What does the one function $\mathbf{1}_{i,y^{(t)}}$ exactly mean in backward propagation of RNN in the book "Deep learning" of Bengio It confused me for a long time what is $\mathbf{1}_{i,y^{(t)}}$ exactly mean in (10.18) below. 

It is in the Chapter 10 on RNN of the book LeCun, Yann, Yoshua Bengio, and Geoffrey Hinton. "Deep learning." nature 521.7553 (2015): 436.

Because the ${i,y^{(t)}}$ doesn't seem to be a condition while the author has introduced a condition function as $\mathbf{1}_\text{condition} = 1$ if condition is true or $=0$ if the condition is false.  

It is computing the gradient of the log-likelihood with backward propagation in recurrent neural network.

Instead of $\hat{y}_i^{(t)}− \mathbf{1}_{i,y^{(t)}}$, I found my solution might be 
$$
(\hat{y}^{(t)}_i-y_i^{(t)})\dfrac{\exp(o_i^{(t)})\sum_j\exp(z_j)-(\exp(z_i))^2}{(\sum_j\exp(z_j))^2}
$$
It is based on the prior assumption of Gaussian distribution with $\sigma=1$

Below is the equation I am asking about:


  The gradient $\nabla_{o^{(t)}}L$ on the outputs at time step $t$, for all $i$, $t$, is as
  follows:
  $$
(\nabla_{o(t)}L)_i 
= \dfrac{\partial L}{\partial o_i^{(t)}}
= \dfrac{\partial L}{\partial L^{(t)}}\dfrac{\partial L^{(t)}}{\partial o_i^{(t)}}
= \hat{y}_i^{(t)}− \mathbf{1}_{i,y^{(t)}}.   \qquad\qquad (10.18)
$$


While, the corresponding notes are:


  $$
\begin{align*}
\boldsymbol{a}^{(t)} &amp;= \boldsymbol{b} +\boldsymbol{Wh}^{(t−1)} + \boldsymbol{Ux}^{(t)} &amp;(10.8)\\
\boldsymbol{h}^{(t)} &amp;= \tanh(\boldsymbol{a}^{(t)}) &amp;(10.9)\\
\boldsymbol{o}^{(t)} &amp;= \boldsymbol{c} + \boldsymbol{V h}^{(t)} &amp;(10.10)\\
\hat{\boldsymbol{y}}^{(t)} &amp;= \text{softmax}(\boldsymbol{o}^{(t)}) &amp;(10.11)
\end{align*}
$$


And I wonder which version of softmax function is used here?
$$
\text{softmax}(\boldsymbol{z})=\dfrac{\exp(z_i)}{\sum_j\exp(z_j)}
$$
or
$$
\text{softmax}(\boldsymbol{z})=\dfrac{\exp(z_i-\max_kz_k)}{\sum_j\exp(z_j-\max_kz_k)}
$$
?

Thank you very much!
The authors or the publisher may have corrected the inconsistent notation. The current version online looks like below:


Here the $\mathbf{1}_{\text{condition}}$ is the indicator function, as you mentioned.

Regarding the two version of softmax, use the first one for calculating gradient. The second version is for improving numerical stability, and mathmatically it should yield the exact same value as the first version.