[GitHub] leezu commented on issue #11938: l2_normalization for fp16 got 0.0 when data is very large

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leezu commented on issue #11938: l2_normalization for fp16 got 0.0 when data is very large
URL: https://github.com/apache/incubator-mxnet/issues/11938#issuecomment-409411171
 
 
   @TccccD the reason is that `mx.symbol.norm` uses a numerically stable algorithm to compute the 2-norm (https://github.com/apache/incubator-mxnet/pull/11573), whereas the L2Normalization is prone to under or overflow.
   
   Below a shorter example of the problem
   ```
   
   In [15]: a = mx.nd.random.uniform(-5, 5, (512,100000), ctx=mx.gpu(0), dtype='float16')
   
   In [16]: mx.nd.L2Normalization(a)
   Out[16]:
   
   [[ 0. -0.  0. ...,  0. -0.  0.]
    [-0.  0. -0. ...,  0.  0.  0.]
    [ 0. -0. -0. ...,  0.  0. -0.]
    ...,
    [-0.  0. -0. ...,  0.  0. -0.]
    [ 0. -0.  0. ...,  0. -0. -0.]
    [-0. -0.  0. ..., -0. -0. -0.]]
   <NDArray 512x100000 @gpu(0)>
   
   In [17]: a / mx.nd.norm(a, axis=1, keepdims=True)
   Out[17]:
   
   [[  2.19726562e-03  -3.61824036e-03   1.11007690e-03 ...,   3.14950943e-04
      -4.92572784e-04   3.10516357e-03]
    [ -4.07028198e-03   4.61578369e-03  -4.51278687e-03 ...,   2.33650208e-03
       5.40542603e-03   3.78608704e-03]
    [  5.27572632e-03  -1.81293488e-03  -1.17683411e-03 ...,   1.86920166e-03
       4.87518311e-03  -3.04412842e-03]
    ...,
    [ -4.39834595e-03   3.74794006e-04  -4.21905518e-03 ...,   1.11007690e-03
       3.81278992e-03  -3.80134583e-03]
    [  7.90953636e-05  -5.31387329e-03   4.95910645e-03 ...,   3.52859497e-03
      -2.10952759e-03  -4.76837158e-04]
    [ -4.53186035e-03  -3.03459167e-03   2.37083435e-03 ...,  -3.93295288e-03
      -4.21524048e-03  -5.36727905e-03]]
   <NDArray 512x100000 @gpu(0)>
   
   ```

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