The energy paradigm, exemplified by Hopfield networks, offers a principled framework for memory in neural systems by interpreting dynamics as descent on an energy surface. While powerful for static associative memories, it falls short in modeling sequential memory, where transitions between memories are essential. We introduce the Exponential Dynamic Energy Network (EDEN), a novel architecture that extends the energy paradigm to temporal domains by evolving the energy function over multiple timescales. EDEN combines a static high-capacity energy network with a slow, asymmetrically interacting modulatory population, enabling robust and controlled memory transitions. We formally derive short-timescale energy functions that govern local dynamics and use them to analytically compute memory escape times, revealing a phase transition between static and dynamic regimes. The analysis of capacity, defined as the number of memories that can be stored with minimal error rate as a function of the dimensions of the state space (number of feature neurons), for EDEN shows that it achieves exponential sequence memory capacity $O(\gamma^N)$, outperforming the linear capacity $O(N)$ of conventional models. Furthermore, EDEN's dynamics resemble the activity of time and ramping cells observed in the human brain during episodic memory tasks, grounding its biological relevance. By unifying static and sequential memory within a dynamic energy framework, EDEN offers a scalable and interpretable model for high-capacity temporal memory in both artificial and biological systems.

翻译：以Hopfield网络为代表的能量范式为神经系统的记忆提供了一个原则性框架，其将动力学过程解释为在能量曲面上的下降。尽管该范式在静态联想记忆方面表现出强大能力，但在建模序列记忆方面存在不足，因为记忆间的转换在序列记忆中至关重要。本文提出指数动态能量网络（EDEN），这是一种新颖的架构，通过使能量函数在多个时间尺度上演化，将能量范式扩展至时序领域。EDEN将静态高容量能量网络与一个缓慢、非对称交互的调节神经元群体相结合，从而实现稳健且受控的记忆转换。我们形式化推导了支配局部动力学的短时程能量函数，并利用这些函数解析计算记忆逃逸时间，揭示了静态与动态机制之间的相变。对EDEN容量的分析（定义为在状态空间维度（特征神经元数量）的函数关系中，能以最小错误率存储的记忆数量）表明，其实现了指数级序列记忆容量 $O(\\gamma^N)$，优于传统模型的线性容量 $O(N)$。此外，EDEN的动力学特性类似于人类大脑在执行情景记忆任务时观察到的时间细胞与斜坡细胞的活动模式，这为其生物学相关性提供了依据。通过在动态能量框架内统一静态与序列记忆，EDEN为人工与生物系统中的高容量时序记忆提供了一个可扩展且可解释的模型。