Straight line equation $y=mx$ with slope $m$, when singularly perturbed as $ay^3+y=mx$ with a positive parameter $a$, results in S-shaped curves or S-curves on a real plane. As $a\rightarrow 0$, we get back $y=mx$ which is a cumulative distribution function of a continuous uniform distribution that describes the occurrence of every event in an interval to be equally probable. As $a\rightarrow\infty$, the derivative of $y$ has finite support only at $y=0$ resembling a degenerate distribution. Based on these arguments, in this work, we propose that these S-curves can represent maximum entropy uniform distribution to a zero entropy single value. We also argue that these S-curves are superposable as they are only parametrically nonlinear but fundamentally linear. So far, the superposed forms have been used to capture the patterns of natural systems such as nonlinear dynamics of biological growth and kinetics of enzyme reactions. Here, we attempt to use the S-curve and its superposed form as statistical models. We fit the models on a classical dataset containing flower measurements of iris plants and analyze their usefulness in pattern recognition. Based on these models, we claim that any non-uniform pattern can be represented as a singular perturbation to uniform distribution. However, our parametric estimation procedure have some limitations such as sensitivity to initial conditions depending on the data at hand.

Neuroblastoma, adrenal-derived, is among the most common pediatric solid malignancies, characterized by significant clinical heterogeneity. Timely and accurate pathological diagnosis from hematoxylin and eosin-stained whole-slide images is critical for patient prognosis. However, current diagnostic practices primarily rely on subjective manual examination by pathologists, leading to inconsistent accuracy. Existing automated whole-slide image classification methods encounter challenges such as poor interpretability, limited feature extraction capabilities, and high computational costs, restricting their practical clinical deployment. To overcome these limitations, we propose CMSwinKAN, a contrastive-learning-based multi-scale feature fusion model tailored for pathological image classification, which enhances the Swin Transformer architecture by integrating a Kernel Activation Network within its multilayer perceptron and classification head modules, significantly improving both interpretability and accuracy. By fusing multi-scale features and leveraging contrastive learning strategies, CMSwinKAN mimics clinicians' comprehensive approach, effectively capturing global and local tissue characteristics. Additionally, we introduce a heuristic soft voting mechanism guided by clinical insights to bridge patch-level predictions to whole-slide image-level classifications seamlessly. We verified the CMSwinKAN on the publicly available BreakHis dataset and the PpNTs dataset, which was established by our hospital. Results demonstrate that CMSwinKAN performs better than existing state-of-the-art pathology-specific models pre-trained on large datasets. Our source code is available at https://github.com/JSLiam94/CMSwinKAN.

Generative Flow Networks (GFNs) were initially introduced on directed acyclic graphs to sample from an unnormalized distribution density. Recent works have extended the theoretical framework for generative methods allowing more flexibility and enhancing application range. However, many challenges remain in training GFNs in continuous settings and for imitation learning (IL), including intractability of flow-matching loss, limited tests of non-acyclic training, and the need for a separate reward model in imitation learning. The present work proposes a family of generative flows called Ergodic Generative Flows (EGFs) which are used to address the aforementioned issues. First, we leverage ergodicity to build simple generative flows with finitely many globally defined transformations (diffeomorphisms) with universality guarantees and tractable flow-matching loss (FM loss). Second, we introduce a new loss involving cross-entropy coupled to weak flow-matching control, coined KL-weakFM loss. It is designed for IL training without a separate reward model. We evaluate IL-EGFs on toy 2D tasks and real-world datasets from NASA on the sphere, using the KL-weakFM loss. Additionally, we conduct toy 2D reinforcement learning experiments with a target reward, using the FM loss.

Policy gradient (PG) methods have played an essential role in the empirical successes of reinforcement learning. In order to handle large state-action spaces, PG methods are typically used with function approximation. In this setting, the approximation error in modeling problem-dependent quantities is a key notion for characterizing the global convergence of PG methods. We focus on Softmax PG with linear function approximation (referred to as $\texttt{Lin-SPG}$) and demonstrate that the approximation error is irrelevant to the algorithm's global convergence even for the stochastic bandit setting. Consequently, we first identify the necessary and sufficient conditions on the feature representation that can guarantee the asymptotic global convergence of $\texttt{Lin-SPG}$. Under these feature conditions, we prove that $T$ iterations of $\texttt{Lin-SPG}$ with a problem-specific learning rate result in an $O(1/T)$ convergence to the optimal policy. Furthermore, we prove that $\texttt{Lin-SPG}$ with any arbitrary constant learning rate can ensure asymptotic global convergence to the optimal policy.

Real-world machine learning models require rigorous evaluation before deployment, especially in safety-critical domains like autonomous driving and surveillance. The evaluation of machine learning models often focuses on data slices, which are subsets of the data that share a set of characteristics. Data slice finding automatically identifies conditions or data subgroups where models underperform, aiding developers in mitigating performance issues. Despite its popularity and effectiveness, data slicing for vision model validation faces several challenges. First, data slicing often needs additional image metadata or visual concepts, and falls short in certain computer vision tasks, such as object detection. Second, understanding data slices is a labor-intensive and mentally demanding process that heavily relies on the expert's domain knowledge. Third, data slicing lacks a human-in-the-loop solution that allows experts to form hypothesis and test them interactively. To overcome these limitations and better support the machine learning operations lifecycle, we introduce VISLIX, a novel visual analytics framework that employs state-of-the-art foundation models to help domain experts analyze slices in computer vision models. Our approach does not require image metadata or visual concepts, automatically generates natural language insights, and allows users to test data slice hypothesis interactively. We evaluate VISLIX with an expert study and three use cases, that demonstrate the effectiveness of our tool in providing comprehensive insights for validating object detection models.

--Machine learning (ML)-based intrusion detection systems (IDS) are vulnerable to adversarial attacks. It is crucial for an IDS to learn to recognize adversarial examples before malicious entities exploit them. In this paper, we generated adversarial samples using the Jacobian Saliency Map Attack (JSMA). We validate the generalization and scalability of the adversarial samples to tackle a broad range of real attacks on Industrial Control Systems (ICS). We evaluated the impact by assessing multiple attacks generated using the proposed method. The model trained with adversarial samples detected attacks with 95% accuracy on real-world attack data not used during training. The study was conducted using an operational secure water treatment (SWaT) testbed. Industrial control systems (ICS) comprise a significant portion of any state or nation's critical infrastructure (CI). Examples of such systems include water treatment plants and electric power grids, where an ICS regulates the physical processes. The physical processes consist of two primary parts: monitoring and controlling. The monitoring part maintains processes and ensures they are operating properly by measuring various signals acquired from sensors.

Fractional-order stochastic gradient descent (FOSGD) leverages fractional exponents to capture long-memory effects in optimization. However, its utility is often limited by the difficulty of tuning and stabilizing these exponents. We propose 2SED Fractional-Order Stochastic Gradient Descent (2SEDFOSGD), which integrates the Two-Scale Effective Dimension (2SED) algorithm with FOSGD to adapt the fractional exponent in a data-driven manner. By tracking model sensitivity and effective dimensionality, 2SEDFOSGD dynamically modulates the exponent to mitigate oscillations and hasten convergence. Theoretically, for onoconvex optimization problems, this approach preserves the advantages of fractional memory without the sluggish or unstable behavior observed in naïve fractional SGD. Empirical evaluations in Gaussian and $α$-stable noise scenarios using an autoregressive (AR) model highlight faster convergence and more robust parameter estimates compared to baseline methods, underscoring the potential of dimension-aware fractional techniques for advanced modeling and estimation tasks.

We present a faster algorithm to generate a warm start for sampling an arbitrary logconcave density specified by an evaluation oracle, leading to the first sub-cubic sampling algorithms for inputs in (near-)isotropic position. A long line of prior work incurred a warm-start penalty of at least linear in the dimension, hitting a cubic barrier, even for the special case of uniform sampling from convex bodies. Our improvement relies on two key ingredients of independent interest. (1) We show how to sample given a warm start in weaker notions of distance, in particular $q$-Rényi divergence for $q=\widetilde{\mathcal{O}}(1)$, whereas previous analyses required stringent $\infty$-Rényi divergence (with the exception of Hit-and-Run, whose known mixing time is higher). This marks the first improvement in the required warmness since Lovász and Simonovits (1991). (2) We refine and generalize the log-Sobolev inequality of Lee and Vempala (2018), originally established for isotropic logconcave distributions in terms of the diameter of the support, to logconcave distributions in terms of a geometric average of the support diameter and the largest eigenvalue of the covariance matrix.

We revisit the Bayesian Black-Litterman (BL) portfolio model and remove its reliance on subjective investor views. Classical BL requires an investor "view": a forecast vector $q$ and its uncertainty matrix $Ω$ that describe how much a chosen portfolio should outperform the market. Our key idea is to treat $(q,Ω)$ as latent variables and learn them from market data within a single Bayesian network. Consequently, the resulting posterior estimation admits closed-form expression, enabling fast inference and stable portfolio weights. Building on these, we propose two mechanisms to capture how features interact with returns: shared-latent parametrization and feature-influenced views; both recover classical BL and Markowitz portfolios as special cases. Empirically, on 30-year Dow-Jones and 20-year sector-ETF data, we improve Sharpe ratios by 50% and cut turnover by 55% relative to Markowitz and the index baselines. This work turns BL into a fully data-driven, view-free, and coherent Bayesian framework for portfolio optimization.

Because ODE models allow one to embed inherent properties--for example, Hamiltonian structure [4] or stability guarantees [5-7]--Neural ODEs often achieve accurate long-term forecasting. Moreover, treating the solution map of an ODE as a diffeomorphism has led to applications in generative modeling. Compared to normalizing flows [8], such continuous-time models can yield low-parameter, memory-efficient generators [9]. Gradient-based optimization is the de-facto standard for learning NN-defined dynamics, enabled by the adjoint method [1] for efficient gradient computation. Nonetheless, several issues arise: (i) Sensitivity of gradients to the sampling interval of time-series data, (ii) V ariation of convergence speed depending on NN initialization, (iii) Difficulty of tuning hyper-parameters such as leaning rate. These factors often cause training instability or gradient vanishing/explosion. Existing work addresses them heuristically by restricting the search space of dynamics [9] or by tailored initialization [10]. However, the fundamental question-- why is training Neural ODE hard?