Timely monetary policy decision-making requires timely core inflation measures. We create a new core inflation series that is explicitly designed to succeed at that goal. Precisely, we introduce the Assemblage Regression, a generalized nonnegative ridge regression problem that optimizes the price index's subcomponent weights such that the aggregate is maximally predictive of future headline inflation. Ordering subcomponents according to their rank in each period switches the algorithm to be learning supervised trimmed inflation - or, put differently, the maximally forward-looking summary statistic of the realized price changes distribution. In an extensive out-of-sample forecasting experiment for the US and the euro area, we find substantial improvements for signaling medium-term inflation developments in both the pre- and post-Covid years. Those coming from the supervised trimmed version are particularly striking, and are attributable to a highly asymmetric trimming which contrasts with conventional indicators. We also find that this metric was indicating first upward pressures on inflation as early as mid-2020 and quickly captured the turning point in 2022. We also consider extensions, like assembling inflation from geographical regions, trimmed temporal aggregation, and building core measures specialized for either upside or downside inflation risks.