Recurrent Neural Networks (RNNs): Motivation

Feedforward networks, such as Multi-Layer Perceptrons (MLPs), process inputs independently. Given an input vector $x$, the network computes an output $y$. If you provide another input vector $x'$, it computes a corresponding $y'$ without any memory of having processed $x$ just moments before. This works well when each input is self-contained, like classifying individual images or analyzing rows in a spreadsheet where each row represents a distinct observation.

However, many important types of data are sequential in nature. Consider:

• Natural Language: The meaning of a sentence depends critically on the order of words. "The cat chased the dog" has a very different meaning from "The dog chased the cat." To understand the role of "dog" in the first sentence, you need to know that "cat" and "chased" came before it.
• Time Series Data: Predicting tomorrow's stock price likely requires knowing the prices from previous days. The sequence of past events holds predictive information. Analyzing sensor readings over time often involves understanding trends and patterns that emerge from the sequence.
• Speech Recognition: Spoken language unfolds over time. Recognizing a word depends on the sequence of sounds (phonemes) that precede and follow each other.
• Video Analysis: Understanding actions in a video requires processing a sequence of frames, as motion and events happen over time.

For these kinds of data, the assumption of input independence made by standard feedforward networks breaks down. Processing each element of the sequence (like a word in a sentence or a data point in a time series) in isolation throws away valuable contextual information embedded in the order. How could a standard MLP effectively translate a sentence if it forgets the beginning of the sentence by the time it reaches the end? How could it predict the next note in a melody without remembering the preceding notes?

This limitation highlights the need for a different kind of network architecture, one that possesses a form of memory. We need models that can process sequential inputs step-by-step while retaining information about the previous steps. The output or decision at a specific point in the sequence should be influenced not only by the current input but also by the history of inputs processed so far.

This is precisely the motivation behind Recurrent Neural Networks (RNNs). RNNs are designed specifically to operate on sequences. They incorporate a looping mechanism and maintain an internal "state" or "memory" that captures information about what has been processed previously in the sequence. This state is updated at each step, allowing the network to exhibit dynamic temporal behavior and model dependencies across different positions in the input sequence. This inherent ability to handle order and context makes RNNs a foundational tool for tackling tasks involving sequential data.