Although various aspects of soft-constraint based norms have been explored, it is still challenging to understand preemption. Preemption is a situation where higher-level norms override lower-level norms when new information emerges. To address this, we propose a derivation state argumentation framework (DSA-framework). DSA-framework incorporates derivation states to explain how preemption arises based on evolving situational knowledge. Based on DSA-framework, we present an argumentative approach for explaining preemption. We formally prove that, under local optimality, DSA-framework can provide explanations why one consequence is obligatory or forbidden by soft-constraint based norms represented as logical constraint hierarchies.

Representing robotic manipulation tasks as constraints that associate the robot and the environment is a promising way to encode desired robot behaviors. However, it remains unclear how to formulate the constraints such that they are 1) versatile to diverse tasks, 2) free of manual labeling, and 3) optimizable by off-the-shelf solvers to produce robot actions in real-time. In this work, we introduce Relational Keypoint Constraints (ReKep), a visually-grounded representation for constraints in robotic manipulation. Specifically, ReKep is expressed as Python functions mapping a set of 3D keypoints in the environment to a numerical cost. We demonstrate that by representing a manipulation task as a sequence of Relational Keypoint Constraints, we can employ a hierarchical optimization procedure to solve for robot actions (represented by a sequence of end-effector poses in SE(3)) with a perception-action loop at a real-time frequency. Furthermore, in order to circumvent the need for manual specification of ReKep for each new task, we devise an automated procedure that leverages large vision models and vision-language models to produce ReKep from free-form language instructions and RGB-D observations. We present system implementations on a wheeled single-arm platform and a stationary dual-arm platform that can perform a large variety of manipulation tasks, featuring multi-stage, in-the-wild, bimanual, and reactive behaviors, all without task-specific data or environment models. Website at https://rekep-robot.github.io.

In procedural content generation, modeling the generation task as a constraint satisfaction problem lets us define local and global constraints on the generated output. However, a generator's perceived quality often involves statistics rather than just hard constraints. For example, we may desire that generated outputs use design elements with a similar distribution to that of reference designs. However, such statistical properties cannot be expressed directly as a hard constraint on the generation of any one output. In contrast, methods which do not use a general-purpose constraint solver, such as Gumin's implementation of the WaveFunctionCollapse (WFC) algorithm, can control output statistics but have limited constraint propagation ability and cannot express non-local constraints. In this paper, we introduce You-Only-Randomize-Once (YORO) pre-rolling, a method for crafting a decision variable ordering for a constraint solver that encodes desired statistics in a constraint-based generator. Using a solver-based WFC as an example, we show that this technique effectively controls the statistics of tile-grid outputs generated by several off-the-shelf SAT solvers, while still enforcing global constraints on the outputs.1 Our approach is immediately applicable to WFC-like generation problems and it offers a conceptual starting point for controlling the design element statistics in other constraint-based generators.

While FL is a widely popular distributed ML strategy that protects data privacy, time-varying wireless network parameters and heterogeneous system configurations of the wireless device pose significant challenges. Although the limited radio and computational resources of the network and the clients, respectively, are widely acknowledged, two critical yet often ignored aspects are (a) wireless devices can only dedicate a small chunk of their limited storage for the FL task and (b) new training samples may arrive in an online manner in many practical wireless applications. Therefore, we propose a new FL algorithm called OSAFL, specifically designed to learn tasks relevant to wireless applications under these practical considerations. Since it has long been proven that under extreme resource constraints, clients may perform an arbitrary number of local training steps, which may lead to client drift under statistically heterogeneous data distributions, we leverage normalized gradient similarities and exploit weighting clients' updates based on optimized scores that facilitate the convergence rate of the proposed OSAFL algorithm. Our extensive simulation results on two different tasks -- each with three different datasets -- with four popular ML models validate the effectiveness of OSAFL compared to six existing state-of-the-art FL baselines.

Computational models of atmospheric composition are not always physically consistent. For example, not all models respect fundamental conservation laws such as conservation of atoms in an interconnected chemical system. In well performing models, these nonphysical deviations are often ignored because they are frequently minor, and thus only need a small nudge to perfectly conserve mass. Here we introduce a method that anchors a prediction from any numerical model to physically consistent hard constraints, nudging concentrations to the nearest solution that respects the conservation laws. This closed-form model-agnostic correction uses a single matrix operation to minimally perturb the predicted concentrations to ensure that atoms are conserved to machine precision. To demonstrate this approach, we train a gradient boosting decision tree ensemble to emulate a small reference model of ozone photochemistry and test the effect of the correction on accurate but non-conservative predictions. The nudging approach minimally perturbs the already well-predicted results for most species, but decreases the accuracy of important oxidants, including radicals. We develop a weighted extension of this nudging approach that considers the uncertainty and magnitude of each species in the correction. This species-level weighting approach is essential to accurately predict important low concentration species such as radicals. We find that applying the uncertainty-weighted correction to the nonphysical predictions slightly improves overall accuracy, by nudging the predictions to a more likely mass-conserving solution.

The constraint satisfaction problem asks to decide if a set of constraints over a relational structure $\mathcal{A}$ is satisfiable (CSP$(\mathcal{A})$). We consider CSP$(\mathcal{A} \cup \mathcal{B})$ where $\mathcal{A}$ is a structure and $\mathcal{B}$ is an alien structure, and analyse its (parameterized) complexity when at most $k$ alien constraints are allowed. We establish connections and obtain transferable complexity results to several well-studied problems that previously escaped classification attempts. Our novel approach, utilizing logical and algebraic methods, yields an FPT versus pNP dichotomy for arbitrary finite structures and sharper dichotomies for Boolean structures and first-order reducts of $(\mathbb{N},=)$ (equality CSPs), together with many partial results for general $\omega$-categorical structures.

Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the search space effectively. In brief, a vector of Lagrangian multipliers is associated with each sub-problem, and an iterative procedure (e.g., a sub-gradient optimization) adjusts these multipliers to find the tightest bound. Initially applied to integer programming, Lagrangian decomposition also had success in constraint programming due to its versatility and the fact that global constraints provide natural sub-problems. However, the non-linear and combinatorial nature of sub-problems in constraint programming makes it computationally intensive to optimize the Lagrangian multipliers with sub-gradient methods at each node of the tree search. This currently limits the practicality of LD as a general bounding mechanism for constraint programming. To address this challenge, we propose a self-supervised learning approach that leverages neural networks to generate multipliers directly, yielding tight bounds. This approach significantly reduces the number of sub-gradient optimization steps required, enhancing the pruning efficiency and reducing the execution time of constraint programming solvers. This contribution is one of the few that leverage learning to enhance bounding mechanisms on the dual side, a critical element in the design of combinatorial solvers. To our knowledge, this work presents the first generic method for learning valid dual bounds in constraint programming.

Speaker diarization, the process of segmenting an audio stream or transcribed speech content into homogenous partitions based on speaker identity, plays a crucial role in the interpretation and analysis of human speech. Most existing speaker diarization systems rely exclusively on unimodal acoustic information, making the task particularly challenging due to the innate ambiguities of audio signals. Recent studies have made tremendous efforts towards audio-visual or audio-semantic modeling to enhance performance. However, even the incorporation of up to two modalities often falls short in addressing the complexities of spontaneous and unstructured conversations. To exploit more meaningful dialogue patterns, we propose a novel multimodal approach that jointly utilizes audio, visual, and semantic cues to enhance speaker diarization. Our method elegantly formulates the multimodal modeling as a constrained optimization problem. First, we build insights into the visual connections among active speakers and the semantic interactions within spoken content, thereby establishing abundant pairwise constraints. Then we introduce a joint pairwise constraint propagation algorithm to cluster speakers based on these visual and semantic constraints. This integration effectively leverages the complementary strengths of different modalities, refining the affinity estimation between individual speaker embeddings. Extensive experiments conducted on multiple multimodal datasets demonstrate that our approach consistently outperforms state-of-the-art speaker diarization methods.

Knowledge refactoring compresses a logic program by introducing new rules. Current approaches struggle to scale to large programs. To overcome this limitation, we introduce a constrained optimisation refactoring approach. Our first key idea is to encode the problem with decision variables based on literals rather than rules. Our second key idea is to focus on linear invented rules. Our empirical results on multiple domains show that our approach can refactor programs quicker and with more compression than the previous state-of-the-art approach, sometimes by 60%.

The ICP registration algorithm has been a preferred method for LiDAR-based robot localization for nearly a decade. However, even in modern SLAM solutions, ICP can degrade and become unreliable in geometrically ill-conditioned environments. Current solutions primarily focus on utilizing additional sources of information, such as external odometry, to either replace the degenerate directions of the optimization solution or add additional constraints in a sensor-fusion setup afterward. In response, this work investigates and compares new and existing degeneracy mitigation methods for robust LiDAR-based localization and analyzes the efficacy of these approaches in degenerate environments for the first time in the literature at this scale. Specifically, this work proposes and investigates i) the incorporation of different types of constraints into the ICP algorithm, ii) the effect of using active or passive degeneracy mitigation techniques, and iii) the choice of utilizing global point cloud registration methods on the ill-conditioned ICP problem in LiDAR degenerate environments. The study results are validated through multiple real-world field and simulated experiments. The analysis shows that active optimization degeneracy mitigation is necessary and advantageous in the absence of reliable external estimate assistance for LiDAR-SLAM. Furthermore, introducing degeneracy-aware hard constraints in the optimization before or during the optimization is shown to perform better in the wild than by including the constraints after. Moreover, with heuristic fine-tuned parameters, soft constraints can provide equal or better results in complex ill-conditioned scenarios. The implementations used in the analysis of this work are made publicly available to the community.