Neural Network Pruning via QUBO Optimization

Neural network pruning can be formulated as a combinatorial optimization problem, yet most existing approaches rely on greedy heuristics that ignore complex interactions between filters. Formal optimization methods such as Quadratic Unconstrained Binary Optimization (QUBO) provide a principled alternative but have so far underperformed due to oversimplified objective formulations based on metrics like the L1-norm. In this work, we propose a unified Hybrid QUBO framework that bridges heuristic importance estimation with global combinatorial optimization. Our formulation integrates gradient-aware sensitivity metrics - specifically first-order Taylor and second-order Fisher information - into the linear term, while utilizing data-driven activation similarity in the quadratic term. This allows the QUBO objective to jointly capture individual filter relevance and inter-filter functional redundancy. We further introduce a dynamic capacity-driven search to strictly enforce target sparsity without distorting the optimization landscape. Finally, we employ a two-stage pipeline featuring a Tensor-Train (TT) Refinement stage - a gradient-free optimizer that fine-tunes the QUBO-derived solution directly against the true evaluation metric. Experiments on the SIDD image denoising dataset demonstrate that the proposed Hybrid QUBO significantly outperforms both greedy Taylor pruning and traditional L1-based QUBO, with TT Refinement providing further consistent gains at appropriate combinatorial scales. This highlights the potential of hybrid combinatorial formulations for robust, scalable, and interpretable neural network compression.

Benchmarking Reinforcement Learning via Stochastic Converse Optimality: Generating Systems with Known Optimal Policies

The objective comparison of Reinforcement Learning (RL) algorithms is notoriously complex as outcomes and benchmarking of performances of different RL approaches are critically sensitive to environmental design, reward structures, and stochasticity inherent in both algorithmic learning and environmental dynamics. To manage this complexity, we introduce a rigorous benchmarking framework by extending converse optimality to discrete-time, control-affine, nonlinear systems with noise. Our framework provides necessary and sufficient conditions, under which a prescribed value function and policy are optimal for constructed systems, enabling the systematic generation of benchmark families via homotopy variations and randomized parameters. We validate it by automatically constructing diverse environments, demonstrating our framework's capacity for a controlled and comprehensive evaluation across algorithms. By assessing standard methods against a ground-truth optimum, our work delivers a reproducible foundation for precise and rigorous RL benchmarking.

SCOPE: Smooth Convex Optimization for Planned Evolution of Deformable Linear Objects

We present SCOPE, a fast and efficient framework for modeling and manipulating deformable linear objects (DLOs). Unlike conventional energy-based approaches, SCOPE leverages convex approximations to significantly reduce computational cost while maintaining smooth and physically plausible deformations. This trade-off between speed and accuracy makes the method particularly suitable for applications requiring real-time or near-real-time response. The effectiveness of the proposed framework is demonstrated through comprehensive simulation experiments, highlighting its ability to generate smooth shape trajectories under geometric and length constraints.

Quantum-Inspired Episode Selection for Monte Carlo Reinforcement Learning via QUBO Optimization

Monte Carlo (MC) reinforcement learning suffers from high sample complexity, especially in environments with sparse rewards, large state spaces, and correlated trajectories. We address these limitations by reformulating episode selection as a Quadratic Unconstrained Binary Optimization (QUBO) problem and solving it with quantum-inspired samplers. Our method, MC+QUBO, integrates a combinatorial filtering step into standard MC policy evaluation: from each batch of trajectories, we select a subset that maximizes cumulative reward while promoting state-space coverage. This selection is encoded as a QUBO, where linear terms favor high-reward episodes and quadratic terms penalize redundancy. We explore both Simulated Quantum Annealing (SQA) and Simulated Bifurcation (SB) as black-box solvers within this framework. Experiments in a finite-horizon GridWorld demonstrate that MC+QUBO outperforms vanilla MC in convergence speed and final policy quality, highlighting the potential of quantum-inspired optimization as a decision-making subroutine in reinforcement learning.