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Even if anthropogenic warming were constrained to less than 2 degrees C above pre-industrial, the Greenland and Antarctic ice sheets will continue to lose mass this century, with rates similar to those observed over the past decade. However, nonlinear responses cannot be excluded, which may lead to larger rates of mass loss. Furthermore, large uncertainties in future projections still remain, pertaining to knowledge gaps in atmospheric (Greenland) and oceanic (Antarctica) forcing. On millennial timescales, both ice sheets have tipping points at or slightly above the 1.5-2.0 degrees C threshold; for Greenland, this may lead to irreversible mass loss due to the surface mass balance-elevation feedback, whereas for Antarctica, this could result in a collapse of major drainage basins due to ice-shelf weakening.