  We introduce a generalized Spiking Locally Competitive Algorithm (LCA) that
is biologically plausible and exhibits adaptability to a large variety of
neuron models and network connectivity structures. In addition, we provide
theoretical evidence demonstrating the algorithm's convergence in optimization
problems of signal recovery. Furthermore, our algorithm demonstrates superior
performance over traditional optimization methods, such as FISTA, particularly
by achieving faster early convergence in practical scenarios including signal
denoising, seismic wave detection, and computed tomography reconstruction.
Notably, our algorithm is compatible with neuromorphic chips, such as Loihi,
facilitating efficient multitasking within the same chip architecture - a
capability not present in existing algorithms. These advancements make our
generalized Spiking LCA a promising solution for real-world applications,
offering significant improvements in execution speed and flexibility for
neuromorphic computing systems.
