One Filter Is All You Need: Understanding Pattern Recognition in 1D Convolutional Neural Networks

Pattern recognition in sequential data is a fundamental problem encountered across digital communications, cryptography, and computational biology. Although convolutional neural networks (CNNs) have demonstrated strong performance in sequence classification tasks, the mechanisms by which they achieve this remain insufficiently understood. In this work, we examine how a simple one-dimensional CNN performs binary classification on sequences containing hidden target patterns, using artificially generated data under tightly controlled conditions that isolate network behavior from domain-specific noise. We demonstrate, through both theoretical analysis and empirical evaluation, that a single convolutional filter aligned with the target pattern is sufficient for perfect classification. We further show that constraining the fully connected layer to have equal weights yields a substantial reduction in the number of parameters and extends accurate classification from sequences of 1,200 bits to 20,000 bits. The effects of sequence length and target pattern length on classification performance are also investigated. These results provide insight into the mechanisms underlying the effectiveness of shallow 1D-CNNs in sequence classification and suggest practical guidelines for the design of interpretable models.