arXiv:2610.37203v1 Announce Type: new Abstract: Humanoids and other legged robots operating in complex environments must remember information that leaves their field of view and only becomes relevant much later. Reinforcement learning policies address this using memory networks such as LSTMs that are trained end-to-end with the policy to memorize such task-relevant aspects. Yet, such architectures often fail to preserve sufficient information over long horizons. In this work, we propose a network architecture based on Hadamard memory that specifically targets robot navigation. Our Local Spatial Matrix Memory (LSMM) enables RL agents to store generic task-relevant information at specific, position-based memory cells, enabling flexible and spatially grounded memorization. We evaluate LSMM on the task of autonomous maze exploration, where it matches the maze coverage of strong recurrent and finite-history baselines while being the only architecture that remembers the maze layout, reducing the reconstruction error threefold.