We find that the cross-entropy loss curves of neural language models empirically adhere to a scaling law with learning rate (LR) annealing over training steps: L(s) = L0 +A S α1 C S2, where L(s)is the validation loss at step s, S1 is the area under the LR curve, S2 is the LR annealing area, and L0, A, C, αare constant parameters.

The behavior emerges and becomes more robust as the architecture scales up its number of parameters.

We also propose a loss function adapted to the severe class imbalance. We show that our model outperforms state-of-the-art alternatives on UA V point clouds.

The most extensive model described to date is the base model size encompasses 77.6M parameters

Y The constraint P X,P Y Prob(X) states that P X and P Y are valid probability distributions. For brevity, we shall ignore explicitly stating it in the rest of the proof. The above equation is similar in spirit to the Kantrovich-Rubinstein duality. An important observation to note is that the above optimization only maximizes over a single discriminator function (as opposed to two functions in optimization (2)). Hence, it is easier to train it in large-scale deep learningproblemssuchasGANs.

In both cases we observe that the predicted curve is reasonably close to the actual curve, more so at the beginning of the training (which is expected, sincethelinearapproximation ismorelikelytohold). Point-wise similarity of predicted and observed loss curve. Up to now we focused on prediction error rates (see e.g. We started defining training time as the first time the (smoothed) loss is belowagiventhreshold(whichwethennormalizedw.r.t. In Section 4we suggest that, in the case of MSE loss, itispossible to predict the training time on alargedataset using asubset ofthesamples. However,sinceourtraining time definition measures the time to reach the asymptotic value (which is what is most useful in practice) rather than the time reach an absolute threshold, this does not affect the accuracy of the prediction(seeAppendixC).