March 2026

arXiv:2511.01137v2 Announce Type: replace-cross Abstract: We use geometric invariant theory (GIT) to study the deep linear network (DLN). The Kempf-Ness theorem is used to establish that the $L^2$ regularizer is minimized on the balanced manifold. We introduce related balancing flows using the Riemannian geometry of fibers. The balancing flow defined by the $L^2$ regularizer is shown to converge to the balanced manifold at a uniform exponential rate. The balancing flow defined by the squared moment map is computed […]

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arXiv:2510.03798v2 Announce Type: replace-cross Abstract: The batched multi-armed bandit (MAB) problem, in which rewards are collected in batches, is crucial for applications such as clinical trials. Existing research predominantly assumes light-tailed reward distributions, yet many real-world scenarios, including clinical outcomes, exhibit heavy-tailed characteristics. This paper bridges this gap by proposing robust batched bandit algorithms designed for heavy-tailed rewards, within both finite-arm and Lipschitz-continuous settings. We reveal a surprising phenomenon: in the instance-independent regime, as well as in the […]

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arXiv:2509.20721v2 Announce Type: replace-cross Abstract: Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive. In this work, we show that scaling laws can be formally explained as redundancy laws. Using kernel regression, we show that a polynomial tail in the data covariance spectrum yields an excess risk power law with exponent alpha = 2s […]

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arXiv:2508.14936v2 Announce Type: replace-cross Abstract: Synthetic data holds substantial potential to address practical challenges in epidemiology due to restricted data access and privacy concerns. However, many current methods suffer from limited quality, high computational demands, and complexity for non-experts. Furthermore, common evaluation strategies for synthetic data often fail to directly reflect statistical utility and measure privacy risks sufficiently. Against this background, a critical underexplored question is whether synthetic data can reliably reproduce key findings from epidemiological research while […]

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arXiv:2508.07392v3 Announce Type: replace-cross Abstract: Modern methods of generative modelling and unpaired data translation based on Schr”odinger bridges and stochastic optimal control theory aim to transform an initial density to a target one in an optimal way. In the present paper, we assume that we only have access to i.i.d. samples from the initial and final distributions. This makes our setup suitable for both generative modelling and unpaired data translation. Relying on the stochastic optimal control approach, we […]

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arXiv:2507.16749v3 Announce Type: replace-cross Abstract: Monitoring for changes in a predictive relationship represented by a fitted supervised learning model (i.e., concept drift detection) is a widespread problem in modern data-driven applications. A general and powerful Fisher score-based concept drift approach was recently proposed, in which detecting concept drift reduces to detecting changes in the mean of the model’s score vector using a multivariate exponentially weighted moving average (MEWMA). To implement the approach, the initial data must be split […]

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arXiv:2504.09396v2 Announce Type: replace-cross Abstract: We develop a reinforcement learning (RL) framework for insurance loss reserving that formulates reserve setting as a finite-horizon sequential decision problem under claim development uncertainty, macroeconomic stress, and solvency governance. The reserving process is modeled as a Markov Decision Process (MDP) in which reserve adjustments influence future reserve adequacy, capital efficiency, and solvency outcomes. A Proximal Policy Optimization (PPO) agent is trained using a risk-sensitive reward that penalizes reserve shortfall, capital inefficiency, and […]

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arXiv:2501.06404v2 Announce Type: replace-cross Abstract: Reinsurance optimization is a cornerstone of solvency and capital management, yet traditional approaches often rely on restrictive distributional assumptions and static program designs. We propose a hybrid framework that combines Variational Autoencoders (VAEs) to learn joint distributions of multi-line and multi-year claims data with Proximal Policy Optimization (PPO) reinforcement learning to adapt treaty parameters dynamically. The framework explicitly targets expected surplus under capital and ruin-probability constraints, bridging statistical modeling with sequential decision-making. Using […]

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arXiv:2412.07971v2 Announce Type: replace-cross Abstract: In distributed training of machine learning models, gradient descent with local iterative steps, commonly known as Local (Stochastic) Gradient Descent (Local-(S)GD) or Federated averaging (FedAvg), is a very popular method to mitigate communication burden. In this method, gradient steps based on local datasets are taken independently in distributed compute nodes to update the local models, which are then aggregated intermittently. In the interpolation regime, Local-GD can converge to zero training loss. However, with […]

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arXiv:2407.18707v3 Announce Type: replace-cross Abstract: Infinitely wide or deep neural networks (NNs) with independent and identically distributed (i.i.d.) parameters have been shown to be equivalent to Gaussian processes. Because of the favorable properties of Gaussian processes, this equivalence is commonly employed to analyze neural networks and has led to various breakthroughs over the years. However, neural networks and Gaussian processes are equivalent only in the limit; in the finite case there are currently no methods available to approximate […]

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