吉布斯测量来自深形多层感知子的测量
Boris Hanin1, Alexander Zlokapa2
1Princeton University, Department of Operations Research and Financial Engineering, Princeton, New Jersey 08544, USA.
Physical review letters
|March 1, 2026
概括
我们介绍了一个深度神经网络学习的可解决模型. 网络深度和宽度的比率决定了不同的学习模式,影响了特征学习能力.
科学领域:
- 机器学习 机器学习
- 统计物理 统计物理
- 深度学习 (Deep Learning) 是一种深度学习.
背景情况:
- 在深度神经网络中分析贝叶斯后面是复杂的.
- 现有的模型通常需要对初始化或数据做出强有力的假设.
研究的目的:
- 为深层多层感知子开发一种具有扰乱性的可解决模型.
- 在没有限制性假设的情况下,探索大型神经网络中的学习模式.
主要方法:
- 分析吉布斯尺度的图形方法 (贝叶斯后期).
- 在任意温度下分析深形状的多层感知子.
- 对输入维度,深度,宽度和样本都接近无限的极限的研究.
主要成果:
- 极限N0,N,L,P → ∞不通勤,产生一个丰富的相位图.
- LP/N比率定义了特征学习的临界深度.
- 对于LP/N → 0,后部与内核方法相匹配;对于LP/N → λ > 0,发生数据依赖的内核变形.
结论:
- 开发的模型提供了深度神经网络中特征学习的见解.
- 临界比率LP/N控制了内核和数据依赖学习模式之间的过渡.
- 学习特征的明确公式是以1/N的第一顺序推导的.
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