LoRA、QLoRA 与量化：低成本适配模型

import java.util.*;
public class Main {
    static void matrix(double[][] m,int rows,int cols){
        if(m.length!=rows)throw new IllegalArgumentException("rows");
        for(double[] row:m){
            if(row==null || row.length!=cols)throw new IllegalArgumentException("cols");
            for(double value:row)if(!Double.isFinite(value))throw new IllegalArgumentException("value");
        }
    }
    static double[] apply(double[][] w,double[][] a,double[][] b,double[] x,double alpha){
        int in=x.length,out=w.length,r=a.length;
        if(in==0 || out==0 || r==0 || !Double.isFinite(alpha))throw new IllegalArgumentException();
        matrix(w,out,in);matrix(a,r,in);matrix(b,out,r);
        for(double value:x)if(!Double.isFinite(value))throw new IllegalArgumentException();
        double[] mid=new double[r],y=new double[out];
        // 先计算低维投影，不显式构造完整增量矩阵
        for(int k=0;k<r;k++)for(int j=0;j<in;j++)mid[k]+=a[k][j]*x[j];
        for(int i=0;i<out;i++){
            // 基础权重在计算中只读，不会被适配器修改
            for(int j=0;j<in;j++)y[i]+=w[i][j]*x[j];
            for(int k=0;k<r;k++)y[i]+=(alpha/r)*b[i][k]*mid[k];
            // 有限输入仍可能算术溢出，结果必须再检查
            if(!Double.isFinite(y[i]))throw new ArithmeticException("overflow");
        }
        return y;
    }
    static void check(boolean ok){if(!ok)throw new AssertionError();}
    public static void main(String[] args){
        double[][] w={{1,0},{0,1}},a={{1,2}},b={{3},{4}};
        check(Arrays.equals(apply(w,a,b,new double[]{1,1},1),new double[]{10,13}));
        check(Arrays.equals(apply(w,a,b,new double[]{1,1},0),new double[]{1,1}));
        check(Arrays.equals(apply(w,a,new double[][]{{0},{0}},new double[]{1,1},1),new double[]{1,1}));
        double[][] merged={{4,6},{4,9}};
        check(Arrays.equals(apply(merged,a,new double[][]{{0},{0}},new double[]{1,1},1),
                            apply(w,a,b,new double[]{1,1},1)));
        try{apply(w,a,new double[][]{{1,2},{3,4}},new double[]{1,1},1);throw new AssertionError();}
        catch(IllegalArgumentException expected){}
        try{apply(w,a,b,new double[]{Double.NaN,1},1);throw new AssertionError();}
        catch(IllegalArgumentException expected){}
        System.out.println("6 low-rank update checks passed");
    }
}