Comparison of Loss Functions Sample Clauses

Comparison of Loss Functions. We first compared the three loss functions as described in Section 3 on the validation set for Chinese-to-English trans- lation. The evaluation metric is case-insensitive BLEU. As shown in Table 1, the square of addition loss function (i.e., ∆SOA) achieves the lowest BLEU among the three loss functions. This can be possibly attributed to the fact that a larger sum does not necessarily lead to increased agreement. For example, while 0.9 + 0.1 hardly agree, 0.2 + 0.2 perfectly does. Therefore, ∆SOA seems to be an inaccurate measure of agreement. The square of subtraction loss function (i.e, ∆SOS) is ca- pable of addressing the above problem by encouraging the training algorithm to minimize the difference between two probabilities: (0.2 - 0.2)2 = 0. However, the loss function fails to distinguish between (0.9 - 0.9)2 and (0.2 - 0.2)2. Ap- parently, the former should be preferred because both models have high confidence in the matrix cell. It is unfavorable for two models agree on a matrix cell but both have very low con- fidence. Therefore, ∆SOS is perfect for measuring agreement but ignores confidence. As the multiplication loss function (i.e., ∆MUL) is able to × take both agreement and confidence into account (e.g., 0.9 × 0.9 > 0.2 0.2), it achieves significant improvements over ∆SOA and ∆SOS. As a result, we use ∆MUL in the following experiments. System Training Direction NIST06 NIST02 NIST03 NIST04 NIST05 NIST08 XXXXX indep. C→E E→C 32.48 14.27 32.69 18.28 32.39 15.36 33.62 13.96 30.23 14.11 25.17 10.84 RNNSEARCH indep. C→E E→C 30.74 15.71 35.16 20.76 33.75 16.56 34.63 16.85 31.74 15.14 23.63 12.70 joint C→E E→C 32.65++ 16.25∗++ 35.68∗∗+ 21.70∗∗++ 34.79∗∗++ 17.45∗∗++ 35.72∗∗++ 16.98∗∗ 32.98∗∗++ 15.70∗∗+ 25.62∗++ 13.80∗∗++
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