We employ a variational neural annealing approach for solving large-scale constrained portfolio optimization problems, mapped onto classical Ising-like Hamiltonians, and study its performance under finite annealing times. The method enables efficient exploration of high-dimensional feasible spaces and achieves competitive solutions on standard financial indices. To characterize the underlying optimization dynamics, we analyze the decay of the residual energy as a function of annealing steps and observe a power-law behavior for fixed problem size. Extending this analysis across different portfolio sizes, we examine whether the optimization dynamics are consistent with a dynamical finite-size scaling form and find that the residual energy data collapse onto a single scaling curve within the studied range. This scaling analysis yields an effective annealing-time exponent that quantifies how computational effort grows with problem size. Our results demonstrate that finite-size scaling concepts provide a useful framework for understanding and forecasting the performance of neural annealing-based optimization methods in realistic, constrained settings.

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• Adiabatic quantum optimization
• Complex systems
• Dynamical phase transitions
• NP-hard problems
• Nonequilibrium statistical mechanics
• Optimization problems
• Scaling laws of complex systems
• Artificial neural networks
• Spin glasses
• Finite-size scaling
• Ising model
• Neural network simulations
• Simulated annealing
• Variational approach