Spectral Kernel Dynamics via Maximum Caliber: Fixed Points, Geodesics, and Phase Transitions
We derive a closed-form geometric functional for kernel dynamics on finite graphs by applying the Maximum Caliber (MaxCal) variational principle to the spectral transfer function h(lambda) of the graph Laplacian eigenbasis. The main result is that the MaxCal stationarity condition decouples into N one-dimensional problems with explicit solution: h*(lambda_l) = h_0(lambda_l) exp(-1 - T_l[h*]), yielding self-consistent (fixed-point) kernels via exponential tilting (Corollary 1), log-linear Fisher-Rao geodesics (Corollary 2), a diagonal Hessian stability criterion (Corollary 3), and an l^2_+ isometry for the spectral kernel space (Proposition 3). The spectral entropy H[h_t] provides a comput...
| Authors | Jnaneshwar Das |
|---|---|
| Primary category | cs.RO |
| Published | 10 April 2026 |
| Last updated at source | 10 April 2026 |
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