Abstract
The Hopfield model provides a mathematical framework for understanding the mechanisms of memory storage and retrieval in the human brain. This model has inspired decades of research on learning and retrieval dynamics, capacity estimates, and sequential transitions among memories. Notably, the role of external inputs has been largely underexplored, from their effects on neural dynamics to how they facilitate effective memory retrieval. To bridge this gap, we propose a dynamical system framework in which the external input directly influences the neural synapses and shapes the energy landscape of the Hopfield model. This plasticity-based mechanism provides a clear energetic interpretation of the memory retrieval process and proves effective at correctly classifying mixed inputs. Furthermore, we integrate this model within the framework of modern Hopfield architectures to elucidate how current and past information are combined during the retrieval process. Last, we embed both the classic and the proposed model in an environment disrupted by noise and compare their robustness during memory retrieval.