Affine extractors over large fields with exponential error

We describe a construction of explicit affine extractors over large finite fields with exponentially small error and linear output length. Our construction relies on a deep theorem of Deligne giving tight estimates for exponential sums over smooth varieties in high dimensions.Comment: To appear in Comput. Comple

Andre-Quillen (co)homology and equivariant stable homotopy theory

Andre and Quillen introduced a (co)homology theory for augmented commutative rings. Strickland [31] initially proposed some issues with the analogue of the abelianization functor in the equivariant setting. These were resolved by Hill [15] who further gave the notion of a genuine derivation and a module of Kähler differentials. We build on this endeavor by expanding to incomplete Tambara functors, introducing the cotangent complex and its various properties, and producing an analogue of the fundamental spectral sequence.Mathematic

Regression with Label Differential Privacy

We study the task of training regression models with the guarantee of label differential privacy (DP). Based on a global prior distribution on label values, which could be obtained privately, we derive a label DP randomization mechanism that is optimal under a given regression loss function. We prove that the optimal mechanism takes the form of a ``randomized response on bins'', and propose an efficient algorithm for finding the optimal bin values. We carry out a thorough experimental evaluation on several datasets demonstrating the efficacy of our algorithm