numerically safe softmax in VW

vw/Normalizer.h

@@ -2,6 +2,7 @@
 #define moses_Normalizer_h
 
 #include <vector>
+#include <algorithm>
 #include "Util.h"
 
 namespace Discriminative
@@ -45,16 +46,25 @@ public:
   virtual ~SquaredLossNormalizer() {}
 };
 
+// safe softmax
 class LogisticLossNormalizer : public Normalizer
 {
 public:
   virtual void operator()(std::vector<float> &losses) const {
-    float sum = 0;
     std::vector<float>::iterator it;
+
+    float sum = 0;
+    float max = 0;
     for (it = losses.begin(); it != losses.end(); it++) {
-      *it = exp(-*it);
+      *it = -*it;
+      max = std::max(max, *it);
+    }
+
+    for (it = losses.begin(); it != losses.end(); it++) {
+      *it = exp(*it - max);
       sum += *it;
     }
+
     for (it = losses.begin(); it != losses.end(); it++) {
       *it /= sum;
     }