LogSumExp

<p>The LogSumExp (LSE) (also called RealSoftMax or multivariable <a href="/facts/Softplus/pwzdU9jF">softplus</a>) <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> is a <a href="/facts/Smooth_maximum/7M2EJwSN">smooth maximum</a> – a <a href="/facts/Smooth_function/mffL4ch2">smooth</a> <a href="/facts/Approximation/LvYHsXzq">approximation</a> to the <a href="/facts/Maximum/ADlgnyzV">maximum</a> function, mainly used by <a href="/facts/Machine_learning/e0w0XJTu">machine learning</a> algorithms. It is defined as the <a href="/facts/Logarithm/QeXaV97q">logarithm</a> of the sum of the <a href="/facts/Exponential_function/ewlYxvR2">exponentials</a> of the arguments:
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          L
          S
          E
        
        (
        
          x
          
            1
          
        
        ,
        …
        ,
        
          x
          
            n
          
        
        )
        =
        log
        ⁡
        
          (
          
            exp
            ⁡
            (
            
              x
              
                1
              
            
            )
            +
            ⋯
            +
            exp
            ⁡
            (
            
              x
              
                n
              
            
            )
          
          )
        
        .
      
    
    {\displaystyle \mathrm {LSE} (x_{1},\dots ,x_{n})=\log \left(\exp(x_{1})+\cdots +\exp(x_{n})\right).}

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LogSumExp open-in-new

LogSumExp