Bootstrapping variables in algebraic circuits

Bootstrapping variables in algebraic circuits

We show that for the blackbox polynomial identity testing (PIT) problem it suffices to study circuits that depend only on the first extremely few variables. One only need to consider size-s degree-s circuits that depend on the first log◦c s variables (where c is a constant and we are composing c logarithms). Thus, hitting-set generator (hsg) manifests a bootstrapping behavior— a partial hsg aga...

Optimization of Bootstrapping in Circuits

In 2009, Gentry proposed the first Fully Homomorphic Encryption (FHE) scheme, an extremely powerful cryptographic primitive that enables to perform computations, i.e., to evaluate circuits, on encrypted data without decrypting them first. This has many applications, in particular in cloud computing. In all currently known FHE schemes, encryptions are associated to some (non-negative integer) no...

Bootstrapping Errors-in-Variables Models

The bootstrap is a numerical technique, with solid theoretical foundations, to obtain statistical measures about the quality of an estimate by using only the available data. Performance assessment through bootstrap provides the same or better accuracy than the traditional error propagation approach, most often without requiring complex analytical derivations. In many computer vision tasks a reg...

Circuits versus Trees in Algebraic Complexity

Arithmetic Circuits with Locally Low Algebraic Rank

In recent years there has been a flurry of activity proving lower bounds for homogeneous depth-4 arithmetic circuits [GKKS13, FLMS14, KLSS14, KS14c], which has brought us very close to statements that are known to imply VP 6= VNP. It is a big question to go beyond homogeneity, and in this paper we make progress towards this by considering depth-4 circuits of low algebraic rank, which are a natu...