisy datasets via an eigen-decomposition: data from different classes resides in distinct regions, identified by analyzing the spectrum of the associated operators. We validate FINDER on several challenging, data-deficient scientific domains, producing state of the art breakthroughs in: (i) Alzheimer's Disease stage classification, (ii) Remote sensing detection of deforestation. We end with a discussion on when FINDER is expected to outperform existing methods, its failure modes, and other limitations.