We introduce Neural Attention Memory Models (NAMMs) to improve the performance and efficiency of transformer foundation models. NAMMs are evolved atop pre-trained transformers to provide different latent contexts containing 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 attention matrices produced in each layer. NAMMs learned on a relatively small set of problems substantially improve performance across multiple unseen long-context language tasks while cutting the model's input contexts up to a fraction of the original sizes, setting them apart from prior hand-designed KV cache eviction strategies that only aim to preserve model behavior. 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.