Event-encoding thresholds stop being trial-and-error: normal-condition variability sets an information boundary, and event density falls about 7.6-fold at comparable accuracy

Threshold selection for event encoding becomes a computable design rule: normal-condition data fixes an information-sufficiency boundary, and the sparsest threshold above it that retains a required information fraction is chosen. Thresholds were previously set by empirical search or manual tuning, requiring repeated evaluation of the learning model over candidate thresholds and offering guidance that transferred poorly across models or datasets. On power-system transient data with eleven fault classes plus normal operation, 80 instances per class and 960 instances in total, the rule selected a threshold giving 2.87% event density, a 7.59-fold reduction relative to the information-sufficiency boundary, with 94.14% overall classification accuracy.

The construction treats signed threshold encoding as a three-region discretization of the signal's temporal gradient, so the threshold plays the role of resolution and normal-condition fluctuation the role of noise scale. Discretized learning systems already had an information-limit result governed by the ratio of noise to resolution, but event encoding had not been analyzed under that ratio. The correspondence requires no distributional assumption on signal increments; in the power-system experiment the normal-condition gradient standard deviation sets the normalized boundary, and candidate thresholds are expressed as multiples of it.

The operating threshold is not placed at the boundary but at the largest threshold still retaining a prescribed fraction of peak discriminative information, estimated as mutual information between class labels and the event representation. The boundary only marks the onset of the information-sufficient regime; used directly as an operating point, the Gaussian approximation leaves roughly thirty percent of normal-condition samples generating events there. On the power-system data mutual information peaks at 0.987 nats at a threshold of 2.0 standard deviations, and requiring 75% of peak selects 5.0 standard deviations; the mutual information at that threshold is stated inconsistently in the source, with one passage giving 0.767 nats (77.7% of peak) and a table listing 0.899 nats at 5.0 standard deviations and 0.767 nats at 8.0.

The demonstrated scope is a physical event-camera encoding illustration plus one power-system transient dataset with eleven fault classes and normal operation, 80 instances per class and 960 instances in total, with a spiking-neural-network convolutional variational autoencoder fault classifier as the downstream task. Threshold design neither trains nor evaluates the classifier, and the classifier architecture and training are held fixed across thresholds with no classifier-based retuning.

Under the Gaussian approximation the information-sufficiency boundary still lets roughly thirty percent of normal-condition samples generate events, so the boundary is not the recommended operating point. Mutual information is estimated from a compact 12-bit activity-pattern representation; as the activity cutoff moves from 0.25% to 10%, the peak-information threshold shifts between 2.0 and 3.0 standard deviations, and the sparsity-selected threshold varies with the representation. At cutoffs of 15% to 20% only one or two candidate thresholds retain enough activity for estimation. The mutual information at the selected threshold is stated inconsistently in the source: the text gives 0.767 nats (77.7% of peak), while the table lists 0.899 nats at 5.0 standard deviations and 0.767 nats at 8.0. The classifier uses the full temporal event sequence while mutual information comes from the compact representation, so classification performance need not vary monotonically with estimated mutual information. A closed-form solution would require an analytical characterization of the class-conditional gradient distributions and is left for future work.