Prior methods propose to offset the escalating costs of modern foundation models by dropping specific parts of their contexts with hand-designed rules, while attempting to preserve their original performance. We overcome this trade-off with Neural Attention Memory Models (NAMMs), introducing a learned network for memory management that improves both the performance and efficiency of transformers. We evolve NAMMs atop pre-trained transformers to provide different latent contexts focusing on the most relevant information for individual layers and attention heads. NAMMs are universally applicable to any model using self-attention as they condition exclusively on the values in the produced attention matrices. Learning NAMMs on a small set of problems, we achieve substantial performance improvements across multiple long-context benchmarks while cutting the model's input contexts up to a fraction of the original sizes. We show the generality of our conditioning enables zero-shot transfer of NAMMs trained only on language to entirely new transformer architectures even across input modalities, with their benefits carrying over to vision and reinforcement learning.