Related papers: Cube vs. Cube Low Degree Test
We study the problem of testing the covariance matrix of a high-dimensional Gaussian in a robust setting, where the input distribution has been corrupted in Huber's contamination model. Specifically, we are given i.i.d. samples from a…
We consider the notions of (i) critical points, (ii) second-order points, (iii) local minima, and (iv) strict local minima for multivariate polynomials. For each type of point, and as a function of the degree of the polynomial, we study the…
Hardness magnification reduces major complexity separations (such as $\mathsf{\mathsf{EXP}} \nsubseteq \mathsf{NC}^1$) to proving lower bounds for some natural problem $Q$ against weak circuit models. Several recent works [OS18, MMW19,…
We consider the surface code under errors featuring both coherent and incoherent components and study the coherence of the corresponding logical noise channel and how this impacts information-theoretic measures of code performance, namely…
We introduce the concept of disjunctive sum of squares for certifying nonnegativity of polynomials. Unlike the popular sum of squares approach where nonnegativity is certified by a single algebraic identity, the disjunctive sum of squares…
A natural problem in high-dimensional inference is to decide if a classifier $f:\mathbb{R}^n \rightarrow \{-1,1\}$ depends on a small number of linear directions of its input data. Call a function $g: \mathbb{R}^n \rightarrow \{-1,1\}$, a…
Let $X$ be a $d$-dimensional simplicial complex. A function $F\colon X(k)\to \{0,1\}^k$ is said to be a direct product function if there exists a function $f\colon X(1)\to \{0,1\}$ such that $F(\sigma) = (f(\sigma_1), \ldots, f(\sigma_k))$…
In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on…
In this paper, we consider the problem of testing properties of joint distributions under the Conditional Sampling framework. In the standard sampling model, the sample complexity of testing properties of joint distributions is exponential…
The emergence of large-margin softmax cross-entropy losses in training deep speaker embedding neural networks has triggered a gradual shift from parametric back-ends to a simpler cosine similarity measure for speaker verification. Popular…
Proximity gaps and correlated agreement have become central tools in the analysis of interactive oracle proofs of proximity (IOPPs) and code-based SNARKs. Informally, a proximity-gap statement says that for a structured set of words -- such…
We show that for all $\varepsilon>0$, for sufficiently large $q\in\mathbb{N}$ power of $2$, for all $\delta>0$, it is NP-hard to distinguish whether a given $2$-Prover-$1$-Round projection game with alphabet size $q$ has value at least…
The robustness of a neural network to adversarial examples can be provably certified by solving a convex relaxation. If the relaxation is loose, however, then the resulting certificate can be too conservative to be practically useful.…
With the explosion of massive, widely available unlabeled data in the past years, finding label and time efficient, robust learning algorithms has become ever more important in theory and in practice. We study the paradigm of active…
Understanding the difference between universal low-temperature properties of amorphous and crystalline solids requires an explanation of the stronger damping of long-wavelength phonons in amorphous solids. A longstanding sound attenuation…
A variety of past research on superconducting qubits shows that these devices exhibit considerable variation and thus cannot be accurately depicted by a uniform noise model. To combat this often unrealistic picture of homogeneous noise in…
State-of-art speaker verification (SV) systems use a back-end model to score the similarity of speaker embeddings extracted from a neural network model. The commonly used back-end models are the cosine scoring and the probabilistic linear…
We provide a new construction for a set of boxes approximating axis-parallel boxes of fixed volume in $[0, 1]^d$. This improves upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and…
We study the simultaneous embeddability of a pair of partitions of the same underlying set into disjoint blocks. Each element of the set is mapped to a point in the plane and each block of either of the two partitions is mapped to a region…
We study the slices of the parameter space of cubic polynomials where we fix the multiplier of a fixed point to some value $\lambda$. The main object of interest here is the radius of convergence of the linearizing parametrization. The…