Learning Interpretable Differentiable Logic Networks for Time-Series Classification

The synthesis of symbolic logic and deep learning has given rise to a new class of interpretable models that stand as a powerful alternative to opaque, black-box architectures. The pioneering work in this domain includes deep differentiable logic gate networks (LGNs) and their successor, convolutional LGNs, both proposed by Petersen et al. [1, 2]. These models establish a method for training networks of Boolean logic gates via gradient descent by creating differentiable relaxations of the logic operations. This core strategy yields transparent models from which logical rules can be extracted, while extensions like logical convolutions and pooling enable these architectures to scale effectively to complex classification tasks. The LGN paradigm was significantly generalized with the development of differentiable logic networks (DLNs) [3]. By removing prior constraints, such as fixed network topologies and binary-only inputs, DLNs broadened the framework's applicability to general tabular classification, resulting in highly efficient models that match or exceed the performance of traditional neural networks (NNs) on a wide range of benchmarks. The scope of these logic-based systems was expanded once more to handle continuous targets through the regression DLN [4]. This extension integrates a weighted sum of the final layer's logical rule outputs to produce a numerical prediction, successfully adapting the architecture to regression while maintaining its inherent interpretability. Despite the success of DLNs in tabular classification and their extension to regression, their application to time series data, particularly for classification tasks, remains largely unexplored.