Finally, we conduct numerical experiments to validate our theoretical results.

We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems (CSP), via a common generalization in terms of random bipartite graphs. Our algorithm matches up to a constant factor the best-known bounds for the number of edges (or constraints) needed for perfect recovery and its running time is linear in the number of edges used. The time complexity is significantly better than both spectral and SDP-based approaches. The main contribution of the algorithm is in the case of unequal sizes in the bi-partition that arises in our reduction from the planted CSP . Here our algorithm succeeds at a significantly lower density than the spectral approaches, surpassing a barrier based on the spectral norm of a random matrix. Other significant features of the algorithm and analysis include (i) the critical use of power iteration with subsampling, which might be of independent interest; its analysis requires keeping track of multiple norms of an evolving solution (ii) the algorithm can be implemented statistically, i.e., with very limited access to the input distribution (iii) the algorithm is extremely simple to implement and runs in linear time, and thus is practical even for very large instances.

Symmetry breaking is a technique for speeding up propositional satisfiability testing by adding constraints to the theory that restrict the search space while preserving satisfiability. In this work, we extend symmetry breaking to the problem of model finding in weighted and unweighted relational theories, a class of problems that includes MAP inference in Markov Logic and similar statistical-relational languages. We introduce term symmetries, which are induced by an evidence set and extend to symmetries over a relational theory. We provide the important special case of term equivalent symmetries, showing that such symmetries can be found in low-degree polynomial time. We show how to break an exponential number of these symmetries with added constraints whose number is linear in the size of the domain. We demonstrate the effectiveness of these techniques through experiments in two relational domains. We also discuss the connections between relational symmetry breaking and work on lifted inference in statistical-relational reasoning.

Lifted inference rules exploit symmetries for fast reasoning in statistical relational models. Computational complexity of these rules is highly dependent on the choice of the constraint language they operate on and therefore coming up with the right kind of representation is critical to the success of lifted inference. In this paper, we propose a new constraint language, called setineq, which allows subset, equality and inequality constraints, to represent substitutions over the variables in the theory. Our constraint formulation is strictly more expressive than existing representations, yet easy to operate on. We reformulate the three main lifting rules: decomposer, generalized binomial and the recently proposed single occurrence for MAP inference, to work with our constraint representation. Experiments on benchmark MLNs for exact and sampling based inference demonstrate the effectiveness of our approach over several other existing techniques.

This work presents a two-layer, human-centric production planning framework designed to optimize both operational efficiency and workforce fairness in industrial manufacturing. The first layer formulates the Order-Line allocation as a Constraint Programming (CP) problem, generating high-utilization production schedules that respect machine capacities, processing times, and due dates. The second layer models Worker-Line allocation as a Markov Decision Process (MDP), integrating human factors such as worker preference, experience, resilience, and medical constraints into the assignment process. Three solution strategies, greedy allocation, MCTS, and RL, are implemented and compared across multiple evaluation scenarios. The proposed system is validated through 16 test sessions with domain experts from the automotive industry, combining quantitative key performance indicators (KPIs) with expert ratings. Results indicate that the CP-based scheduling approach produces compact, feasible production plans with low tardiness, while the MDP-based worker allocation significantly improves fairness and preference alignment compared to baseline approaches. Domain experts rated both the Order-Line and Worker-Line components as effective and highlighted opportunities to further refine the objective function to penalize excessive earliness and improve continuity in worker assignments. Overall, the findings demonstrate that combining CP with learning-based decision-making provides a robust approach for human-centric production planning. The approach enables simultaneous optimization of throughput and workforce well-being, offering a practical foundation for fair and efficient manufacturing scheduling in industrial settings.

Coordinated multi-arm manipulation requires satisfying multiple simultaneous geometric constraints across high-dimensional configuration spaces, which poses a significant challenge for traditional planning and control methods. In this work, we propose Adaptive Diffusion Constrained Sampling (ADCS), a generative framework that flexibly integrates both equality (e.g., relative and absolute pose constraints) and structured inequality constraints (e.g., proximity to object surfaces) into an energy-based diffusion model. Equality constraints are modeled using dedicated energy networks trained on pose differences in Lie algebra space, while inequality constraints are represented via Signed Distance Functions (SDFs) and encoded into learned constraint embeddings, allowing the model to reason about complex spatial regions. A key innovation of our method is a Transformer-based architecture that learns to weight constraint-specific energy functions at inference time, enabling flexible and context-aware constraint integration. Moreover, we adopt a two-phase sampling strategy that improves precision and sample diversity by combining Langevin dynamics with resampling and density-aware re-weighting. Experimental results on dual-arm manipulation tasks show that ADCS significantly improves sample diversity and generalization across settings demanding precise coordination and adaptive constraint handling.

Abstract--Accurate, fair, and explainable allocation of candidates to roles represents a fundamental challenge across multiple domains including corporate hiring, academic admissions, fellowship awards, and volunteer placement systems. Current state-of-the-art approaches suffer from semantic inflexibility, persistent demographic bias, opacity in decision-making processes, and poor scalability under dynamic policy constraints. Our experimental evaluation on large-scale international benchmarks comprising 20,000 candidate profiles and 3,000 role specifications demonstrates superior performance with 94.5% top-3 allocation accuracy, 37% improvement in diversity representation, 0.98 fairness score across demographic categories, and sub-second end-to-end latency. Additionally, GESA incorporates hybrid recommendation capabilities and glass-box explainability, making it suitable for deployment across diverse international contexts in industry, academia, and non-profit sectors. The problem of matching candidates to appropriate roles efficiently and fairly represents one of the most critical challenges in modern organizational and institutional decision-making processes. This challenge spans multiple domains: corporate talent acquisition where companies struggle to identify optimal candidates from thousands of applications [1], academic admissions where universities must select students who will thrive in specific programs [2], research fellowship allocation where funding bodies need to match candidates with projects [3], and volunteer placement systems where non-profit organizations seek to optimize volunteer-task assignments [4]. Despite decades of research and development, existing allocation systems continue to exhibit fundamental limitations that significantly impact their effectiveness and fairness. First, semantic inflexibility remains a persistent issue--traditional keyword-based and static embedding approaches fail to capture the nuanced contextual relationships between candidate qualifications and role requirements [5].

Modifications to test-time sampling have emerged as an important extension to diffusion algorithms, with the goal of biasing the generative process to achieve a given objective without having to retrain the entire diffusion model. However, generating jointly correlated samples from multiple pre-trained diffusion models while simultaneously enforcing task-specific constraints without costly retraining has remained challenging. To this end, we propose Projected Coupled Diffusion (PCD), a novel test-time framework for constrained joint generation. PCD introduces a coupled guidance term into the generative dynamics to encourage coordination between diffusion models and incorporates a projection step at each diffusion step to enforce hard constraints. Empirically, we demonstrate the effectiveness of PCD in application scenarios of image-pair generation, object manipulation, and multi-robot motion planning. Our results show improved coupling effects and guaranteed constraint satisfaction without incurring excessive computational costs.

We present a recurrent neuronal network, modeled as a continuous-time dynamical system, that can solve constraint satisfaction problems. Discrete variables are represented by coupled Winner-Take-All (WTA) networks, and their values are encoded in localized patterns of oscillations that are learned by the recurrent weights in these networks. Constraints over the variables are encoded in the network connectivity. Although there are no sources of noise, the network can escape from local optima in its search for solutions that satisfy all constraints by modifying the effective network connectivity through oscillations. If there is no solution that satisfies all constraints, the network state changes in a pseudo-random manner and its trajectory approximates a sampling procedure that selects a variable assignment with a probability that increases with the fraction of constraints satisfied by this assignment.