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深度神经网络中的类别学习:内部表示的信息内容和几何结构
Laurent Bonnasse-Gahot1, Jean-Pierre Nadal1,2
1CNRS, École des Hautes Études en Sciences Sociales, Centre d'Analyse et de Mathématique Sociales, F-75006 Paris, France.
Physical review. E
|December 23, 2025
概括
人工神经网络中的类别学习增强了边界附近的歧视,反映了人类的感知. 这种高效的学习过程通过在决策边界扩大神经空间来优化信息处理.
科学领域:
- 计算神经科学是一种神经科学.
- 机器学习 机器学习
- 信息理论 信息理论
背景情况:
- 类别感知,以类别内压缩和类别间分离为特征,在人类和人工神经网络中观察到.
- 之前的研究表明,这种现象是有效学习在理论框架中的必要结果.
- 这种高效的学习减少了噪声在关键类别边界的影响.
研究的目的:
- 将高效学习和分类感知理论框架扩展到人工前网络.
- 研究如何将贝叶斯成本最小化与最大化神经网络中相互信息的关系.
- 分析结构化数据和网络宽度在实现最佳表示中的作用.
主要方法:
- 将信息理论方法应用于人工前网络,将贝叶斯成本视为交叉损失.
- 证明将贝叶斯成本最小化相当于最大化类别和神经活动之间的相互信息.
- 用结构化数据分析了广泛的网络,将相互信息最大化与基于费舍尔信息的最佳投影空间和神经表征联系起来.
主要成果:
- 在前网络中最大限度地降低贝叶斯成本意味着最大限度地提高类别和神经活动之间的相互信息.
- 广泛网络中的最佳学习导致基于费舍尔信息的神经表征与指标,与特定类别的费舍尔信息保持一致.
- 分类学习诱导了决策边界附近的神经空间的扩张,这是分类感知的一个关键相关物,费舍尔信息最大值在类边界附近,但不完全在类边界.
结论:
- 这项研究提供了一个理论框架,解释了类别感知是人工前网络中高效学习的结果.
- 最佳的学习涉及最大限度地提高相互信息,从而导致在类别界限上加强歧视的表示.
- 这些发现表明,人工神经网络表现出关键的神经关联的分类感知,验证在玩具模型和MNIST数据集.
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