U-RNNs, or Unidirectional Recurrent Neural Networks, are a type of neural network architecture that allows for information to be accumulated in the forward direction of time. Unlike Bi-RNNs, which have symmetry in both time directions, U-RNNs can be useful in cases where there is a preferred direction in time for the data being processed.

What are Bi-RNNs?

Before delving into U-RNNs, it's important to understand Bi-RNNs, or Bidirectional Recurrent Neural Networks. Bi-RNNs are often used in natural language processing, where the order of words is determined by grammatical rules rather than by temporal sequentiality.

Bi-RNNs work by processing the input data in both the forward and backward direction simultaneously. The forward hidden state $(h^f_t)$ is computed by passing the input at time $t$, $e_t$, and the hidden state from the previous time step, $h^f_{t-1}$, through a neural network (let's call it $RNN_f$). The backward hidden state $(h^b_t)$ is computed similarly, but in the opposite direction, using a different neural network ($RNN_b$).

Both hidden states are then concatenated to form the final output of the Bi-RNN at time $t$:

$$o_t = [h^f_t, h^b_t]$$

This output can be used for various tasks, such as language modeling and named entity recognition. However, one potential drawback of Bi-RNNs is that they do not take into account future information when processing the input data. This is because the backward pass is done before the forward pass, and the output is simply the concatenation of the two.

So, is there a way to address this drawback and allow for accumulation of information in the forward direction? Enter U-RNNs.

How do U-RNNs work?

The idea behind U-RNNs is to first do a backward pass, and then use information about the future during the forward pass.

Here's how it works:

  1. Compute the backward hidden states $(h^b_t)$ for all time steps $t$ using $RNN_b$.
  2. Start the forward pass at the last time step $T_{obs}$ and compute the forward hidden states $(h^f_t)$ for all time steps $t\leq T_{obs}$ using $RNN_f$. At each time step $t$, concatenate the current input $e_t$ with the corresponding backward hidden state $h^b_t$: $[e_t, h^b_t]$.
  3. Use the last forward hidden state $h^f_{T_{obs}}$ as the encoding of the sequence.

Here, $T_{obs}$ denotes the last time step before any padding is added to the input sequence.

The equations for obtaining $h^b_t$ and $h^f_t$ are as follows:

\begin{equation} \begin{aligned} &h_{t-1}^{b}=R N N\left(h_{t}^{b}, e_{t}, W_{b}\right) \\ &h_{t+1}^{f}=R N N\left(h_{t}^{f},\left[e_{t}, h_{t}^{b}\right], W_{f}\right) \end{aligned} \end{equation}

where $W_b$ and $W_f$ are learnable weights that are shared among pedestrians, and $[\cdot, \cdot]$ denotes concatenation. Note that $h^f_t$ depends not only on the current input $e_t$, but also on the corresponding backward hidden state $h^b_t$.

The backward pass is done first because it allows for the accumulation of information about the future, which can then be used during the forward pass. By starting the forward pass at the last observed time step and using the corresponding backward hidden state at each time step, U-RNNs can effectively accumulate information in the forward direction.

U-RNNs have been used for various tasks, such as video captioning and speech recognition. They have shown to outperform Bi-RNNs on some tasks, particularly those where temporal sequentiality is important.

U-RNNs are a type of neural network architecture that allows for information to be accumulated in the forward direction of time. They address a potential drawback of Bi-RNNs, which do not take into account future information when processing the input data. By first doing a backward pass and then using information about the future during the forward pass, U-RNNs can effectively accumulate information in the forward direction. U-RNNs have shown to outperform Bi-RNNs on some tasks, particularly those where temporal sequentiality is important.

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