[2603.27880] Kernel Dynamics under Path Entropy Maximization

Computer Science > Machine Learning arXiv:2603.27880 (cs) [Submitted on 29 Mar 2026] Title:Kernel Dynamics under Path Entropy Maximization Authors:Jnaneshwar Das View a PDF of the paper titled Kernel Dynamics under Path Entropy Maximization, by Jnaneshwar Das View PDF HTML (experimental) Abstract:We propose a variational framework in which the kernel function k : X x X -> R, interpreted as the foundational object encoding what distinctions an agent can represent, is treated as a dynamical variable subject to path entropy maximization (Maximum Caliber, MaxCal). Each kernel defines a representational structure over which an information geometry on probability space may be analyzed; a trajectory through kernel space therefore corresponds to a trajectory through a family of effective geometries, making the optimization landscape endogenous to its own traversal. We formulate fixed-point conditions for self-consistent kernels, propose renormalization group (RG) flow as a structured special case, and suggest neural tangent kernel (NTK) evolution during deep network training as a candidate empirical instantiation. Under explicit information-thermodynamic assumptions, the work required for kernel change is bounded below by delta W >= k_B T delta I_k, where delta I_k is the mutual information newly unlocked by the updated kernel. In this view, stable fixed points of MaxCal over kernels correspond to self-reinforcing distinction structures, with biological niches, scientific paradigm...