Chain-based Adaptive Reconfiguration Over Lattices for Hallucination Reduction

We introduce CAROL (Chain-based Adaptive Reconfiguration Over Lattices), a probabilistic framework for test-time hallucination reduction in large language models. Rather than relying on token-level uncertainty, CAROL defines a semantic uncertainty measure based on the consistency between generated responses and a trusted context, inducing a string-submodular objective over a lattice of textual sequences. This formulation enables hallucination mitigation to be cast as a Markov chain accept-reject process with provable convergence and near-optimality guarantees, allowing the model to iteratively refine outputs toward semantic consistency. By operating at the level of meaning, CAROL unifies hallucination detection and mitigation within a single framework. Empirical results on question answering and multi-agent reasoning benchmarks show that CAROL significantly reduces hallucinations and improves reliability and interpretability compared to likelihood-based and retrieval-augmented baselines, while maintaining competitive computational efficiency.

Hierarchical Prompt-Domain Control and Learning for Resource-Constrained Agentic Language Models

Large Language Models are increasingly deployed inside agentic systems, where they must follow structured protocols, adapt to evolving states, and operate under memory, latency, and cost constraints. In such regimes, prompt extension is unreliable: growing contexts can push compact models outside their effective prompt domain, while deployment-time fine-tuning remains limited by scarce data and compute. We propose a hierarchical control-and-learning framework in which a compact model is first distilled to learn the required output schema, then supervised online by an oracle-controller loop. The controller monitors protocol validity and semantic performance, projects accumulated histories into a feasible prompt domain, and triggers lightweight oracle-supervised fine-tuning under drift. This separates schema learning for communication compatibility from semantic adaptation for task-level correction. We formalize prompt-domain feasibility and attention-induced saturation, motivating control of the effective prompt state rather than reliance on nominal context length. Using Multi-Fidelity Bayesian Optimization as a controlled sequential testbed, we characterize a core deployment failure mode and show improved reliability and cost-efficiency over non-hierarchical, distillation-only, and non-distilled baselines.

E-Globe: Scalable $ε$-Global Verification of Neural Networks via Tight Upper Bounds and Pattern-Aware Branching

Neural networks achieve strong empirical performance, but robustness concerns still hinder deployment in safety-critical applications. Formal verification provides robustness guarantees, but current methods face a scalability-completeness trade-off. We propose a hybrid verifier in a branch-and-bound (BaB) framework that efficiently tightens both upper and lower bounds until an $ε-$global optimum is reached or early stop is triggered. The key is an exact nonlinear program with complementarity constraints (NLP-CC) for upper bounding that preserves the ReLU input-output graph, so any feasible solution yields a valid counterexample and enables rapid pruning of unsafe subproblems. We further accelerate verification with (i) warm-started NLP solves requiring minimal constraint-matrix updates and (ii) pattern-aligned strong branching that prioritizes splits most effective at tightening relaxations. We also provide conditions under which NLP-CC upper bounds are tight. Experiments on MNIST and CIFAR-10 show markedly tighter upper bounds than PGD across perturbation radii spanning up to three orders of magnitude, fast per-node solves in practice, and substantial end-to-end speedups over MIP-based verification, amplified by warm-starting, GPU batching, and pattern-aligned branching.

Constraint-Informed Active Learning for End-to-End ACOPF Optimization Proxies

This paper studies optimization proxies, machine learning (ML) models trained to efficiently predict optimal solutions for AC Optimal Power Flow (ACOPF) problems. While promising, optimization proxy performance heavily depends on training data quality. To address this limitation, this paper introduces a novel active sampling framework for ACOPF optimization proxies designed to generate realistic and diverse training data. The framework actively explores varied, flexible problem specifications reflecting plausible operational realities. More importantly, the approach uses optimization-specific quantities (active constraint sets) that better capture the salient features of an ACOPF that lead to the optimal solution. Numerical results show superior generalization over existing sampling methods with an equivalent training budget, significantly advancing the state-of-practice for trustworthy ACOPF optimization proxies.

A General and Streamlined Differentiable Optimization Framework

Differentiating through constrained optimization problems is increasingly central to learning, control, and large-scale decision-making systems, yet practical integration remains challenging due to solver specialization and interface mismatches. This paper presents a general and streamlined framework-an updated DiffOpt.jl-that unifies modeling and differentiation within the Julia optimization stack. The framework computes forward - and reverse-mode solution and objective sensitivities for smooth, potentially nonconvex programs by differentiating the KKT system under standard regularity assumptions. A first-class, JuMP-native parameter-centric API allows users to declare named parameters and obtain derivatives directly with respect to them - even when a parameter appears in multiple constraints and objectives - eliminating brittle bookkeeping from coefficient-level interfaces. We illustrate these capabilities on convex and nonconvex models, including economic dispatch, mean-variance portfolio selection with conic risk constraints, and nonlinear robot inverse kinematics. Two companion studies further demonstrate impact at scale: gradient-based iterative methods for strategic bidding in energy markets and Sobolev-style training of end-to-end optimization proxies using solver-accurate sensitivities. Together, these results demonstrate that differentiable optimization can be deployed as a routine tool for experimentation, learning, calibration, and design-without deviating from standard JuMP modeling practices and while retaining access to a broad ecosystem of solvers.

Nonlinear Optimization with GPU-Accelerated Neural Network Constraints

We propose a reduced-space formulation for optimizing over trained neural networks where the network's outputs and derivatives are evaluated on a GPU. To do this, we treat the neural network as a "gray box" where intermediate variables and constraints are not exposed to the optimization solver. Compared to the full-space formulation, in which intermediate variables and constraints are exposed to the optimization solver, the reduced-space formulation leads to faster solves and fewer iterations in an interior point method. We demonstrate the benefits of this method on two optimization problems: Adversarial generation for a classifier trained on MNIST images and security-constrained optimal power flow with transient feasibility enforced using a neural network surrogate.

Sobolev Training of End-to-End Optimization Proxies

Optimization proxies - machine learning models trained to approximate the solution mapping of parametric optimization problems in a single forward pass - offer dramatic reductions in inference time compared to traditional iterative solvers. This work investigates the integration of solver sensitivities into such end to end proxies via a Sobolev training paradigm and does so in two distinct settings: (i) fully supervised proxies, where exact solver outputs and sensitivities are available, and (ii) self supervised proxies that rely only on the objective and constraint structure of the underlying optimization problem. By augmenting the standard training loss with directional derivative information extracted from the solver, the proxy aligns both its predicted solutions and local derivatives with those of the optimizer. Under Lipschitz continuity assumptions on the true solution mapping, matching first order sensitivities is shown to yield uniform approximation error proportional to the training set covering radius. Empirically, different impacts are observed in each studied setting. On three large Alternating Current Optimal Power Flow benchmarks, supervised Sobolev training cuts mean squared error by up to 56 percent and the median worst case constraint violation by up to 400 percent while keeping the optimality gap below 0.22 percent. For a mean variance portfolio task trained without labeled solutions, self supervised Sobolev training halves the average optimality gap in the medium risk region (standard deviation above 10 percent of budget) and matches the baseline elsewhere. Together, these results highlight Sobolev training whether supervised or self supervised as a path to fast reliable surrogates for safety critical large scale optimization workloads.

Formulations and scalability of neural network surrogates in nonlinear optimization problems

We compare full-space, reduced-space, and gray-box formulations for representing trained neural networks in nonlinear constrained optimization problems. We test these formulations on a transient stability-constrained, security-constrained alternating current optimal power flow (SCOPF) problem where the transient stability criteria are represented by a trained neural network surrogate. Optimization problems are implemented in JuMP and trained neural networks are embedded using a new Julia package: MathOptAI.jl. To study the bottlenecks of the three formulations, we use neural networks with up to 590 million trained parameters. The full-space formulation is bottlenecked by the linear solver used by the optimization algorithm, while the reduced-space formulation is bottlenecked by the algebraic modeling environment and derivative computations. The gray-box formulation is the most scalable and is capable of solving with the largest neural networks tested. It is bottlenecked by evaluation of the neural network's outputs and their derivatives, which may be accelerated with a graphics processing unit (GPU). Leveraging the gray-box formulation and GPU acceleration, we solve our test problem with our largest neural network surrogate in 2.5$\times$ the time required for a simpler SCOPF problem without the stability constraint.

LEVIS: Large Exact Verifiable Input Spaces for Neural Networks

The robustness of neural networks is paramount in safety-critical applications. While most current robustness verification methods assess the worst-case output under the assumption that the input space is known, identifying a verifiable input space $\mathcal{C}$, where no adversarial examples exist, is crucial for effective model selection, robustness evaluation, and the development of reliable control strategies. To address this challenge, we introduce a novel framework, $\texttt{LEVIS}$, comprising $\texttt{LEVIS}$-$\alpha$ and $\texttt{LEVIS}$-$\beta$. $\texttt{LEVIS}$-$\alpha$ locates the largest possible verifiable ball within the central region of $\mathcal{C}$ that intersects at least two boundaries. In contrast, $\texttt{LEVIS}$-$\beta$ integrates multiple verifiable balls to encapsulate the entirety of the verifiable space comprehensively. Our contributions are threefold: (1) We propose $\texttt{LEVIS}$ equipped with three pioneering techniques that identify the maximum verifiable ball and the nearest adversarial point along collinear or orthogonal directions. (2) We offer a theoretical analysis elucidating the properties of the verifiable balls acquired through $\texttt{LEVIS}$-$\alpha$ and $\texttt{LEVIS}$-$\beta$. (3) We validate our methodology across diverse applications, including electrical power flow regression and image classification, showcasing performance enhancements and visualizations of the searching characteristics.

Physics-Informed Heterogeneous Graph Neural Networks for DC Blocker Placement

The threat of geomagnetic disturbances (GMDs) to the reliable operation of the bulk energy system has spurred the development of effective strategies for mitigating their impacts. One such approach involves placing transformer neutral blocking devices, which interrupt the path of geomagnetically induced currents (GICs) to limit their impact. The high cost of these devices and the sparsity of transformers that experience high GICs during GMD events, however, calls for a sparse placement strategy that involves high computational cost. To address this challenge, we developed a physics-informed heterogeneous graph neural network (PIHGNN) for solving the graph-based dc-blocker placement problem. Our approach combines a heterogeneous graph neural network (HGNN) with a physics-informed neural network (PINN) to capture the diverse types of nodes and edges in ac/dc networks and incorporates the physical laws of the power grid. We train the PIHGNN model using a surrogate power flow model and validate it using case studies. Results demonstrate that PIHGNN can effectively and efficiently support the deployment of GIC dc-current blockers, ensuring the continued supply of electricity to meet societal demands. Our approach has the potential to contribute to the development of more reliable and resilient power grids capable of withstanding the growing threat that GMDs pose.