广义残差闭包：稳定性-可塑性兼容的通用学习动力学

中文摘要 AI 辅助

学习必须获取新能力，同时保留先前职责和再次学习的能力。我们提出广义残差闭包（GRC），一个将学习视为未来相关差异的递归闭包的框架：闭合残差为后续预测、交互和学习建立条件。在固定的学习者-世界边界下，基于完整的表示-关系描述，持久内部学习具有两种原始模式：表示内的变换和表示本身的修订。我们在正则性假设下建立了局部切分解，并给出了表示修订必要性的判据。在仿射模型中，我们推导出稳定性-可塑性兼容的充要条件，以及一个约束二次更新问题的唯一解，该解在保留已登记旧职责的同时，通过有效的安全响应减少残差。我们证明，重建性语义保护相对于保留精确历史实现，能弱扩展安全响应算子。动态充分性和未来闭包可行性将表示充分性从当前预测扩展到合法未来更新和持续学习。增长学习扩展合法闭包域或降低最优闭包成本，而不使已登记能力-成本前沿退化；条件提交规则维持此序。受限部门恢复和条件表示定理将该框架与优化、机器学习和控制联系起来。这些结果共同在持续学习的统一框架中组织了适应、表示修订和可复用能力。

英文摘要

Learning must acquire new capabilities while preserving both prior responsibilities and the capacity to learn again. We introduce Generalized Residual Closure (GRC), a framework for learning as recursive closure of future-relevant discrepancies: closing a residual establishes the conditions for subsequent prediction, interaction, and learning. Under a complete representation-relation description at a fixed learner-world boundary, persistent internal learning has two primitive modes: Transformation within a representation and revision of the Representation itself. We establish a local tangent decomposition under regularity assumptions and a criterion for when representation revision is necessary. In an affine model, we derive a necessary-and-sufficient condition for stability-plasticity compatibility and the unique solution of a constrained quadratic update problem, which preserves registered old responsibilities while reducing residuals with an effective safe response. We prove that reconstructive semantic protection weakly enlarges the safe-response operator relative to preserving an exact historical realization. Dynamic sufficiency and future-closure viability extend representation adequacy from current prediction to lawful future updating and continued learning. Growth Learning expands the lawful closure domain or lowers optimal closure cost without regression of the registered capability-cost frontier; a conditional commit rule maintains this order. Restricted-sector recoveries and a conditional representation theorem connect the framework to optimization, machine learning, and control. Together, these results organize adaptation, representation revision, and reusable capability within a common account of continued learning.

发表机构

• Xi’an Jiaotong University（西安交通大学）
• Xi’an University of Architecture and Technology（西安建筑科技大学）

机构由 AI 辅助整理，请以论文原文为准。