After rebuttal: I have carefully read the comments from other reviewers and the feedback from the authors. My main concern was the generalization ability of NGD, but the experiments in the feedback are a bit confused to me because GD doesn't seem to achieve zero training loss but NGD converges to 0 very quickly in MNIST regression. I would suggest the authors provide more details about that experiment setting, e.g., how do you select the hyperparameter. Thus, I would like to keep my score unchanged. The framework for the proof follows the recent line of work about over-parametrization, e.g., the papers written by Du et al, Li and Liang, and Allen-Zhu et al., the core of which is the Gram matrix.

This paper proves fast convergence of natural gradient descent for over-parameterized neural networks, and its generalization error bound. This paper is on the borderline and was carefully discussed. The main concern is about the novelty of this paper, as well as lack of details in the experiments. The paper gathered some support from the reviewers to merit acceptance, after author response and reviewer discussion.

Summary and Contributions: The paper makes the following contributions: 1) Interpretation (up to a constant factor of 2) of SVGD as (kernelized) gradient flow of the Chi-squared divergence, called as CSF 2) Establishing exponential ergodicity of CSF (continuous case) with respect to the KL metric and Chi-squared divergence metric, under certain Poincare condition (or LSI) on the target. Indeed this is an issue with any kernel method (from SVM to MMD to SVGD) and it has been addressed in various ways. If one were critical, there is still no "nice" way to pick a kernel. Indeed as mentioned in Line 16 and 17, a single integral operator depending on target \pi is good (in a way it is also along expected lines - for example in MMD context something similar leads to optimality properties). However I tend to not agree 100% with lines 27-28 that "solving high-dimensional PDEs is precisely the target of intensive research in modern numerical PDE" which is my main concern with the practical applicability of the proposed work. There is no "concrete" progress in this direction to the best of the reviewer's knowledge despite several ad-hoc approaches recently.

The reviewers had some concerns about the empirical evaluation and the lack of discrete-time results, but agree that this paper would be a useful addition to NeurIPS. Please see the reviews (and your response) for ways to improve the final manuscript (especially in terms of clarifying the context and scope of this work).

In many real-world scenarios, such as gas leak detection or environmental pollutant tracking, solving the Inverse Source Localization and Characterization problem involves navigating complex, dynamic fields with sparse and noisy observations. Traditional methods face significant challenges, including partial observability, temporal and spatial dynamics, out-of-distribution generalization, and reward sparsity. To address these issues, we propose a hierarchical framework that integrates Bayesian inference and reinforcement learning. The framework leverages an attention-enhanced particle filtering mechanism for efficient and accurate belief updates, and incorporates two complementary execution strategies: Attention Particle Filtering Planning and Attention Particle Filtering Reinforcement Learning. These approaches optimize exploration and adaptation under uncertainty. Theoretical analysis proves the convergence of the attention-enhanced particle filter, while extensive experiments across diverse scenarios validate the framework's superior accuracy, adaptability, and computational efficiency. Our results highlight the framework's potential for broad applications in dynamic field estimation tasks.

In Nepal, air pollution is a serious public health concern, especially in cities like Kathmandu where particulate matter (PM2.5 and PM10) has a major influence on respiratory health and air quality. The Air Quality Index (AQI) is predicted in this work using a Random Forest Regressor, and the model's predictions are interpreted using SHAP (SHapley Additive exPlanations) analysis. With the lowest Testing RMSE (0.23) and flawless R2 scores (1.00), CatBoost performs better than other models, demonstrating its greater accuracy and generalization which is cross validated using a nested cross validation approach. NowCast Concentration and Raw Concentration are the most important elements influencing AQI values, according to SHAP research, which shows that the machine learning results are highly accurate. Their significance as major contributors to air pollution is highlighted by the fact that high values of these characteristics significantly raise the AQI. This study investigates the Hydrogen-Alpha (HA) biodegradable filter as a novel way to reduce the related health hazards. With removal efficiency of more than 98% for PM2.5 and 99.24% for PM10, the HA filter offers exceptional defense against dangerous airborne particles. These devices, which are biodegradable face masks and cigarette filters, address the environmental issues associated with traditional filters' non-biodegradable trash while also lowering exposure to air contaminants.

This study focuses on membrane-based systems for CO$_2$ separation, addressing the urgent need for efficient carbon capture solutions to mitigate climate change. Linear regression models, based on membrane equations, were utilized to estimate key parameters, including porosity ($\epsilon$) of 0.4805, Kozeny constant (K) of 2.9084, specific surface area ($\sigma$) of 105.3272 m$^2$/m$^3$, mean pressure (Pm) of 6.2166 MPa, viscosity ($\mu$) of 0.1997 Ns/m$^2$, and gas flux (Jg) of 3.2559 kg m$^{-2}$ s$^{-1}$. These parameters were derived from the analysis of synthetic datasets using linear regression. The study also provides insights into the performance of the membrane, with a flow rate (Q) of 9.8778 $\times$ 10$^{-4}$ m$^3$/s, an injection pressure (P$_1$) of 2.8219 MPa, and an exit pressure (P$_2$) of 2.5762 MPa. The permeability value of 0.045 for CO$_2$ indicates the potential for efficient separation. Optimizing membrane properties to selectively block CO$_2$ while allowing other gases to pass is crucial for improving carbon capture efficiency. By integrating these technologies into industrial processes, significant reductions in greenhouse gas emissions can be achieved, fostering a circular carbon economy and contributing to global climate goals. This study also explores how artificial intelligence (AI) can aid in designing membranes for carbon capture, addressing the global climate change challenge and supporting the Sustainable Development Goals (SDGs) set by the United Nations.

Multiple Sclerosis (MS) is a chronic disease characterized by progressive or alternate impairment of neurological functions (motor, sensory, visual, and cognitive). Predicting disease progression with a probabilistic and time-dependent approach might help in suggesting interventions that can delay the progression of the disease. However, extracting informative knowledge from irregularly collected longitudinal data is difficult, and missing data pose significant challenges. MS progression is measured through the Expanded Disability Status Scale (EDSS), which quantifies and monitors disability in MS over time. EDSS assesses impairment in eight functional systems (FS). Frequently, only the EDSS score assigned by clinicians is reported, while FS sub-scores are missing. Imputing these scores might be useful, especially to stratify patients according to their phenotype assessed over the disease progression. This study aimed at i) exploring different methodologies for imputing missing FS sub-scores, and ii) predicting the EDSS score using complete clinical data. Results show that Exponential Weighted Moving Average achieved the lowest error rate in the missing data imputation task; furthermore, the combination of Classification and Regression Trees for the imputation and SVM for the prediction task obtained the best accuracy.

Modern cybersecurity landscapes increasingly demand sophisticated detection frameworks capable of identifying evolving threats with precision and adaptability. The proposed Zero-Space Detection framework introduces a novel approach that dynamically identifies latent behavioral patterns through unsupervised clustering and advanced deep learning techniques. Designed to address the limitations of signature-based and heuristic methods, it operates effectively in high-velocity environments by integrating multi-phase filtering and ensemble learning for refined decision-making. Experimental evaluation reveals high detection rates across diverse ransomware families, including LockBit, Conti, REvil, and BlackMatter, while maintaining low false positive rates and scalable performance. Computational overhead remains minimal, with average processing times ensuring compatibility with real-time systems even under peak operational loads. The framework demonstrates resilience against adversarial strategies such as obfuscation and encryption speed variability, which frequently challenge conventional detection systems. Analysis across multiple data sources highlights its versatility in handling diverse file types and operational contexts. Comprehensive metrics, including detection probability, latency, and resource efficiency, validate its efficacy under real-world conditions. Through its modular architecture, the framework achieves seamless integration with existing cybersecurity infrastructures without significant reconfiguration. The results demonstrate its robustness and scalability, offering a transformative paradigm for ransomware identification in dynamic and resource-constrained environments.

In sensitive application domains, multi-objective hyperparameter selection can ensure the reliability of AI models prior to deployment, while optimizing auxiliary performance metrics. The state-of-the-art Pareto Testing (PT) method guarantees statistical reliability constraints by adopting a multiple hypothesis testing framework. In PT, hyperparameters are validated one at a time, following a data-driven order determined by expected reliability levels. This paper introduces a novel framework for multi-objective hyperparameter selection that captures the interdependencies among the reliability levels of different hyperparameter configurations using a directed acyclic graph (DAG), which is termed the reliability graph (RG). The RG is constructed based on prior information and data by using the Bradley-Terry model. The proposed approach, RG-based PT (RG-PT), leverages the RG to enable the efficient, parallel testing of multiple hyperparameters at the same reliability level. By integrating False Discovery Rate (FDR) control, RG-PT ensures robust statistical reliability guarantees and is shown via experiments across diverse domains to consistently yield superior solutions for multi-objective calibration problems.