I feel like the words here were insufficient to explain the difference between the synapse and LIF models. In the other word, why do we need a synapse model? Why could this function solve the two problems in binary signals?

Why can't binary representations of spikes store "memory"? In Computer Science, aren't codes later transformed into binary representations? Could you explain more on the difference between continuous signals and discontinuous signals, and why do they differ from each other when it comes to "memory".

In spiking neural networks (SNNs), neurons are not usually represented as binary units. This is because SNNs seek to emulate the temporal dynamics and spike-based communication found in biological neural networks. Unlike traditional artificial neural networks (ANNs), where neurons are commonly depicted as continuous activation values or binary values of 0 or 1, SNNs rely on the precise timing of individual spikes or their frequency for their operation. As for codes being transformed into binary representations - a single bit is incapable of storing information other than its state (0 or 1) and needs complex encoding schemes, interpretation, and higher-level structures to store and convey meaningful data. Bits alone do not possess inherent meaning or context.