识别由增益与流形外位移引起的神经状态变化
Identifying Neural State Changes due to Gain versus Off-Manifold Displacement
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中文总结 AI 辅助
本文提出一种几何分解方法，区分神经状态变化中由增益调制与流形外位移引起的成分，并通过几何门控明确可识别性条件，为神经状态转变机制提供可解释的量化框架。
中文摘要 AI 辅助
记忆分割被认为源于神经活动的快速去相关，通常通过欧几里得距离或余弦角度来量化。尽管这些指标能检测到转变，但它们无法揭示新状态与神经流形所表征的 repertoire（表征库）之间的关系。这一点很重要，因为驱动状态转变的神经调节物质也会改变兴奋性，而学习可能重新利用现有表征或创建新表征。在此，我引入一种几何分解方法，将可归因于邻近流形状态增益调制的变化与流形内的移动以及真正的流形外位移区分开来。该方法利用神经群体活动的径向轴来划分局部流形区域的法空间。一个核心挑战是可识别性：仅给定一个静态参考流形和一个测试状态，通常无法唯一恢复扰动起始的状态、其增益幅度及机制分解。因此，我将可识别性表述为一系列几何门控，用以指定每个组件何时可被解释。这些门控区分结构性失败（包括缺乏局部坐标图或内在维度错误）与由参考采样、切框架误差、增益轴错位、锚点位移及不良比率条件引起的估计误差和系统性偏差。模拟表明，邻域大小、曲率、采样密度、环境维度及噪声通过少量几何量起作用。该框架明确了增益或新颖性的分配何时可识别、如何产生偏差，以及哪些诊断揭示相关失效模式。通过量化神经状态变化的性质而不仅是幅度，它为评估神经状态转变机制提供了一个清晰、易于解释的框架。
英文摘要
Memory segmentation is thought to arise from rapid decorrelation in neural activity, often quantified by Euclidean distance or cosine angle. Although these metrics detect a transition, they do not reveal how the new state relates to the repertoire represented by the neural manifold. This matters because neuromodulators that drive state transitions also alter excitability, and learning may repurpose existing representations or create new ones. Here, I introduce a geometric decomposition that separates changes attributable to gain modulation of a nearby manifold state from movement within the manifold and genuine off-manifold displacement. The approach uses the radial axis of neural population activity to partition the normal space of a local manifold region. A central challenge is identifiability: given only a static reference manifold and a single test state, neither the state from which a perturbation began nor its gain magnitude and mechanistic decomposition can generally be recovered uniquely. I therefore formulate identifiability as a cascade of geometric gates specifying when each component can be interpreted. The gates distinguish structural failures, including the absence of a local chart or incorrect intrinsic dimensionality, from estimation error and systematic bias caused by reference sampling, tangent-frame error, gain-axis misalignment, anchor displacement, and poor ratio conditioning. Simulations show that neighborhood size, curvature, sampling density, ambient dimension, and noise act through a small set of geometric quantities. The framework specifies when assignments to gain or novelty are identifiable, how they become biased, and which diagnostics reveal the relevant failure regime. By quantifying the nature rather than only the magnitude of neural state change, it provides a clear, readily interpretable framework for evaluating mechanisms of neural state transitions.
发表机构
- University of New Mexico Health Sciences Center（新墨西哥大学健康科学中心）
机构由 AI 辅助整理，请以论文原文为准。
