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一层网络拟合任意连续函数(HWlayer)

One-layer network fitting any continuous function (HWlayer)

说明

Instruction

  • 这是HWnet(https://github.com/FFiot/HWnet)的升级版本。
  • This is an upgraded version of HWnet (https://github.com/FFiot/HWnet). avatar
  • 稀疏矩阵使网络训练速度加快,但是会引起过拟合,为了兼顾训练速度与泛化能力,设计了HWlayer。
  • The sparse matrix makes the network training faster, but it will cause overfitting. In order to take into account the training speed and generalization ability, HWlayer is designed.
  • 网络调整后的重新训练,也会耗费大量的资源。
  • Retraining after network adjustment will also consume a lot of resources.

方法

Method

  • 对于一个维度的样本集合 [x],通过指定数量的分位数,获得 evaluate_list。
  • For a sample set [x] of one dimension, get evaluate_list with the specified number of quantiles.
  • 通过 softmax(abs(x - evaluate_list) * -1.0 * focus),获得某一个值 x 在 evaluate_list上的分布。
  • Obtain the distribution of a value x on evaluate_list by softmax(abs(x - evaluate_list) * -1.0 * focus).
    • focus 越大,对距离最近的 evaluate 集中度越高;越小,则会关注周边的 evaluate。
    • The larger the focus, the higher the concentration of the nearest evaluate; the smaller the focus, the surrounding evaluate.
    • 解决了归一化问题,每一个数值转换为 一组 0 ~ 1.0 的概率值。
    • Solved the normalization problem, where each value is converted into a set of probability values ​​from 0 to 1.0.
    • 相对于简单的嵌入式向量简单的 0 或者 1,这组概率值同样增加了维度,但是也兼顾了“线性”。
    • Compared to the simple 0 or 1 of the simple embedded vector, this set of probability values ​​also increases the dimension, but also takes into account the "linearity".
    • 基于分位数,使得网络参数使用率基本相同。
    • Based on quantiles, the network parameter usage rates are basically the same.

升级

Upgrade

  • 对于一个维度,数据的分布是不均匀的,如使用相同的 focus 值会导致网络异常。
  • For a dimension, the distribution of data is not uniform, such as using the same focus value will cause network exceptions.
  • 对每一个 evaluate 值,计算 focus,使得每一个 evaluate 计算获得的概率值大致相同。
  • For each evaluate value, calculate focus, so that the probability value obtained by each evaluate calculation is roughly the same.
  • 累计各值域损失: 大于预期的值域进行分裂,小于预期的值域与周围值域合并。
  • By accumulating the loss of each value field: larger than expected will be split, less than expected will be merged.

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