Alloy design can be framed as a constraint-satisfaction problem. Building on previous methodologies, we propose equipping Gaussian Process Classifiers (GPCs) with physics-informed prior mean functions to model the boundaries of feasible design spaces. Through three case studies, we highlight the utility of informative priors for handling constraints on continuous and categorical properties. (1) Phase Stability: By incorporating CALPHAD predictions as priors for solid-solution phase stability, we enhance model validation using a publicly available XRD dataset. (2) Phase Stability Prediction Refinement: We demonstrate an in silico active learning approach to efficiently correct phase diagrams. (3) Continuous Property Thresholds: By embedding priors into continuous property models, we accelerate the discovery of alloys meeting specific property thresholds via active learning. In each case, integrating physics-based insights into the classification framework substantially improved model performance, demonstrating an efficient strategy for constraint-aware alloy design.

This work addresses the problem of multi-robot coordination under unknown robot transition models, ensuring that tasks specified by Time Window Temporal Logic are satisfied with user-defined probability thresholds. We present a bi-level framework that integrates (i) high-level task allocation, where tasks are assigned based on the robots' estimated task completion probabilities and expected rewards, and (ii) low-level distributed policy learning and execution, where robots independently optimize auxiliary rewards while fulfilling their assigned tasks. To handle uncertainty in robot dynamics, our approach leverages real-time task execution data to iteratively refine expected task completion probabilities and rewards, enabling adaptive task allocation without explicit robot transition models. We theoretically validate the proposed algorithm, demonstrating that the task assignments meet the desired probability thresholds with high confidence. Finally, we demonstrate the effectiveness of our framework through comprehensive simulations.

Recent advances in diffusion models show promising potential for learning-based optimization by leveraging their multimodal sampling capability to escape local optima. However, existing diffusion-based optimization approaches, often reliant on supervised training, lacks a mechanism to ensure strict constraint satisfaction which is often required in real-world applications. One resulting observation is the distributional misalignment, i.e. the generated solution distribution often exhibits small overlap with the feasible domain. In this paper, we propose DiOpt, a novel diffusion paradigm that systematically learns near-optimal feasible solution distributions through iterative self-training. Our framework introduces several key innovations: a target distribution specifically designed to maximize overlap with the constrained solution manifold; a bootstrapped self-training mechanism that adaptively weights candidate solutions based on the severity of constraint violations and optimality gaps; and a dynamic memory buffer that accelerates convergence by retaining high-quality solutions over training iterations. To our knowledge, DiOpt represents the first successful integration of self-supervised diffusion with hard constraint satisfaction. Evaluations on diverse tasks, including power grid control, motion retargeting, wireless allocation demonstrate its superiority in terms of both optimality and constraint satisfaction.

Large language models (LLMs) have been enormously successful in solving a wide variety of structured and unstructured generative tasks, but they struggle to generate procedural geometry in Computer Aided Design (CAD). These difficulties arise from an inability to do spatial reasoning and the necessity to guide a model through complex, long range planning to generate complex geometry. We enable generative CAD Design with LLMs through the introduction of a solver-aided, hierarchical domain specific language (DSL) called AIDL, which offloads the spatial reasoning requirements to a geometric constraint solver. Additionally, we show that in the few-shot regime, AIDL outperforms even a language with in-training data (OpenSCAD), both in terms of generating visual results closer to the prompt and creating objects that are easier to post-process and reason about.

This paper addresses the challenge of occluded robot grasping, i.e. grasping in situations where the desired grasp poses are kinematically infeasible due to environmental constraints such as surface collisions. Traditional robot manipulation approaches struggle with the complexity of non-prehensile or bimanual strategies commonly used by humans in these circumstances. State-of-the-art reinforcement learning (RL) methods are unsuitable due to the inherent complexity of the task. In contrast, learning from demonstration requires collecting a significant number of expert demonstrations, which is often infeasible. Instead, inspired by human bimanual manipulation strategies, where two hands coordinate to stabilise and reorient objects, we focus on a bimanual robotic setup to tackle this challenge. In particular, we introduce Constraint-based Manipulation for Bimanual Occluded Grasping (COMBO-Grasp), a learning-based approach which leverages two coordinated policies: a constraint policy trained using self-supervised datasets to generate stabilising poses and a grasping policy trained using RL that reorients and grasps the target object. A key contribution lies in value function-guided policy coordination. Specifically, during RL training for the grasping policy, the constraint policy's output is refined through gradients from a jointly trained value function, improving bimanual coordination and task performance. Lastly, COMBO-Grasp employs teacher-student policy distillation to effectively deploy point cloud-based policies in real-world environments. Empirical evaluations demonstrate that COMBO-Grasp significantly improves task success rates compared to competitive baseline approaches, with successful generalisation to unseen objects in both simulated and real-world environments.

While deep generative models~(DGMs) have demonstrated remarkable success in capturing complex data distributions, they consistently fail to learn constraints that encode domain knowledge and thus require constraint integration. Existing solutions to this challenge have primarily relied on heuristic methods and often ignore the underlying data distribution, harming the generative performance. In this work, we propose a probabilistically sound approach for enforcing the hard constraints into DGMs to generate constraint-compliant and realistic data. This is achieved by our proposed gradient estimators that allow the constrained distribution, the data distribution conditioned on constraints, to be differentiably learned. We carry out extensive experiments with various DGM model architectures over five image datasets and three scientific applications in which domain knowledge is governed by linear equality constraints. We validate that the standard DGMs almost surely generate data violating the constraints. Among all the constraint integration strategies, ours not only guarantees the satisfaction of constraints in generation but also archives superior generative performance than the other methods across every benchmark.

Ensuring neural networks adhere to domain-specific constraints is crucial for addressing safety and ethical concerns while also enhancing prediction accuracy. Despite the nonlinear nature of most real-world tasks, existing methods are predominantly limited to affine or convex constraints. We introduce ENFORCE, a neural network architecture that guarantees predictions to satisfy nonlinear constraints exactly. ENFORCE is trained with standard unconstrained gradient-based optimizers (e.g., Adam) and leverages autodifferentiation and local neural projections to enforce any $\mathcal{C}^1$ constraint to arbitrary tolerance $\epsilon$. We build an adaptive-depth neural projection (AdaNP) module that dynamically adjusts its complexity to suit the specific problem and the required tolerance levels. ENFORCE guarantees satisfaction of equality constraints that are nonlinear in both inputs and outputs of the neural network with minimal (and adjustable) computational cost.

In this paper, we assume that the (b) Concept shift. Thus, in the above SCM, X and e are concept shift. We compare structural causal models (SCMs) for covariate shift and concept shift. The language of causal inference provides further intuition for the structure imposed on Problem 3.1 by Assumptions 4.1 and 4.2. In particular, the structural causal model (SCM) for problems in which data is generated according to the mechanism described in Assumptions 4.1 and 4.2 is shown in Figure 7a. Recall that in Assumption 4.1 imposes that X and e are causes of the random variable X X. Further, in Assumption 4.2, we assume that P(Y To offer a point of comparison, in Figure 7b, we show a different SCM that does not fulfill our assumptions.

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.

The frequency of the preferred order for a noun phrase formed by demonstrative, numeral, adjective and noun has received significant attention over the last two decades. We investigate the actual distribution of the preferred 24 possible orders. There is no consensus on whether it can be well-fitted by an exponential or a power law distribution. We find that an exponential distribution is a much better model. This finding and other circumstances where an exponential-like distribution is found challenge the view that power-law distributions, e.g., Zipf's law for word frequencies, are inevitable. We also investigate which of two exponential distributions gives a better fit: an exponential model where the 24 orders have non-zero probability or an exponential model where the number of orders that can have non-zero probability is variable. When parsimony and generalizability are prioritized, we find strong support for the exponential model where all 24 orders have non-zero probability. This finding suggests that there is no hard constraint on word order variation and then unattested orders merely result from undersampling, consistently with Cysouw's view.