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A lifting theorem with a constant-sized gadget that lifts the DNF to a communication problem, while losslessly translating the separation in certificate complexity to a separation in communication complexity is proved.
This work exhibits a learnable multiclass problem that becomes altogether unlearnable under a monotone adversary, and shows an analogous result for partial binary concept classes, and demonstrates that monotone adversaries are frighteningly more powerful in each of these settings.
It is shown that the maximum hypergraph density of any multiclass hypothesis class is upper-bounded by its DS dimension, which proves a longstanding conjecture of Daniely and Shalev-Shwartz (2014) and determines the optimal dependence of the sample complexity on the DS dimension for multiclass as well as list learning.
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