Modern AI agents such as large language models are trained on diverse tasks -- translation, code generation, mathematical reasoning, and text prediction -- simultaneously. A key question is how to quantify the influence of each individual training task on performance on a target task, a problem we refer to as task attribution. The direct approach, leave-one-out retraining, measures the effect of removing each task, but is computationally infeasible at scale. An alternative approach that builds surrogate models to predict the performance on a target task for any subset of training tasks has emerged in the recent literature. Prior work focuses on linear surrogate models, which capture first-order relationships but miss nonlinear interactions such as XOR-type effects. In this paper, we first consider a unified task-weighting framework for analyzing task-attribution methods and establish a new connection between linear surrogate models and influence functions via a second-order analysis. Then, we introduce kernel surrogate models, which more effectively represent second-order task interactions. To efficiently learn the kernel surrogate, we develop a gradient-based estimation procedure that leverages a first-order approximation of pretrained models; empirically, this yields accurate surrogate estimates with less than $2\%$ relative error without repeated retraining. Experiments across multiple settings -- including mathematical reasoning in transformers, in-context learning, and multi-objective reinforcement learning -- demonstrate the effectiveness of kernel surrogate models. They achieve a $25\%$ higher correlation with the leave-one-out ground truth than linear surrogates and influence-function baselines, enabling more accurate and scalable task attribution. When used for downstream data selection, kernel surrogate models further yield a $40\%$ improvement in the aforementioned settings.