Large Language Models (LLMs) have shown significant capability across various tasks, with their real-world effectiveness often driven by prompt design. While recent research has focused on optimizing prompt content, the role of prompt formatting, a critical but often overlooked dimension, has received limited systematic investigation. In this paper, we introduce Content-Format Integrated Prompt Optimization (CFPO), an innovative methodology that jointly optimizes both prompt content and formatting through an iterative refinement process. CFPO leverages natural language mutations to explore content variations and employs a dynamic format exploration strategy that systematically evaluates diverse format options. Our extensive evaluations across multiple tasks and open-source LLMs demonstrate that CFPO demonstrates measurable performance improvements compared to content-only optimization methods. This highlights the importance of integrated content-format optimization and offers a practical, model-agnostic approach to enhancing LLM performance. Code is available at https://github.com/HenryLau7/CFPO.

Recent advancements in language models have led to significant improvements in mathematical reasoning across various benchmarks. However, most of these benchmarks rely on automatic evaluation methods that only compare final answers using heuristics, without verifying the underlying reasoning steps. This limitation results in false positive solutions, where models may produce correct final answers but with flawed deduction paths. In this paper, we systematically examine the prevalence of false positive solutions in mathematical problem solving for language models. We analyze the characteristics and extent of this issue across different open-source models, datasets of varying difficulty levels, and decoding strategies. Specifically, we explore how false positives influence the inference time scaling behavior of language models. Our experimental results reveal that: (1) false positive solutions persist across different models, datasets, and decoding methods, (2) sampling-based inference time scaling methods do not alleviate the problem, and (3) the pass@N evaluation metric is more susceptible to false positives, suggesting a significantly lower scaling ceiling than what automatic evaluations indicate. Additionally, we analyze specific instances of false positives and discuss potential limitations in self-improvement techniques and synthetic data generation under such conditions.

During crowd navigation, robot motion plan needs to consider human motion uncertainty, and the human motion uncertainty is dependent on the robot motion plan. We introduce Interaction-aware Conformal Prediction (ICP) to alternate uncertainty-aware robot motion planning and decision-dependent human motion uncertainty quantification. ICP is composed of a trajectory predictor to predict human trajectories, a model predictive controller to plan robot motion with confidence interval radii added for probabilistic safety, a human simulator to collect human trajectory calibration dataset conditioned on the planned robot motion, and a conformal prediction module to quantify trajectory prediction error on the decision-dependent calibration dataset. Crowd navigation simulation experiments show that ICP strikes a good balance of performance among navigation efficiency, social awareness, and uncertainty quantification compared to previous works. ICP generalizes well to navigation tasks under various crowd densities. The fast runtime and efficient memory usage make ICP practical for real-world applications. Code is available at https://github.com/tedhuang96/icp.

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and require large amounts of {\em labeled} training data. We propose the Deep Generative Neural Operator (DGNO), a physics-aware framework that addresses these challenges by leveraging a deep, generative, probabilistic model in combination with a set of lower-dimensional, latent variables that simultaneously encode PDE-inputs and PDE-outputs. This formulation can make use of unlabeled data and significantly improves inverse problem-solving, particularly for discontinuous or discrete-valued input functions. DGNO enforces physics constraints without labeled data by incorporating as virtual observables, weak-form residuals based on compactly supported radial basis functions (CSRBFs). These relax regularity constraints and eliminate higher-order derivatives from the objective function. We also introduce MultiONet, a novel neural operator architecture, which is a more expressive generalization of the popular DeepONet that significantly enhances the approximating power of the proposed model. These innovations make DGNO particularly effective for challenging forward and inverse, PDE-based problems, such as those involving multi-phase media. Numerical experiments demonstrate that DGNO achieves higher accuracy across multiple benchmarks while exhibiting robustness to noise and strong generalization to out-of-distribution cases. Its adaptability, and the ability to handle sparse, noisy data while providing probabilistic estimates, make DGNO a powerful tool for scientific and engineering applications.

Stochastic optimal control problems typically involve a dynamical system described by a stochastic differential equation (SDE) dx t = b (t, x t, u t)dt + σ (t, x t) dB t, t [0, T], (1.1) in Stratonovich or Itˆ o form, where x t is the state of the system at time t, u t is the control input, b is the drift, σ is the diffusion, B is a Brownian motion, T is the final time, and consist of optimizing an objective E[null T 0 f ( t, x t, u t)dt + g (x T)] over a set of control input trajectories subject to state and control constraints. By now, a rich literature on stochastic optimal control is available, with optimality conditions characterized by the dynamic programming principle as Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs) [6-8], and by the Pontryagin Maximum Principle (PMP) as forward-backward stochastic differential equations (FBSDEs) [8-11]. For problems with linear dynamics and linear-quadratic costs, both approaches lead to tractable solutions characterized by stochastic Riccati equations [7,12,13]. However, for general nonlinear problems, solving HJB-PDEs or FBSDEs remains computationally challenging for high-dimensional state spaces, despite recent progress [14-17]. In practice, an effective approach consists of optimizing over a class of solutions u θ t parameterized by finitely-many parameters θ R k [18,19] (see [20,21] for machine learning applications). However, restricting solutions to a finite-dimensional space may obscure the structure of solutions and lead to suboptimality.

Hard computing generally deals with precise data, which provides ideal solutions to problems. However, in the civil engineering field, amongst other disciplines, that is not always the case as real-world systems are continuously changing. Here lies the need to explore soft computing methods and artificial intelligence to solve civil engineering shortcomings. The integration of advanced computational models, including Artificial Neural Networks (ANNs), Fuzzy Logic, Genetic Algorithms (GAs), and Probabilistic Reasoning, has revolutionized the domain of civil engineering. These models have significantly advanced diverse sub-fields by offering innovative solutions and improved analysis capabilities. Sub-fields such as: slope stability analysis, bearing capacity, water quality and treatment, transportation systems, air quality, structural materials, etc. ANNs predict non-linearities and provide accurate estimates. Fuzzy logic uses an efficient decision-making process to provide a more precise assessment of systems. Lastly, while GAs optimizes models (based on evolutionary processes) for better outcomes, probabilistic reasoning lowers their statistical uncertainties.

Abstract--This work introduces a spike-based wearable analytics system utilizing Spiking Neural Networks (SNNs) deployed on an In-memory Computing engine based on RRAM crossbars, which are known for their compactness and energy-efficiency. Given the hardware constraints and noise characteristics of the underlying RRAM crossbars, we propose online adaptation of pre-trained SNNs in real-time using Direct Feedback Alignment (DFA) against traditional backpropagation (BP). Direct Feedback Alignment (DFA) learning, that allows layer-parallel gradient computations, acts as a fast, energy & area-efficient method for online adaptation of SNNs on RRAM crossbars, unleashing better algorithmic performance against those adapted using BP. Through extensive simulations using our in-house hardware evaluation engine called DF A Sim, we find that DFA achieves upto 64.1% lower energy consumption, 10.1% lower area overhead, and a 2.1 reduction in latency compared to BP, while delivering upto 7.55% higher inference accuracy on human Figure 1: Pictorial depiction of SNNs used in wearables for temporal activity recognition (HAR) tasks. Pre-trained SNNs in the cloud are adapted online according to the constraints of resource-constrained edge devices.

Model Predictive Control has emerged as a popular tool for robots to generate complex motions. However, the real-time requirement has limited the use of hard constraints and large preview horizons, which are necessary to ensure safety and stability. In practice, practitioners have to carefully design cost functions that can imitate an infinite horizon formulation, which is tedious and often results in local minima. In this work, we study how to approximate the infinite horizon value function of constrained optimal control problems with neural networks using value iteration and trajectory optimization. Furthermore, we demonstrate how using this value function approximation as a terminal cost provides global stability to the model predictive controller. The approach is validated on two toy problems and a real-world scenario with online obstacle avoidance on an industrial manipulator where the value function is conditioned to the goal and obstacle.

Fine-tuning pre-trained vision models for specific tasks is a common practice in computer vision. However, this process becomes more expensive as models grow larger. Recently, parameter-efficient fine-tuning (PEFT) methods have emerged as a popular solution to improve training efficiency and reduce storage needs by tuning additional low-rank modules within pre-trained backbones. Despite their advantages, they struggle with limited representation capabilities and misalignment with pre-trained intermediate features. To address these issues, we introduce an innovative Multi-Kernel Kronecker Adaptation with Re-Scaling Transmission (KARST) for various recognition tasks. Specifically, its multi-kernel design extends Kronecker projections horizontally and separates adaptation matrices into multiple complementary spaces, reducing parameter dependency and creating more compact subspaces. Besides, it incorporates extra learnable re-scaling factors to better align with pre-trained feature distributions, allowing for more flexible and balanced feature aggregation. Extensive experiments validate that our KARST outperforms other PEFT counterparts with a negligible inference cost due to its re-parameterization characteristics. Code is publicly available at: https://github.com/Lucenova/KARST.

The nonlinear, non-convex AC Optimal Power Flow (AC-OPF) problem is fundamental for power systems operations. The intrinsic complexity of AC-OPF has fueled a growing interest in the development of optimization proxies for the problem, i.e., machine learning models that predict high-quality, close-to-optimal solutions. More recently, dual conic proxy architectures have been proposed, which combine machine learning and convex relaxations of AC-OPF, to provide valid certificates of optimality using learning-based methods. Building on this methodology, this paper proposes, for the first time, a dual conic proxy architecture for the semidefinite (SDP) relaxation of AC-OPF problems. Although the SDP relaxation is stronger than the second-order cone relaxation considered in previous work, its practical use has been hindered by its computational cost. The proposed method combines a neural network with a differentiable dual completion strategy that leverages the structure of the dual SDP problem. This approach guarantees dual feasibility, and therefore valid dual bounds, while providing orders of magnitude of speedups compared to interior-point algorithms. The paper also leverages self-supervised learning, which alleviates the need for time-consuming data generation and allows to train the proposed models efficiently. Numerical experiments are presented on several power grid benchmarks with up to 500 buses. The results demonstrate that the proposed SDP-based proxies can outperform weaker conic relaxations, while providing several orders of magnitude speedups compared to a state-of-the-art interior-point SDP solver.