Dual Computational Horizons: Incompleteness and Unpredictability in Intelligent Systems

We formalize two independent computational limitations that constrain algorithmic intelligence: formal incompleteness and dynamical unpredictability. The former limits the deductive power of consistent reasoning systems while the latter bounds long-term prediction under finite precision. We show that these two extrema together impose structural bounds on an agent's ability to reason about its own predictive capabilities. In particular, an algorithmic agent cannot verify its own maximal prediction horizon universally. This perspective clarifies inherent trade-offs between reasoning, prediction, and self-analysis in intelligent systems. The construction presented here constitutes one representative instance of a broader logical class of such limitations.

A kinetic-based regularization method for data science applications

We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce corrections that impose constraints on the lower-order moments of the data distribution. This minimizes the discrepancy between the discrete and continuum representations of the data, in turn allowing to access more favorable energy landscapes, thus improving the accuracy of the interpolator. Our approach improves performance in both interpolation and regression tasks, even in high-dimensional spaces. Unlike traditional methods, it does not require empirical parameter tuning, making it particularly effective for handling noisy data. We also show that thanks to its local nature, the method offers computational and memory efficiency advantages over Radial Basis Function interpolators, especially for large datasets.