Follow-up on #129: Naming of node parameters

[benkroehs]

This is a follow-up issue on the discussion from #129 about the naming of node parameters that are more digital or more analog. This came up because of the newly introduced parameter for the reset of spiking neurons, where either a reset or a subtraction can be implemented. The question is how to implement this mechanism as parameter(s) in NIR.

[Jegp]

I suggest adding a separate reset mechanism node which parameterizes the reset. Any neuron model can, according to the spike response model, be described by a set of linear kernels with a feedback loop.

In NIR, we're parameterizing $\kappa$ (LI) and $H$ (Spike). But, we're not parameterizing $\eta$. We could define a LIF node more accurately as a composition of $\kappa \circ H \circ Reset$ with an added Reset primitive. The primitive would consist of three parameters: one to indicate the reset_type (dirac or exponential - maybe even more?), an amplitude parameter, and a parameter of the exponential reset (tau):

@dataclass
class Reset(NIRNode):
    """
    Reset primitive implementing the η kernel from spike response model.
    
    Applies a continuous-time reset response when triggered by a spike signal.
    The reset kernel is parameterized analytically to maintain continuous-time semantics.
    """
    
    # Parametric reset specification (continuous-time)
    reset_type: str = "exponential"          # "dirac", "exponential", "alpha", "biexponential"
    amplitude: float = -1.0                  # Reset amplitude (negative for hyperpolarization)
    
    # Exponential reset parameters: η(t) = A * exp(-t/τ) * H(t)
    tau: Optional[float] = None              # Time constant for exponential decay
    

The LIF model (and other spiking models) would then have a reset field with a dirac default value:

    ...
    # Reset dynamics (η kernel) - new!
    reset: Reset = field(default_factory=lambda: Reset(
        reset_type="dirac", 
        amplitude=-1.0  # Subtractive reset by default
    ))

Such that the entire LIF graph would be

input → LeakyIntegrator → Spike → output_spike
           ↑                ↓
           └── Reset ←──────┘
           ↓
        voltage_out

That would give us a (1) a mathematically sound model that stays true to the continuous-time nature of NIR, (2) a more correct and expressive picture of the computation, which should (in theory) lead to fewer changes going forward, and (3) a composable set of primitives that can be ignored by existing platforms if they don't care/support it.

[benkroehs]

I like this modular implementation of the reset mechanism — it’s clean and easy to follow. One thing we might consider adding is a refractory_time parameter for the neuron. This could be optional for the Reset node, defaulting to 0.