The ability to acquire new skills and knowledge continually is one of the defining qualities of the human brain, which is critically missing in most modern machine vision systems. In this work, we focus on knowledge transfer in the lifelong learning setting. We propose a lifelong learner that models the similarities between the optimal weight spaces of tasks and exploits this in order to enable knowledge transfer across tasks in a continual learning setting. To characterize the'task-parameter relationships', we propose a metric called adaptation rate integral (ARI), which measures the expected rate of adaptation over a finite number of steps for a (task, parameter) pair. These task-parameter relationships are learned using an auxiliary network trained on guided explorations of parameter space. The learned auxiliary network is then used to heuristically select the best parameter sets on seen tasks, which are consolidated using a hypernetwork. Given a new (unseen) task, knowledge transfer occurs through the selection of the most suitable parameter set from the hypernetwork that can be rapidly finetuned. We show that the proposed approach can improve knowledge transfer between tasks across standard benchmarks without any increase in overall model capacity, while naturally mitigating catastrophic forgetting.