Laplacetransformer

Laplacetransformer is a neural network architecture that combines the Laplace transform with the Transformer model to model sequential data. The core idea is to represent a sequence in the Laplace domain, where temporal patterns are encoded with complex frequency variables, and to perform core computations in that domain before returning to the time domain. This approach aims to improve the modeling of long-range dependencies and potentially reduce computation for very long sequences.

In mathematical terms, the Laplace transform maps a time series x(t) to X(s) = ∫ x(t) e^{-s t} dt, with s a complex frequency parameter. Discrete or continuous variants of the transform can be used depending on the data. In a Laplacetransformer, attention-like interactions or kernel operations are parameterized in the Laplace domain, allowing the model to emphasize temporal scales or patterns that are most informative for a given task. An inverse Laplace transform is then applied to reconstruct the time-domain output.

Architecturally, the model may include modules that project tokens or time steps into Laplace-domain representations, apply transformations or attention in s-space, and combine results with residual connections or hybrid time-domain pathways. Some designs explore hybrid architectures that fuse Laplace-domain processing with conventional time-domain components to balance interpretability and performance.

Applications include long-sequence modeling, time-series forecasting, and signal processing. Challenges involve numerical stability in the complex plane, handling boundary conditions, interpretability of learned frequency components, and the availability of optimized tooling and benchmarks.