This short paper gives an overview of the XCSP3 solver implemented in Picat. Picat provides several constraint modules, and the Picat XCSP3 solver uses the sat module. The XCSP3 solver mainly consists of a parser implemented in Picat, which converts constraints from XCSP3 format to Picat. The solver demonstrates the strengths of Picat, a logic-based language, in parsing, modeling, and encoding constraints into SAT. The high performance of the solver in recent XCSP competitions demonstrates the viability of using a SAT solver to solve general constraint satisfaction and optimization problems.

Deep Neural Networks (DNNs) have revolutionized various fields, but their deployment on GPUs often leads to significant energy consumption. Unlike existing methods for reducing GPU energy consumption, which are either hardware-inflexible or limited by workload constraints, this paper addresses the problem at the GPU kernel level. We propose a novel search-based compilation method to generate energy-efficient GPU kernels by incorporating energy efficiency into the search process. To accelerate the energy evaluation process, we develop an accurate energy cost model based on high-level kernel features. Furthermore, we introduce a dynamic updating strategy for the energy cost model, reducing the need for on-device energy measurements and accelerating the search process. Our evaluation demonstrates that the proposed approach can generate GPU kernels with up to 21.69% reduced energy consumption while maintaining low latency.

In-context Learning (ICL) enables large language models (LLMs) to tackle downstream tasks through sophisticated prompting and high-quality demonstrations. However, this traditional ICL paradigm shows limitations when facing complex mathematical reasoning tasks, primarily due to its heavy dependence on example quality and the necessity for human intervention in challenging scenarios. To address these limitations, this paper presents HiAR-ICL, a \textbf{Hi}gh-level \textbf{A}utomated \textbf{R}easoning paradigm in \textbf{ICL} that shifts focus from specific examples to abstract thinking patterns, extending the conventional concept of context in ICL. HiAR-ICL introduces five atomic reasoning actions as fundamental components for constructing chain-structured patterns. Using Monte Carlo Tree Search, we explore reasoning paths and construct thought cards to guide subsequent inference. We then develop a cognitive complexity framework that dynamically matches problems with appropriate thought cards. Experimental results demonstrate HiAR-ICL's effectiveness, achieving state-of-the-art accuracy (79.6$\%$) on the MATH benchmark with Qwen2.5-7B-Instruct, surpassing GPT-4o (76.6$\%$) and Claude 3.5 (71.1$\%$).

Modern Mixed Integer Linear Programming (MILP) solvers use the Branch-and-Bound algorithm together with a plethora of auxiliary components that speed up the search. In recent years, there has been an explosive development in the use of machine learning for enhancing and supporting these algorithmic components. Within this line, we propose a methodology for predicting the optimal objective value, or, equivalently, predicting if the current incumbent is optimal. For this task, we introduce a predictor based on a graph neural network (GNN) architecture, together with a set of dynamic features. Experimental results on diverse benchmarks demonstrate the efficacy of our approach, achieving high accuracy in the prediction task and outperforming existing methods. These findings suggest new opportunities for integrating ML-driven predictions into MILP solvers, enabling smarter decision-making and improved performance.

We study the problem of learning Lyapunov-stable neural controllers which provably satisfy the Lyapunov asymptotic stability condition within a region-of-attraction. Compared to previous works which commonly used counterexample guided training on this task, we develop a new and generally formulated certified training framework named CT-BaB, and we optimize for differentiable verified bounds, to produce verification-friendly models. In order to handle the relatively large region-of-interest, we propose a novel framework of training-time branch-and-bound to dynamically maintain a training dataset of subregions throughout training, such that the hardest subregions are iteratively split into smaller ones whose verified bounds can be computed more tightly to ease the training. We demonstrate that our new training framework can produce models which can be more efficiently verified at test time. On the largest 2D quadrotor dynamical system, verification for our model is more than 5X faster compared to the baseline, while our size of region-of-attraction is 16X larger than the baseline.

Ice conditions often require ships to reduce speed and deviate from their main course to avoid damage to the ship. In addition, broken ice fields are becoming the dominant ice conditions encountered in the Arctic, where the effects of collisions with ice are highly dependent on where contact occurs and on the particular features of the ice floes. In this paper, we present AUTO-IceNav, a framework for the autonomous navigation of ships operating in ice floe fields. Trajectories are computed in a receding-horizon manner, where we frequently replan given updated ice field data. During a planning step, we assume a nominal speed that is safe with respect to the current ice conditions, and compute a reference path. We formulate a novel cost function that minimizes the kinetic energy loss of the ship from ship-ice collisions and incorporate this cost as part of our lattice-based path planner. The solution computed by the lattice planning stage is then used as an initial guess in our proposed optimization-based improvement step, producing a locally optimal path. Extensive experiments were conducted both in simulation and in a physical testbed to validate our approach.

We investigate the approximation and estimation rates of conditional diffusion transformers (DiTs) with classifier-free guidance. We present a comprehensive analysis for ``in-context'' conditional DiTs under four common data assumptions. We show that both conditional DiTs and their latent variants lead to the minimax optimality of unconditional DiTs under identified settings. Specifically, we discretize the input domains into infinitesimal grids and then perform a term-by-term Taylor expansion on the conditional diffusion score function under H\"older smooth data assumption. This enables fine-grained use of transformers' universal approximation through a more detailed piecewise constant approximation and hence obtains tighter bounds. Additionally, we extend our analysis to the latent setting under the linear latent subspace assumption. We not only show that latent conditional DiTs achieve lower bounds than conditional DiTs both in approximation and estimation, but also show the minimax optimality of latent unconditional DiTs. Our findings establish statistical limits for conditional and unconditional DiTs, and offer practical guidance toward developing more efficient and accurate DiT models.

Controller tuning is crucial for closed-loop performance but often involves manual adjustments. Although Bayesian optimization (BO) has been established as a data-efficient method for automated tuning, applying it to large and high-dimensional search spaces remains challenging. We extend a recently proposed local variant of BO to include crash constraints, where the controller can only be successfully evaluated in an a-priori unknown feasible region. We demonstrate the efficiency of the proposed method through simulations and hardware experiments. Our findings showcase the potential of local BO to enhance controller performance and reduce the time and resources necessary for tuning.

We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask to select a feasible subset of input items of minimal (or maximal) total weight. This gives simple (near-)linear time algorithms for, e.g., Vertex Cover, Steiner Tree, Min-Weight Perfect Matching, Knapsack, and Clique. Our algorithms produce optimal solutions when provided with perfect predictions and their approximation ratios smoothly degrade with increasing prediction error. With small enough prediction error we achieve approximation guarantees that are beyond reach without predictions in the given time bounds, as exemplified by the NP-hardness and APX-hardness of many of the above problems. Although we show our approach to be optimal for this class of problems as a whole, there is a potential for exploiting specific structural properties of individual problems to obtain improved bounds; we demonstrate this on the Steiner Tree problem. We conclude with an empirical evaluation of our approach.

Estimating causal effects from nonexperimental data is a fundamental problem in many fields of science. A key component of this task is selecting an appropriate set of covariates for confounding adjustment to avoid bias. Most existing methods for covariate selection often assume the absence of latent variables and rely on learning the global network structure among variables. However, identifying the global structure can be unnecessary and inefficient, especially when our primary interest lies in estimating the effect of a treatment variable on an outcome variable. To address this limitation, we propose a novel local learning approach for covariate selection in nonparametric causal effect estimation, which accounts for the presence of latent variables. Our approach leverages testable independence and dependence relationships among observed variables to identify a valid adjustment set for a target causal relationship, ensuring both soundness and completeness under standard assumptions. We validate the effectiveness of our algorithm through extensive experiments on both synthetic and real-world data.