Constraint-Guided Prediction Refinement via Deterministic Diffusion Trajectories

Many real-world machine learning tasks require outputs that satisfy hard constraints, such as physical conservation laws, structured dependencies in graphs, or column-level relationships in tabular data. Existing approaches rely either on domain-specific architectures and losses or on strong assumptions on the constraint space, restricting their applicability to linear or convex constraints. We propose a general-purpose framework for constraint-aware refinement that leverages denoising diffusion implicit models (DDIMs). Starting from a coarse prediction, our method iteratively refines it through a deterministic diffusion trajectory guided by a learned prior and augmented by constraint gradient corrections. The approach accommodates a wide class of non-convex and nonlinear equality constraints and can be applied post hoc to any base model. We demonstrate the method in two representative domains: constrained adversarial attack generation on tabular data with column-level dependencies and in AC power flow prediction under Kirchhoff's laws. Across both settings, our diffusion-guided refinement improves both constraint satisfaction and performance while remaining lightweight and model-agnostic.

KCLNet: Physics-Informed Power Flow Prediction via Constraints Projections

In the modern context of power systems, rapid, scalable, and physically plausible power flow predictions are essential for ensuring the grid's safe and efficient operation. While traditional numerical methods have proven robust, they require extensive computation to maintain physical fidelity under dynamic or contingency conditions. In contrast, recent advancements in artificial intelligence (AI) have significantly improved computational speed; however, they often fail to enforce fundamental physical laws during real-world contingencies, resulting in physically implausible predictions. In this work, we introduce KCLNet, a physics-informed graph neural network that incorporates Kirchhoff's Current Law as a hard constraint via hyperplane projections. KCLNet attains competitive prediction accuracy while ensuring zero KCL violations, thereby delivering reliable and physically consistent power flow predictions critical to secure the operation of modern smart grids.

TRIDENT: Temporally Restricted Inference via DFA-Enhanced Neural Traversal

Large Language Models (LLMs) and other neural architectures have achieved impressive results across a variety of generative and classification tasks. However, they remain fundamentally ill-equipped to ensure that their outputs satisfy temporal constraints, such as those expressible in Linear Temporal Logic over finite traces (LTLf). In this paper, we introduce TRIDENT: a general and model-agnostic inference-time algorithm that guarantees compliance with such constraints without requiring any retraining. TRIDENT compiles LTLf formulas into a Deterministic Finite Automaton (DFA), which is used to guide a constrained variant of beam search. At each decoding step, transitions that would lead to constraint violations are masked, while remaining paths are dynamically re-ranked based on both the model's probabilities and the DFA's acceptance structure. We formally prove that the resulting sequences are guaranteed to satisfy the given LTLf constraints, and we empirically demonstrate that TRIDENT also improves output quality. We validate our approach on two distinct tasks: temporally constrained image-stream classification and controlled text generation. In both settings, TRIDENT achieves perfect constraint satisfaction, while comparison with the state of the art shows improved efficiency and high standard quality metrics.

Three Bricks to Consolidate Watermarks for Large Language Models

The task of discerning between generated and natural texts is increasingly challenging. In this context, watermarking emerges as a promising technique for ascribing generated text to a specific model. It alters the sampling generation process so as to leave an invisible trace in the generated output, facilitating later detection. This research consolidates watermarks for large language models based on three theoretical and empirical considerations. First, we introduce new statistical tests that offer robust theoretical guarantees which remain valid even at low false-positive rates (less than 10$^{\text{-6}}$). Second, we compare the effectiveness of watermarks using classical benchmarks in the field of natural language processing, gaining insights into their real-world applicability. Third, we develop advanced detection schemes for scenarios where access to the LLM is available, as well as multi-bit watermarking.