Sequence prediction is a fundamental task in sequence modeling where the goal is to forecast future elements of a sequence based on its past elements. Having learned the mechanics of RNNs, LSTMs, and GRUs, we can now explore how to configure these networks specifically for prediction tasks, most notably time series forecasting, but also applicable in areas like predicting the next word in a sentence or the next note in a melody.

The core idea is straightforward: we feed a segment of the sequence history into the recurrent network, and the network learns to output one or more future values. The network's internal state, maintained across time steps, allows it to capture temporal dependencies within the input sequence, which are essential for making accurate predictions.

Input-Output Structures for Prediction

Different prediction problems require different input-output mappings. Let's look at the common patterns:

Many-to-One Prediction: This is perhaps the most common setup for basic forecasting. The network receives a sequence of input values (the history) and predicts a single value for the next time step.
- Example: Given stock prices for the last 30 days, predict the price for tomorrow.
- Architecture: The RNN (LSTM/GRU) processes the input sequence. Typically, the output from the final time step's hidden state is fed into a Dense layer (fully connected layer) to produce the single predicted value. The return_sequences parameter in the recurrent layer is usually set to False (or the framework's equivalent) because we only need the last output.
Many-to-Many Prediction (Direct Multi-step): In this approach, the network takes a sequence of inputs and directly predicts a sequence of future outputs.
- Example: Given weather data for the last 72 hours, predict the temperature for the next 12 hours.
- Architecture: The RNN processes the input sequence. Similar to Many-to-One, the final hidden state often summarizes the input sequence. This state is then used, perhaps through one or more Dense layers, to generate an output vector containing predictions for multiple future steps simultaneously.
Many-to-Many Prediction (Iterative Multi-step): Another way to predict multiple steps ahead is iteratively. A Many-to-One model is trained to predict just the next time step. To predict further ahead, the model's prediction for step $t+1$ is appended to the input sequence, which is then used to predict step $t+2$ , and so on.
- Example: Predicting the next 5 seconds of audio by repeatedly predicting the next sample and feeding it back as input.
- Architecture: This uses the Many-to-One architecture described above, but prediction involves a loop where the model is called repeatedly. While conceptually simple, errors can accumulate over longer prediction horizons.
Many-to-Many Prediction (Aligned Output - Less common for forecasting): Here, the network produces an output for each input time step. This is more typical for tasks like sequence labeling (e.g., part-of-speech tagging) than standard forecasting, but it's a possible structure. For prediction, it might mean predicting a processed version of the input at each step.
- Architecture: The RNN layer needs to output the hidden state for every time step (e.g., return_sequences=True). These outputs are then typically processed by a TimeDistributed wrapper around a Dense layer (or equivalent mechanism) to produce an output for each time step.

Building Prediction Models

Let's focus on the common Many-to-One setup for predicting the next value in a time series.

Input Shaping: As discussed in Chapter 8, time series data is often prepared using a sliding window approach. If we want to predict the value at time $t$ using the previous $k$ values, our input sequence is $[x_{t-k}, x_{t-k+1}, ..., x_{t-1}]$ and the target output is $x_t$ . Each input sample fed to the RNN will have the shape (k, num_features), where num_features is the number of data streams measured at each time step (e.g., 1 for just temperature, or multiple if including pressure, humidity, etc.). Batched input would have the shape (batch_size, k, num_features).
Model Structure:
- An Input layer specifies the shape of the input sequences (e.g., (k, num_features)).
- One or more recurrent layers (SimpleRNN, LSTM, or GRU) process the input sequence. For Many-to-One, the last recurrent layer typically has return_sequences=False. The number of units in these layers is a hyperparameter to tune.
- A Dense output layer maps the final hidden state from the recurrent layer to the desired output shape. For predicting a single value, this layer has 1 unit. The activation function depends on the nature of the data being predicted. For unbounded continuous values (like stock prices or temperature), a linear activation (i.e., no activation function) is common. For values bounded between 0 and 1, a sigmoid might be used.

A typical Many-to-One architecture for sequence prediction. The recurrent layer processes the input sequence, and its final hidden state is passed to a Dense layer to produce the single predicted value.

Considerations for Prediction

Choice of Recurrent Unit: LSTMs and GRUs are generally preferred over SimpleRNNs for real-world data, especially when longer-term dependencies might be present, due to their better handling of gradients (as discussed in Chapter 4, 5, and 6).
Multi-step Strategy: For predicting multiple steps ahead, the choice between the direct and iterative methods involves trade-offs. Direct prediction requires a model designed to output multiple values but makes predictions in one pass. Iterative prediction uses a simpler model but can suffer from error accumulation. The best approach often depends on the specific problem and data characteristics.
Evaluation: Evaluating prediction models typically involves metrics like Mean Squared Error (MSE) or Mean Absolute Error (MAE) comparing the predicted values to the actual future values (covered in Chapter 10).

These fundamental approaches form the basis for applying RNNs to a wide variety of sequence prediction problems. The next sections will explore how similar architectures can be adapted for classification and generation tasks.