Metrics

Hard metrics cannot be optimized against

• Hard metrics bin spike times onto a grid before comparing them. That binning has zero gradient, so a hard metric will happily return 0.0 gradients forever. They are the numbers to report.
• Soft metrics take a continuous raster or intensity and are differentiable, so they can be used as fitting terms.

First, it is important to note that spikes are differentiable because livn's event solver root-finds every spike time and differentiates it exactly, including through a hard threshold and reset (see Event-SDE formulation).

env = Env(1, model=GLIF.leaky_integrate_and_fire(mechanism="hard"))

def first_spike(tau):
    run = env.cells.set_params({"tau_m": tau}).run(
      duration, stimulus, dt=dt
    )
    # an exact, root-found event time
    return run.spikes.padded.times[0, 0]

jax.grad(first_spike)(jnp.asarray([12.0])) 
# >>> +0.3566, matching finite differences

The metric, however, has not gradient since spikes_to_idx computes:

idx = jnp.round(spike_times_s / dt).astype(jnp.int32)

Quantizing a continuous time to an integer bin index is piecewise constant, so the gradient vanishes. Thus, while the exact spike-time gradients arrives at the metric, it is thrown away by the binning. So "hard metrics are not differentiable" means not differentiable in the spike times as a property of the metric, not of the simulator.

explained_variance_ratio hard

The Teeter et al. (2018) explained-variance ratio

soft_explained_variance soft

The same ratio over continuous traces, thus differentiable.

bits_per_spike soft

Co-smoothing bits per spike (co-BPS), the standard Neural Latents Benchmark metric. Compares the model's Poisson log-likelihood against a null model a.k.a each neuron's mean firing rate, normalized by the total spike count and expressed in bits. Higher is better; 0 means no better than the null model.

rates are firing rates, not log-rates, and both arguments are binned to (batch, time, neurons). NaN entries in spikes are treated as missing and dropped.