Scholarlink

<p>Modern AI systems excel at pattern recognition and task execution, but they often fall short of replicating the layered, self-referential structure of human thought that unfolds over time. In this paper, we present a mathematically grounded and conceptually simple framework based on smoothed step functions—sigmoid approximations of Heaviside functions—to model the recursive development of mental activity. Each cognitive layer becomes active at a specific temporal threshold, with the abruptness or gradualness of activation governed by an impressiveness parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( s_i \)</EquationSource> </InlineEquation>, which we interpret as a measure of emotional salience or situational impact. Small values of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( s_i \)</EquationSource> </InlineEquation> represent intense or traumatic experiences, producing sharp and impulsive responses, while large values correspond to persistent background stress, yielding slow but sustained cognitive activation. We formulate the recursive dynamics of these cognitive layers and demonstrate how they give rise to layered cognition, time-based attention, and adaptive memory reinforcement. Unlike conventional memory models, our approach captures thoughts and recall events through a recursive, impressiveness-sensitive pathway, leading to context-dependent memory traces. This recursive structure offers a new perspective on how awareness and memory evolve over time, and provides a promising foundation for designing artificial systems capable of simulating recursive, temporally grounded consciousness.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Irreversibility of recursive Heaviside memory functions: a distributional perspective on structural cognition

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年11月28日

查看全文
  • Changsoo Shin

摘要

Modern AI systems excel at pattern recognition and task execution, but they often fall short of replicating the layered, self-referential structure of human thought that unfolds over time. In this paper, we present a mathematically grounded and conceptually simple framework based on smoothed step functions—sigmoid approximations of Heaviside functions—to model the recursive development of mental activity. Each cognitive layer becomes active at a specific temporal threshold, with the abruptness or gradualness of activation governed by an impressiveness parameter \( s_i \) , which we interpret as a measure of emotional salience or situational impact. Small values of \( s_i \) represent intense or traumatic experiences, producing sharp and impulsive responses, while large values correspond to persistent background stress, yielding slow but sustained cognitive activation. We formulate the recursive dynamics of these cognitive layers and demonstrate how they give rise to layered cognition, time-based attention, and adaptive memory reinforcement. Unlike conventional memory models, our approach captures thoughts and recall events through a recursive, impressiveness-sensitive pathway, leading to context-dependent memory traces. This recursive structure offers a new perspective on how awareness and memory evolve over time, and provides a promising foundation for designing artificial systems capable of simulating recursive, temporally grounded consciousness.