The proliferation of Large Language Models (LLMs) in real-world applications poses unprecedented risks of generating harmful, biased, or misleading information to vulnerable populations including LGBTQ+ individuals, single parents, and marginalized communities. While existing safety approaches rely on post-hoc filtering or generic alignment techniques, they fail to proactively prevent harmful outputs at the generation source. This paper introduces PromptGuard, a novel modular prompting framework with our breakthrough contribution: VulnGuard Prompt, a hybrid technique that prevents harmful information generation using real-world data-driven contrastive learning. VulnGuard integrates few-shot examples from curated GitHub repositories, ethical chain-of-thought reasoning, and adaptive role-prompting to create population-specific protective barriers. Our framework employs theoretical multi-objective optimization with formal proofs demonstrating 25-30% analytical harm reduction through entropy bounds and Pareto optimality. PromptGuard orchestrates six core modules: Input Classification, VulnGuard Prompting, Ethical Principles Integration, External Tool Interaction, Output Validation, and User-System Interaction, creating an intelligent expert system for real-time harm prevention. We provide comprehensive mathematical formalization including convergence proofs, vulnerability analysis using information theory, and theoretical validation framework using GitHub-sourced datasets, establishing mathematical foundations for systematic empirical research.

Model-free diffusion planners have shown great promise for robot motion planning, but practical robotic systems often require combining them with model-based optimization modules to enforce constraints, such as safety. Naively integrating these modules presents compatibility challenges when diffusion's multi-modal outputs behave adversarially to optimization-based modules. To address this, we introduce Joint Model-based Model-free Diffusion (JM2D), a novel generative modeling framework. JM2D formulates module integration as a joint sampling problem to maximize compatibility via an interaction potential, without additional training. Using importance sampling, JM2D guides modules outputs based only on evaluations of the interaction potential, thus handling non-differentiable objectives commonly arising from non-convex optimization modules. We evaluate JM2D via application to aligning diffusion planners with safety modules on offline RL and robot manipulation. JM2D significantly improves task performance compared to conventional safety filters without sacrificing safety. Further, we show that conditional generation is a special case of JM2D and elucidate key design choices by comparing with SOTA gradient-based and projection-based diffusion planners. More details at: https://jm2d-corl25.github.io/.

Ising Machines are emerging hardware architectures that efficiently solve NP-Hard combinatorial optimization problems. Generally, combinatorial problems are transformed into quadratic unconstrained binary optimization (QUBO) form, but this transformation often complicates the solution landscape, degrading performance, especially for multi-state problems. To address this challenge, we model spin interactions as generalized boolean logic function to significantly reduce the exploration space. We demonstrate the effectiveness of our approach on graph coloring problem using probabilistic Ising solvers, achieving similar accuracy compared to state-of-the-art heuristics and machine learning algorithms. It also shows significant improvement over state-of-the-art QUBO-based Ising solvers, including probabilistic Ising and simulated bifurcation machines. We also design 1024-neuron all-to-all connected probabilistic Ising accelerator on FPGA with the proposed approach that shows ~10000x performance acceleration compared to GPU-based Tabucol heuristics and reducing physical neurons by 1.5-4x over baseline Ising frameworks. Thus, this work establishes superior efficiency, scalability and solution quality for multi-state optimization problems.

We propose a method for inferring entropy production (EP) in high-dimensional stochastic systems, including many-body systems and non-Markovian systems with long memory. Standard techniques for estimating EP become intractable in such systems due to computational and statistical limitations. We infer trajectory-level EP and lower bounds on average EP by exploiting a nonequilibrium analogue of the Maximum Entropy principle, along with convex duality. Our approach uses only samples of trajectory observables, such as spatiotemporal correlations. It does not require reconstruction of high-dimensional probability distributions or rate matrices, nor impose any special assumptions such as discrete states or multipartite dynamics. In addition, it may be used to compute a hierarchical decomposition of EP, reflecting contributions from different interaction orders, and it has an intuitive physical interpretation as a "thermodynamic uncertainty relation." We demonstrate its numerical performance on a disordered nonequilibrium spin model with 1000 spins and a large neural spike-train dataset.

The increasing availability of personal data has enabled significant advances in fields such as machine learning, healthcare, and cybersecurity. However, this data abundance also raises serious privacy concerns, especially in light of powerful re-identification attacks and growing legal and ethical demands for responsible data use. Differential privacy (DP) has emerged as a principled, mathematically grounded framework for mitigating these risks. This review provides a comprehensive survey of DP, covering its theoretical foundations, practical mechanisms, and real-world applications. It explores key algorithmic tools and domain-specific challenges - particularly in privacy-preserving machine learning and synthetic data generation. The report also highlights usability issues and the need for improved communication and transparency in DP systems. Overall, the goal is to support informed adoption of DP by researchers and practitioners navigating the evolving landscape of data privacy.

The Hirschfeld-Gebelein-Rényi (HGR) correlation coefficient is an extension of Pearson's correlation that is not limited to linear correlations, with potential applications in algorithmic fairness, scientific analysis, and causal discovery. Recently, novel algorithms to estimate HGR in a differentiable manner have been proposed to facilitate its use as a loss regularizer in constrained machine learning applications. However, the inherent uncomputability of HGR requires a bias-variance trade-off, which can possibly compromise the robustness of the proposed methods, hence raising technical concerns if applied in real-world scenarios. We introduce a novel computational approach for HGR that relies on user-configurable polynomial kernels, offering greater robustness compared to previous methods and featuring a faster yet almost equally effective restriction. Our approach provides significant advantages in terms of robustness and determinism, making it a more reliable option for real-world applications. Moreover, we present a brief experimental analysis to validate the applicability of our approach within a constrained machine learning framework, showing that its computation yields an insightful subgradient that can serve as a loss regularizer.

We propose REpresentation-Aware Distributionally Robust Estimation (READ), a novel framework for Wasserstein distributionally robust learning that accounts for predictive representations when guarding against distributional shifts. Unlike classical approaches that treat all feature perturbations equally, READ embeds a multidimensional alignment parameter into the transport cost, allowing the model to differentially discourage perturbations along directions associated with informative representations. This yields robustness to feature variation while preserving invariant structure. Our first contribution is a theoretical foundation: we show that seminorm regularizations for linear regression and binary classification arise as Wasserstein distributionally robust objectives, thereby providing tractable reformulations of READ and unifying a broad class of regularized estimators under the DRO lens. Second, we adopt a principled procedure for selecting the Wasserstein radius using the techniques of robust Wasserstein profile inference. This further enables the construction of valid, representation-aware confidence regions for model parameters with distinct geometric features. Finally, we analyze the geometry of READ estimators as the alignment parameters vary and propose an optimization algorithm to estimate the projection of the global optimum onto this solution surface. This procedure selects among equally robust estimators while optimally constructing a representation structure. We conclude by demonstrating the effectiveness of our framework through extensive simulations and a real-world study, providing a powerful robust estimation grounded in learning representation.

Constrained Reinforcement Learning (RL) aims to maximize the return while adhering to predefined constraint limits, which represent domain-specific safety requirements. In continuous control settings, where learning agents govern system actions, balancing the trade-off between reward maximization and constraint satisfaction remains a significant challenge. Policy optimization methods often exhibit instability near constraint boundaries, resulting in suboptimal training performance. To address this issue, we introduce a novel approach that integrates an adaptive incentive mechanism in addition to the reward structure to stay within the constraint bound before approaching the constraint boundary. Building on this insight, we propose Incrementally Penalized Proximal Policy Optimization (IP3O), a practical algorithm that enforces a progressively increasing penalty to stabilize training dynamics. Through empirical evaluation on benchmark environments, we demonstrate the efficacy of IP3O compared to the performance of state-of-the-art Safe RL algorithms. Furthermore, we provide theoretical guarantees by deriving a bound on the worst-case error of the optimality achieved by our algorithm.

In this paper, we propose the Bregman Douglas-Rachford splitting (BDRS) method and its variant Bregman Peaceman-Rachford splitting method for solving maximal monotone inclusion problem. We show that BDRS is equivalent to a Bregman alternating direction method of multipliers (ADMM) when applied to the dual of the problem. A special case of the Bregman ADMM is an alternating direction version of the exponential multiplier method. To the best of our knowledge, algorithms proposed in this paper are new to the literature. We also discuss how to use our algorithms to solve the discrete optimal transport (OT) problem. We prove the convergence of the algorithms under certain assumptions, though we point out that one assumption does not apply to the OT problem.

We address the problem of policy selection in contextual stochastic optimization (CSO), where covariates are available as contextual information and decisions must satisfy hard feasibility constraints. In many CSO settings, multiple candidate policies--arising from different modeling paradigms--exhibit heterogeneous performance across the covariate space, with no single policy uniformly dominating. We propose Prescribe-then-Select (PS), a modular framework that first constructs a library of feasible candidate policies and then learns a meta-policy to select the best policy for the observed covariates. We implement the meta-policy using ensembles of Optimal Policy Trees trained via cross-validation on the training set, making policy choice entirely data-driven. Across two benchmark CSO problems--single-stage newsvendor and two-stage shipment planning--PS consistently outperforms the best single policy in heterogeneous regimes of the covariate space and converges to the dominant policy when such heterogeneity is absent. All the code to reproduce the results can be found at https://anonymous.4open.science/r/Prescribe-then-Select-TMLR.