So far, we've primarily worked with data where the order of features didn't necessarily hold the primary meaning, like the pixels in an image classification task (though spatial arrangement matters for CNNs, the temporal order of input processing wasn't the focus). Now, we shift our attention to a different, yet ubiquitous, type of data: sequence data.

In sequence data, the order is not just incidental; it's fundamental to the information being conveyed. Each element in the sequence exists in relation to the elements that came before and often influences those that come after. Think about understanding language: the sentence "dog bites man" has a vastly different meaning than "man bites dog," even though they contain the exact same words. The sequence is paramount.

What Characterizes Sequence Data?

Sequence data is defined by its ordered nature. We can represent a sequence as $X = (x_1, x_2, ..., x_T)$ , where $x_t$ is the element at time step or position $t$ , and $T$ is the length of the sequence. This structure appears in many forms:

Text Data: Written or spoken language is inherently sequential. Words form sentences, sentences form paragraphs, and the order dictates grammar and meaning. Examples include predicting the next word in a sentence, classifying the sentiment of a review, or translating text between languages.
Time Series Data: Measurements taken over time form a sequence. Examples include stock prices recorded daily, hourly weather readings (temperature, humidity), sensor data from machinery, or patient heart rate monitoring (ECG signals). The temporal relationship is the defining characteristic.
Audio Data: Sound is represented digitally as a sequence of amplitude values over time. Speech recognition, music generation, and sound event detection all operate on sequential audio signals.
Video Data: While individual frames are images, a video is a sequence of these frames. Understanding actions in a video requires processing this temporal sequence.
Biological Sequences: DNA and protein sequences are sequences of nucleotides or amino acids, where the order determines biological function.

A simple time series where the value at each point often follows a pattern established by previous points.

Challenges Posed by Sequential Data

Processing sequence data effectively presents unique challenges compared to static, fixed-size input:

Variable Length: Sequences often have different lengths. Sentences can be short or long, time series can cover different durations. Standard feedforward networks typically expect fixed-size input vectors. How can a model gracefully handle these varying lengths?
Order Dependence: The model must understand that the order matters. Simply shuffling the elements of a sequence can completely change its meaning or invalidate the data. The model needs mechanisms to process elements in their given order.
Long-Range Dependencies: Sometimes, elements far apart in the sequence are related. For instance, in the sentence "The cat, which chased the mouse that stole the cheese, is sleeping," the verb "is" depends on the subject "cat," which appeared much earlier. Similarly, seasonal patterns in weather data represent long-range temporal dependencies. Capturing these relationships requires a model with some form of memory.

Why Standard Networks Fall Short

The feedforward neural networks we've built so far, including Dense networks and even standard CNNs applied naively to sequences, are not inherently designed to handle these challenges well.

Dense Networks: A fully connected network processes its entire input vector simultaneously. If we were to flatten a sequence and feed it in, the network would treat each time step's features somewhat independently, losing the crucial ordering information. Furthermore, it requires a fixed input size, making variable-length sequences problematic.
Convolutional Networks (CNNs): While 1D CNNs can be used for sequences and are effective at capturing local patterns (like specific word combinations or short-term trends in time series), their fixed kernel sizes make it difficult to capture dependencies over arbitrarily long distances within the sequence without very deep architectures or large dilation rates.

To address the specific demands of order dependence, variable lengths, and potentially long-range dependencies, we need a different kind of neural network architecture. This is where Recurrent Neural Networks (RNNs) come into play. They are designed explicitly to operate on sequences, maintaining an internal state that allows information from previous steps to influence the processing of current steps, providing a form of memory essential for understanding sequential patterns. In the following sections, we will examine how RNNs achieve this.