NeuralODE is one example for generative machine learning based on the push forward of a simple source measure with a bijective mapping, which in the case of NeuralODE is given by the flow of a ordinary differential equation. Using Liouville's formula, the log-density of the push forward measure is easy to compute and thus NeuralODE can be trained based on the maximum Likelihood method such that the Kulback-Leibler divergence between the push forward through the flow map and the target measure generating the data becomes small. In this work, we give a detailed account on the consistency of Maximum Likelihood based empirical risk minimization for a generic class of target measures. In contrast to prior work, we do not only consider the statistical learning theory, but also give a detailed numerical analysis of the NeuralODE algorithm based on the 2nd order Runge-Kutta (RK) time integration. Using the universal approximation theory for deep ReQU networks, the stability and convergence rated for the RK scheme as well as metric entropy and concentration inequalities, we are able to prove that NeuralODE is a probably approximately correct (PAC) learning algorithm.

Histo-genomic multimodal survival prediction has garnered growing attention for its remarkable model performance and potential contributions to precision medicine. However, a significant challenge in clinical practice arises when only unimodal data is available, limiting the usability of these advanced multimodal methods. To address this issue, this study proposes a prototype-guided cross-modal knowledge enhancement (ProSurv) framework, which eliminates the dependency on paired data and enables robust learning and adaptive survival prediction. Specifically, we first introduce an intra-modal updating mechanism to construct modality-specific prototype banks that encapsulate the statistics of the whole training set and preserve the modality-specific risk-relevant features/prototypes across intervals. Subsequently, the proposed cross-modal translation module utilizes the learned prototypes to enhance knowledge representation for multimodal inputs and generate features for missing modalities, ensuring robust and adaptive survival prediction across diverse scenarios. Extensive experiments on four public datasets demonstrate the superiority of ProSurv over state-of-the-art methods using either unimodal or multimodal input, and the ablation study underscores its feasibility for broad applicability. Overall, this study addresses a critical practical challenge in computational pathology, offering substantial significance and potential impact in the field.

Air pollution remains one of the most pressing environmental challenges of the modern era, significantly impacting human health, ecosystems, and climate. While traditional air quality monitoring systems provide critical data, their high costs and limited spatial coverage hinder effective real-time pollutant identification. Recent advancements in micro-sensor technology have improved data collection but still lack efficient methods for source identification. This paper explores the innovative application of machine learning (ML) models to classify pollutants in real-time using only data from optical micro-sensors. We propose a novel classification framework capable of distinguishing between four pollutant scenarios: Background Pollution, Ash, Sand, and Candle. Three Machine Learning (ML) approaches - XGBoost, Long Short-Term Memory networks, and Hidden Markov Chains - are evaluated for their effectiveness in sequence modeling and pollutant identification. Our results demonstrate the potential of leveraging micro-sensors and ML techniques to enhance air quality monitoring, offering actionable insights for urban planning and environmental protection.

Classifier-free guidance has become a staple for conditional generation with denoising diffusion models. However, a comprehensive understanding of classifier-free guidance is still missing. In this work, we carry out an empirical study to provide a fresh perspective on classifier-free guidance. Concretely, instead of solely focusing on classifier-free guidance, we trace back to the root, i.e., classifier guidance, pinpoint the key assumption for the derivation, and conduct a systematic study to understand the role of the classifier. We find that both classifier guidance and classifier-free guidance achieve conditional generation by pushing the denoising diffusion trajectories away from decision boundaries, i.e., areas where conditional information is usually entangled and is hard to learn. Based on this classifier-centric understanding, we propose a generic postprocessing step built upon flow-matching to shrink the gap between the learned distribution for a pre-trained denoising diffusion model and the real data distribution, majorly around the decision boundaries. Experiments on various datasets verify the effectiveness of the proposed approach.

Kolmogorov-Arnold networks (KANs) are a remarkable innovation consisting of learnable activation functions with the potential to capture more complex relationships from data. Although KANs are useful in finding symbolic representations and continual learning of one-dimensional functions, their effectiveness in diverse machine learning (ML) tasks, such as vision, remains questionable. Presently, KANs are deployed by replacing multilayer perceptrons (MLPs) in deep network architectures, including advanced architectures such as vision Transformers (ViTs). In this paper, we are the first to design a general learnable Kolmogorov-Arnold Attention (KArAt) for vanilla ViTs that can operate on any choice of basis. However, the computing and memory costs of training them motivated us to propose a more modular version, and we designed particular learnable attention, called Fourier-KArAt. Fourier-KArAt and its variants either outperform their ViT counterparts or show comparable performance on CIFAR-10, CIFAR-100, and ImageNet-1K datasets. We dissect these architectures' performance and generalization capacity by analyzing their loss landscapes, weight distributions, optimizer path, attention visualization, and spectral behavior, and contrast them with vanilla ViTs. The goal of this paper is not to produce parameter- and compute-efficient attention, but to encourage the community to explore KANs in conjunction with more advanced architectures that require a careful understanding of learnable activations. Our open-source code and implementation details are available on: https://subhajitmaity.me/KArAt

Building upon the concepts and mechanisms used for the development in Moving Points Algorithm, we will now explore how non linear decision boundaries can be developed for classification tasks. First we will look at the classification performance of MPA and some minor developments in the original algorithm. We then discuss the concepts behind using cubic splines for classification with a similar learning mechanism and finally analyze training results on synthetic datasets with known properties.

Support Vector Regression (SVR) and its variants are widely used to handle regression tasks, however, since their solution involves solving an expensive quadratic programming problem, it limits its application, especially when dealing with large datasets. Additionally, SVR uses an epsilon-insensitive loss function which is sensitive to outliers and therefore can adversely affect its performance. We propose Granular Ball Support Vector Regression (GBSVR) to tackle problem of regression by using granular ball concept. These balls are useful in simplifying complex data spaces for machine learning tasks, however, to the best of our knowledge, they have not been sufficiently explored for regression problems. Granular balls group the data points into balls based on their proximity and reduce the computational cost in SVR by replacing the large number of data points with far fewer granular balls. This work also suggests a discretization method for continuous-valued attributes to facilitate the construction of granular balls. The effectiveness of the proposed approach is evaluated on several benchmark datasets and it outperforms existing state-of-the-art approaches

High-quality test items are essential for educational assessments, particularly within Item Response Theory (IRT). Traditional validation methods rely on resource-intensive pilot testing to estimate item difficulty and discrimination. More recently, Item-Writing Flaw (IWF) rubrics emerged as a domain-general approach for evaluating test items based on textual features. However, their relationship to IRT parameters remains underexplored. To address this gap, we conducted a study involving over 7,000 multiple-choice questions across various STEM subjects (e.g., math and biology). Using an automated approach, we annotated each question with a 19-criteria IWF rubric and studied relationships to data-driven IRT parameters. Our analysis revealed statistically significant links between the number of IWFs and IRT difficulty and discrimination parameters, particularly in life and physical science domains. We further observed how specific IWF criteria can impact item quality more and less severely (e.g., negative wording vs. implausible distractors). Overall, while IWFs are useful for predicting IRT parameters--particularly for screening low-difficulty MCQs--they cannot replace traditional data-driven validation methods. Our findings highlight the need for further research on domain-general evaluation rubrics and algorithms that understand domain-specific content for robust item validation.

We consider the problem of generating valid and small prediction sets by sampling outputs (e.g., software code and natural language text) from a black-box deep generative model for a given input (e.g., textual prompt). The validity of a prediction set is determined by a user-defined binary admissibility function depending on the target application. For example, requiring at least one program in the set to pass all test cases in code generation application. To address this problem, we develop a simple and effective conformal inference algorithm referred to as Generative Prediction Sets (GPS). Given a set of calibration examples and black-box access to a deep generative model, GPS can generate prediction sets with provable guarantees. The key insight behind GPS is to exploit the inherent structure within the distribution over the minimum number of samples needed to obtain an admissible output to develop a simple conformal regression approach over the minimum number of samples. Experiments on multiple datasets for code and math word problems using different large language models demonstrate the efficacy of GPS over state-of-the-art methods.

Whole-slide image classification represents a key challenge in computational pathology and medicine. Attention-based multiple instance learning (MIL) has emerged as an effective approach for this problem. However, the effect of attention mechanism architecture on model performance is not well-documented for biomedical imagery. In this work, we compare different methods and implementations of MIL, including deep learning variants. We introduce a new method using higher-dimensional feature spaces for deep MIL. We also develop a novel algorithm for whole-slide image classification where extreme machine learning is combined with attention-based MIL to improve sensitivity and reduce training complexity. We apply our algorithms to the problem of detecting circulating rare cells (CRCs), such as erythroblasts, in peripheral blood. Our results indicate that nonlinearities play a key role in the classification, as removing them leads to a sharp decrease in stability in addition to a decrease in average area under the curve (AUC) of over 4%. We also demonstrate a considerable increase in robustness of the model with improvements of over 10% in average AUC when higher-dimensional feature spaces are leveraged. In addition, we show that extreme learning machines can offer clear improvements in terms of training efficiency by reducing the number of trained parameters by a factor of 5 whilst still maintaining the average AUC to within 1.5% of the deep MIL model. Finally, we discuss options of enriching the classical computing framework with quantum algorithms in the future. This work can thus help pave the way towards more accurate and efficient single-cell diagnostics, one of the building blocks of precision medicine.