Update rnn.md

Author: sandra-haerin-ha

rnn.md

@@ -54,13 +54,17 @@ of variable length. Convnets can only take in inputs with a fixed size of width
 inputs with different sizes. In order to tackle this problem, we introduce Recurrent Neural Networks (RNNs). 
 
 ### Recurrent Neural Network
-RNN is basically a blackbox (Figure 2), where it has an “internal state” that is updated as a sequence is processed. At every single timestep, we feed in an input vector into RNN where it modifies that state as a function of what it receives. When we tune RNN weights, 
+RNN is basically a blackbox (Left of Figure 2), where it has an “internal state” that is updated as a sequence is processed. At every single timestep, we feed in an input vector into RNN where it modifies that state as a function of what it receives. When we tune RNN weights, 
 RNN will show different behaviors in terms of how its state evolves as it receives these inputs. 
 We are also interested in producing an output based on the RNN state, so we can produce these output vectors on top of the RNN (as depicted in Figure 2.
 
+If we unroll an RNN model (Right of Figure 2), then there are inputs (e.g. video frame) at different timesteps shown as $$x_1, x_2, x_3$$ ... $$x_t$$. 
+RNN at each timestep takes in two inputs -- an input frame ($$x_i$$) and previous representation of what it seems so far (i.e. history) -- to generate an output $$y_i$$ and update its history, which will get forward propagated over time. All the RNN blocks in Figure 2 (Right) are the same block that share the same parameter, but have different inputs and history at each timestep.
+
 <div class="fig figcenter fighighlight">
-  <img src="/assets/rnn/rnn_blackbox.png" width="20%" >
-  <div class="figcaption"><b>Figure 2. </b>Simplified RNN box.</div>
+  <img src="/assets/rnn/rnn_blackbox.png" width="16%" >
+  <img src="/assets/rnn/unrolledRNN.png" width="60%" >
+  <div class="figcaption"><b>Figure 2. </b>Simplified RNN box (Left) and Unrolled RNN (Right).</div>
 </div>
 
 More precisely, RNN can be represented as a recurrence formula of some function $$f_W$$ with