Amandip Sangha

Amandip Sangha

We present a differential-geometric formulation of automatic differentiation (AD) based on jet functors and Weil algebras. In this framework, forward- and reverse-mode differentiation arise naturally as pushforward and cotangent pullback, while higher-order differentiation corresponds to evaluation in a Weil algebra. This construction provides a unified, coordinate-free view of derivative propagation and clarifies the algebraic structure underlying AD. All results are realized in modern JAX code, where the Weil-mode formulation computes all mixed derivatives in a single forward pass with cost linear in the algebra dimension. The resulting implementation achieves algebraically exact and numerically stable differentiation with predictable scaling, demonstrating that geometric abstraction can yield more efficient and transparent computational differentiation systems. Code is available at https://git.nilu.no/geometric-ad/jet-weil-ad

Amandip Sangha

This paper presents a machine learning-based approach to estimate the energy consumption of virtual servers without access to physical power measurement interfaces. Using resource utilization metrics collected from guest virtual machines, we train a Gradient Boosting Regressor to predict energy consumption measured via RAPL on the host. We demonstrate, for the first time, guest-only resource-based energy estimation without privileged host access with experiments across diverse workloads, achieving high predictive accuracy and variance explained ($0.90 \leq R^2 \leq 0.97$), indicating the feasibility of guest-side energy estimation. This approach can enable energy-aware scheduling, cost optimization and physical host independent energy estimates in virtualized environments. Our approach addresses a critical gap in virtualized environments (e.g. cloud) where direct energy measurement is infeasible.