Generating realistic time series samples is crucial for stress-testing models and protecting applications, user these privac samples y by using must synthetic meet certain data.

Integrating logical constraints into object detection models for autonomous driving (AD) is a promising way to enhance their compliance to rules and thus increase the safety of the system. In this, t-norms have been utilized to calculate the constrained loss, i.e., the violations of logical constraints as losses. While prior works have statically selected few t-norms, we conduct an extensive experimental study to identify the most effective choices, as suboptimal t-norms can lead to undesired model behavior. For this, we present MOD-ECL, a neurosymbolic framework that implements a wide range of t-norms and can use them in an adaptive manner, with an algorithm that selects well-performing t-norms during training and a scheduler that regulates the impact of the constrained loss. We evaluate its effectiveness on the ROAD-R and ROAD-Waymo-R datasets for object detection in AD with attached common-sense constraints. Our results show that careful selection of parameters is crucial for good behavior of the constrained loss and that our framework allows us to obtain not only lower constraint violation but in some cases also an increase in detection performance. Furthermore, our methods allow fine control over the tradeoff between accuracy and violation.1

Reasoning-enhanced large language models (RLLMs), whether explicitly trained for reasoning or prompted via chain-of-thought (CoT), have achieved state-ofthe-art performance on many complex reasoning tasks. However, we uncover a surprising and previously overlooked phenomenon: explicit CoT reasoning can significantly degrade instruction-following accuracy. Evaluating 20+ models on two benchmarks: IFEval (with simple, rule-verifiable constraints) and ComplexBench (with complex, compositional constraints), we consistently observe performance drops when CoT prompting is applied. Through large-scale case studies and an attention-based analysis, we identify common patterns where reasoning either helps (e.g., with formatting or lexical precision) or hurts (e.g., by neglecting simple constraints or introducing unnecessary content). We propose a metric, constraint attention, to quantify model focus during generation and show that CoT reasoning often diverts attention away from instruction-relevant tokens. To mitigate these effects, we introduce and evaluate four strategies: in-context learning, selfreflection, self-selective reasoning, and classifier-selective reasoning. Our results demonstrate that selective reasoning strategies, particularly classifier-selective reasoning, can substantially recover lost performance. To our knowledge, this is the first work to systematically expose reasoning-induced failures in instructionfollowing and offer practical mitigation strategies.

Diffusion models have shown remarkable potential in planning and control tasks due to their ability to represent multimodal distributions over actions and trajectories. However, ensuring safety under constraints remains a critical challenge for diffusion models. This paper proposes Constrained Diffusers, an extended framework for planning and control that incorporates distribution-level constraints into pretrained diffusion models without retraining or architectural modifications. Inspired by constrained optimization, we apply a constrained Langevin sampling method for the reverse diffusion process that jointly optimizes the trajectory and achieves constraint satisfaction through three iterative algorithms: projected method, primaldual method and augmented Lagrangian method. In addition, we incorporate discrete control barrier functions as constraints for constrained diffusers to guarantee safety in online implementation, following a receding-horizon control that we generate a short-horizon plan and execute only the first action before replanning. Experiments in Maze2D, locomotion, and PyBullet ball running tasks demonstrate that our proposed methods achieve constraint satisfaction with less computation time, and are competitive with existing methods in environments with static and time-varying constraints. The implementation can be found here.

Deep generative models have recently been applied to physical systems governed by partial differential equations (PDEs), offering scalable simulation and uncertainty-aware inference. However, enforcing physical constraints, such as conservation laws (linear and nonlinear) and physical consistencies, remains challenging. Existing methods often rely on soft penalties or architectural biases that fail to guarantee hard constraints. In this work, we propose Physics-Constrained Flow Matching (PCFM), a zero-shot inference framework that enforces arbitrary nonlinear constraints in pretrained flow-based generative models. PCFM continuously guides the sampling process through physics-based corrections applied to intermediate solution states, while remaining aligned with the learned flow and satisfying physical constraints. Empirically, PCFM outperforms both unconstrained and constrained baselines on a range of PDEs, including those with shocks, discontinuities, and sharp features, while ensuring exact constraint satisfaction at the final solution. Our method provides a flexible framework for enforcing hard constraints in both scientific and general-purpose generative models, especially in applications where constraint satisfaction is essential.

Diffusion models have shown remarkable potential in planning and control tasks due to their ability to represent multimodal distributions over actions and trajectories. However, ensuring safety under constraints remains a critical challenge for diffusion models. This paper proposes Constrained Diffusers, an extended framework for planning and control that incorporates distribution-level constraints into pre-trained diffusion models without retraining or architectural modifications. Inspired by constrained optimization, we apply a constrained Langevin sampling method for the reverse diffusion process that jointly optimizes the trajectory and achieves constraint satisfaction through three iterative algorithms: projected method, primal-dual method and augmented Lagrangian method. In addition, we incorporate discrete control barrier functions as constraints for constrained diffusers to guarantee safety in online implementation, following a receding-horizon control that we generate a short-horizon plan and execute only the first action before replanning. Experiments in Maze2D, locomotion, and PyBullet ball running tasks demonstrate that our proposed methods achieve constraint satisfaction with less computation time, and are competitive with existing methods in environments with static and time-varying constraints.

Enforcing nonlinear inequality constraints in neural networks remains challenging, especially when the output is subject to many coupled constraints. Existing hard constraint methods often impose structural restrictions on the constraint set or introduce substantial computational overhead for large-scale nonlinear problems. Here, we propose DiffSlack, a differentiable projection layer for nonlinear inequality-constrained neural prediction. DiffSlack reformulates inequalities as equalities with learnable slack variables, which are predicted as part of the augmented network output and provide a data-driven warm start for damped Gauss-Newton projection. The projection layer maps raw predictions onto the augmented feasible manifold while preserving end-to-end differentiability. A two-stage curriculum further stabilizes training and improves constraint satisfaction. We evaluate DiffSlack on vehicle path planning with 200 nonlinear inequality constraints from collision avoidance, curvature limits, and waypoint spacing. Compared with existing learning-based baselines, DiffSlack achieves a higher planning success rate and stronger geometric constraint satisfaction under a comparable inference budget. Ablation studies further show that the hard projection layer reduces sensitivity to supervision quality. Closed-loop tracking in CARLA and real-world vehicle experiments confirms the executability of the generated trajectories. These results demonstrate that DiffSlack provides a practical and scalable approach to embedding hard inequality constraints into neural networks for engineering applications.

We consider the task of training machine learning models with data-dependent constraints. Such constraints often arise as empirical versions of expected value constraints that enforce fairness or stability goals. We reformulate data-dependent constraints so that they are calibrated: enforcing the reformulated constraints guarantees that their expected value counterparts are satisfied with a user-prescribed probability. The resulting optimization problem is amendable to standard stochastic optimization algorithms, and we demonstrate the efficacy of our method on a fairness-sensitive classification task where we wish to guarantee the classifier's fairness (at test time).

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