arXiv:2611.14249v1 Announce Type: new Abstract: One approach to event-driven learning is to encode continuous signals as sparse events generated when signal changes exceed a prescribed threshold. However, this threshold is typically selected empirically, with limited theoretical guidance. This paper establishes a connection between threshold-based event encoding and discretized learning systems and identifies a dimensionless ratio governing information retention. From this connection, we derive an information-sufficiency boundary using normal-condition data and formulate a data-driven criterion that selects the sparsest threshold retaining a prescribed fraction of peak discriminative information. The framework is illustrated using event cameras and evaluated on power-system fault classification. Results show that the proposed design identifies sparse operating thresholds while exposing the tradeoff between information retention, event activity, and classification performance.