Ji-Won Park

Chansu Park, Ji-Won Park, Sewon Park et al.

We extend the Theory of Computation on real numbers, continuous real functions, and bounded closed Euclidean subsets, to compact metric spaces $(X,d)$: thereby generically including computational and optimization problems over higher types, such as the compact 'hyper' spaces of (i) nonempty closed subsets of $X$ w.r.t. Hausdorff metric, and of (ii) equicontinuous functions on $X$. The thus obtained Cartesian closure is shown to exhibit the same structural properties as in the Euclidean case, particularly regarding function pre/image. This allows us to assert the computability of (iii) Fréchet Distances between curves and between loops, as well as of (iv) constrained/Shape Optimization.

Ji-Won Park, Chae Un Kim

In large-scale AI systems, allocating scarce resources such as GPU compute time and bandwidth among multiple agents is a critical challenge. Conventional policies focus on efficiency metrics, potentially leading to dominance concentration that undermines system diversity and stability. We propose Computable Fair Division (CFD), a framework that reinterprets the Boltzmann-Softmax function not as a selection tool but as a probabilistic resource allocation mechanism, redefining the inverse temperature parameter $β$ as a computable control variable governing the efficiency-fairness balance. Static analysis reveals a Pareto frontier with a near-optimal Stability Corridor where total loss remains approximately constant across policy weights. In the dynamic setting, AHC++ (Adaptive Hard-Cap Controller++) updates $β$ in real time using the error between observed dominance and a policy-specified target as feedback. Simulations show that AHC++ suppresses extreme dominance concentration under exogenous shocks while tracking fairness targets without substantial throughput degradation. Scalability analysis confirms that a 100x increase in agents yields only approximately 5.5x increase in execution time. Code: https://github.com/entrofy-ai/computable-fairness