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Reinforcement learning (RL) algorithms can be used to provide personalized services, which rely on users' private and sensitive data. To protect the users' privacy, privacy-preserving RL algorithms are in demand. In this paper, we study RL…

We introduce a neural network architecture to solve inverse problems linked to a one-dimensional integral operator. This architecture is built by unfolding a forward-backward algorithm derived from the minimization of an objective function…

The Bifurcation from a Simple Eigenvalue (BSE) Theorem is the foundation of steady-state bifurcation theory for one-parameter families of functions. When eigenvalues of multiplicity greater than one are caused by symmetry, the Equivariant…

In the current work, we study the eigenvalue distribution results of a class of non-normal matrix-sequences which may be viewed as a low rank perturbation, depending on a parameter $\beta>1$, of the basic Toeplitz matrix-sequence…

Numeric modeling of electromagnetics and acoustics frequently entails matrix-vector multiplication with block Toeplitz structure. When the corresponding block Toeplitz matrix is not highly sparse, e.g. when considering the electromagnetic…

To preserve the data privacy, the federated learning (FL) paradigm emerges in which clients only expose model gradients rather than original data for conducting model training. To enhance the protection of model gradients in FL,…

Protecting the privacy of people whose data is used by machine learning algorithms is important. Differential Privacy is the appropriate mathematical framework for formal guarantees of privacy, and boosted decision trees are a popular…

Diffusion Language Models (DLMs) have recently achieved strong results in text generation. However, their multi-step sampling leads to slow inference, limiting practical use. To address this, we extend Inverse Distillation, a technique…

This paper discusses the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, which arises in the numerical solutions of nonlinear fourth-order differential equation with a finite difference method. A non-recurrence…

In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonlinear Fourier transform (NFT). In particular, we provide…

The turnstile continual release model of differential privacy captures scenarios where a privacy-preserving real-time analysis is sought for a dataset evolving through additions and deletions. In typical applications of real-time data…

Although federated learning improves privacy of training data by exchanging local gradients or parameters rather than raw data, the adversary still can leverage local gradients and parameters to obtain local training data by launching…

In this paper, we first give an introduction to the theoretical basis of the privacy-utility equilibrium in federated learning based on Bayesian privacy definitions and total variation distance privacy definitions. We then present the…

This study explores the estimation of parameters in a matrix-valued linear regression model, where the $T$ responses $(Y_t)_{t=1}^T \in \mathbb{R}^{n \times p}$ and predictors $(X_t)_{t=1}^T \in \mathbb{R}^{m \times q}$ satisfy the…

Smart meter devices enable a better understanding of the demand at the potential risk of private information leakage. One promising solution to mitigating such risk is to inject noises into the meter data to achieve a certain level of…

We introduce a logical framework named Distributed Labeled Tagged Transition System (DLTTS), using concepts from Probabilistic Automata, Probabilistic Concurrent Systems, and Probabilistic labelled transition systems. We show that DLTTS can…

This work addresses the timely yet underexplored problem of performing inference and finetuning of a proprietary LLM owned by a model provider entity on the confidential/private data of another data owner entity, in a way that ensures the…

This paper considers minimax and adaptive transfer learning for nonparametric classification under the posterior drift model with distributed differential privacy constraints. Our study is conducted within a heterogeneous framework,…

Data privacy is important in the AI era, and differential privacy (DP) is one of the golden solutions. However, DP is typically applicable only if data have a bounded underlying distribution. We address this limitation by leveraging…

Bipartite graphs serve as a natural model for representing relationships between two different types of entities. When analyzing bipartite graphs, butterfly counting is a fundamental research problem that aims to count the number of…