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.

The statistical ranking problem--inferring a global ordering of items from incomplete and noisy pairwise comparisons--emerges naturally in competitive sports analysis, preference aggregation, and economic exchange systems. Traditional approaches rooted in social choice theory often falter when confronted with modern datasets characterized by two pervasive challenges: (1) the comparisons are sparsely observed, with measurement graphs far from complete; (2) the noise exhibits strong heterogeneity, where certain subsets of comparisons may be significantly more reliable than others. These limitations are particularly evident in applications like soccer league standings analysis, where the outcome matrix contains both structured noise (e.g., home advantage biases) and random outliers. Recent advances in group synchronization theory provide a novel geometric perspective for this classical problem. By mapping player ranks to phases on the unit circle and rank differences to angular offsets, the ranking task becomes equivalent to solving an instance of the angular synchronization problem over SO(2). This reformulation inherits key theoretical guarantees from the synchronization literature: spectral and semidefinite programming (SDP) relaxations can provably recover the underlying ranking under quantifiable noise thresholds. Crucially, the circular representation inherently handles cyclic inconsistencies through phase wrapping, circumventing the need for explicit outlier removal mechanisms required by linear embedding approaches.

Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples onto the feasible set; however, repeated projection can distort the learned distribution and induce a mismatch with the data manifold. Thus, recent multi-stage procedures attempt to defer projection to clean samples during sampling, but they increase algorithmic complexity and accumulate errors across steps. This paper addresses these challenges by proposing a novel training-free method, Chance-constrained Flow Matching (CCFM), that integrates stochastic optimization into the sampling process, enabling effective enforcement of hard constraints while maintaining high-fidelity sample generation. Importantly, CCFM guarantees feasibility in the same manner as conventional repeated projection, yet, despite operating directly on noisy intermediate samples, it is theoretically equivalent to projecting onto the feasible set defined by clean samples. This yields a sampler that mitigates distributional distortion. Empirical experiments show that CCFM outperforms current state-of-the-art constrained generative models in modeling complex physical systems governed by partial differential equations and molecular docking problems, delivering higher feasibility and fidelity.

Bayesian optimization is a natural candidate for the engineering of antibody therapeutic properties, which is often iterative and expensive. However, finding the optimal choice of surrogate model for optimization over the highly structured antibody space is difficult, and may differ depending on the property being optimized. Moreover, to the best of our knowledge, no prior works have attempted to incorporate structural information into antibody Bayesian optimization. In this work, we explore different approaches to incorporating structural information into Bayesian optimization, and compare them to a variety of sequence-only approaches on two different antibody properties, binding affinity and stability. In addition, we propose the use of a protein language model-based ``soft constraint,'' which helps guide the optimization to promising regions of the space. We find that certain types of structural information improve data efficiency in early optimization rounds for stability, but have equivalent peak performance. Moreover, when incorporating the protein language model soft constraint we find that the data efficiency gap is diminished for affinity and eliminated for stability, resulting in sequence-only methods that match the performance of structure-based methods, raising questions about the necessity of structure in Bayesian optimization for antibodies.

Evaluating language models fairly is becoming harder as static benchmarks available on the internet risk contamination by training data. This makes it unclear whether models are truly reasoning or just recalling answers. In this paper, we introduce BeyondBench, an evaluation framework that avoids this problem by using algorithmic problem generation. Unlike traditional benchmarks that risk contamination from internet-scale training data, BeyondBench creates mathematically grounded problems on the fly, ensuring each test remains fresh and uncontaminated. Our framework covers 44 algorithmic tasks with a total of 117 variations, grouped into three difficulty levels: the Easy Suite (29 tasks) for basic arithmetic and statistics, the Medium Suite (5 tasks, 49 variations) for sequence patterns and reasoning, and the Hard Suite (10 tasks, 68 variations) tackling NP-complete and constraint satisfaction problems. Each task generates problems from a combinatorial space larger than 10^15 unique instances, with solutions verified deterministically by mathematical proofs. We evaluated 101 language models, including 85 open-source and 16 closed-source models, spanning sizes from 0.5B to 141B parameters and multiple quantization schemes. Our results show consistent reasoning deficiencies across model families, with performance degrading sharply as problem complexity increases from polynomial to exponential. In our Hard Suite evaluations, models such as Gemini-2.5-pro, Llama-3.3-70B, and Qwen2.5-72B achieved average accuracies of 56.38%, 26.91%, and 33.60%, respectively. Moreover, we observe that performance drops drastically without tool usage, with GPT-5, GPT-5-mini, and GPT-5-nano showing a decline of 16.81%, 28.05%, and 47.59% accuracy on the hard suite. Our leaderboard is publicly available at https://ctrl-gaurav.github.io/BeyondBench/

Solving Traveling Salesman Problem (TSP) is NP-hard yet fundamental for wide real-world applications. Classical exact methods face challenges in scaling, and heuristic methods often require domain-specific parameter calibration. While learning-based approaches have shown promise, they suffer from poor generalization and limited scalability due to fixed training data. This work proposes ViTSP, a novel framework that leverages pre-trained vision language models (VLMs) to visually guide the solution process for large-scale TSPs. The VLMs function to identify promising small-scale subproblems from a visualized TSP instance, which are then efficiently optimized using an off-the-shelf solver to improve the global solution. ViTSP bypasses the dedicated model training at the user end while maintaining effectiveness across diverse instances. Experiments on real-world TSP instances ranging from 1k to 88k nodes demonstrate that ViTSP consistently achieves solutions with average optimality gaps below 0.2%, outperforming existing learning-based methods. Under the same runtime budget, it surpasses the best-performing heuristic solver, LKH-3, by reducing its gaps by 12% to 100%, particularly on very-large-scale instances with more than 10k nodes. Our framework offers a new perspective in hybridizing pre-trained generative models and operations research solvers in solving combinatorial optimization problems, with practical implications for integration into more complex logistics systems. The code is available at https://anonymous.4open.science/r/ViTSP_codes-6683.