Betteti Simone, Baggio Giacomo, Bullo Francesco, Zampieri Sandro
Department of Information Engineering, University of Padua, Padua 35131, Italy.
Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA 93106, USA.
Sci Adv. 2025 Apr 25;11(17):eadu6991. doi: 10.1126/sciadv.adu6991. Epub 2025 Apr 23.
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.
霍普菲尔德模型为理解人类大脑中记忆存储和检索的机制提供了一个数学框架。该模型激发了数十年来关于学习和检索动力学、容量估计以及记忆之间顺序转换的研究。值得注意的是，外部输入的作用在很大程度上未得到充分探索，从它们对神经动力学的影响到它们如何促进有效的记忆检索。为了弥合这一差距，我们提出了一个动力学系统框架，其中外部输入直接影响神经突触并塑造霍普菲尔德模型的能量景观。这种基于可塑性的机制为记忆检索过程提供了清晰的能量解释，并在正确分类混合输入方面证明是有效的。此外，我们将该模型整合到现代霍普菲尔德架构的框架内，以阐明在检索过程中当前信息和过去信息是如何结合的。最后，我们将经典模型和提出的模型都嵌入到一个受噪声干扰的环境中，并比较它们在记忆检索过程中的鲁棒性。
