混合精度与梯度累积：控制显存与数值误差

import java.util.*;
public class Main {
  record Micro(double[] mean,long count) {}
  static double[] combine(List<Micro> parts){
    if(parts.isEmpty()||parts.get(0).mean().length==0)throw new IllegalArgumentException();
    int d=parts.get(0).mean().length;long total=0;
    for(Micro m:parts){
      if(m.count()<0||m.mean().length!=d)throw new IllegalArgumentException();
      total=Math.addExact(total,m.count()); // 样本计数溢出不能静默回绕
      for(double g:m.mean())if(!Double.isFinite(g))throw new IllegalArgumentException();
    }
    if(total==0)throw new IllegalArgumentException("no effective targets");
    double[] answer=new double[d];
    for(Micro m:parts){
      double weight=(double)m.count()/total; // 先形成占比，避免均值乘巨大计数
      for(int j=0;j<d;j++)answer[j]+=weight*m.mean()[j];
    }
    for(double g:answer)if(!Double.isFinite(g))throw new ArithmeticException("range");
    return answer; // 等权平均仅是各计数相同时的特例
  }
  static void close(double a,double b){if(Math.abs(a-b)>1e-10)throw new AssertionError();}
  public static void main(String[] args){
    close(combine(List.of(new Micro(new double[]{2},1),new Micro(new double[]{6},3)))[0],5);
    double[] v=combine(List.of(new Micro(new double[]{1,2},2),new Micro(new double[]{3,4},2)));
    close(v[0],2);close(v[1],3);
    close(combine(List.of(new Micro(new double[]{99},0),new Micro(new double[]{7},1)))[0],7);
    close(combine(List.of(new Micro(new double[]{-2},1),new Micro(new double[]{2},1)))[0],0);
    boolean bad=false;try{combine(List.of(new Micro(new double[]{0},0)));}catch(IllegalArgumentException e){bad=true;}
    if(!bad)throw new AssertionError();
    bad=false;try{combine(List.of(new Micro(new double[]{1},Long.MAX_VALUE),new Micro(new double[]{1},1)));}catch(ArithmeticException e){bad=true;}
    if(!bad)throw new AssertionError();
    System.out.println("6 weighted gradient checks passed");
  }
}