Related papers: Smoothing Codes and Lattices: Systematic Study and…
This paper examines the asymptotic convergence properties of Lipschitz interpolation methods within the context of bounded stochastic noise. In the first part of the paper, we establish probabilistic consistency guarantees of the classical…
We consider the quantum decoding problem. It consists in recovering a codeword given a superposition of noisy versions of this codeword. By measuring the superposition, we get back to the classical decoding problem. It appears for the first…
Recent results have shown that lattice codes can be used to construct good channel codes, source codes and physical layer network codes for Gaussian channels. On the other hand, for Gaussian channels with secrecy constraints, efforts to…
Any classifier can be "smoothed out" under Gaussian noise to build a new classifier that is provably robust to $\ell_2$-adversarial perturbations, viz., by averaging its predictions over the noise via randomized smoothing. Under the…
We consider the problem of reconstructing a discrete-time signal (sequence) with continuous-valued components corrupted by a known memoryless channel. When performance is measured using a per-symbol loss function satisfying mild regularity…
This work presents a novel and effective method for fitting multidimensional ellipsoids to scattered data in the contamination of noise and outliers. We approach the problem as a Bayesian parameter estimate process and maximize the…
We study the problem of bounding the posterior distribution of discrete probabilistic programs with unbounded support, loops, and conditioning. Loops pose the main difficulty in this setting: even if exact Bayesian inference is possible,…
One of the founding results of lattice based cryptography is a quantum reduction from the Short Integer Solution problem to the Learning with Errors problem introduced by Regev. It has recently been pointed out by Chen, Liu and Zhandry that…
Uniform stability is a notion of algorithmic stability that bounds the worst case change in the model output by the algorithm when a single data point in the dataset is replaced. An influential work of Hardt et al. (2016) provides strong…
Modular architectures are a promising approach to scaling quantum computers to fault tolerance. Small, low-noise quantum processors connected through relatively noisy quantum links are capable of fault-tolerant operation as long as the…
To improve the off-sample generalization of classical procedures minimizing the empirical risk under potentially heavy-tailed data, new robust learning algorithms have been proposed in recent years, with generalized median-of-means…
Motivated by recent studies of population coding in theoretical neuroscience, we examine the optimality of a recently described form of stochastic resonance known as suprathreshold stochastic resonance, which occurs in populations of noisy…
We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…
As a certified defensive technique, randomized smoothing has received considerable attention due to its scalability to large datasets and neural networks. However, several important questions remain unanswered, such as (i) whether the…
Lattice codes are known to achieve capacity in the Gaussian point-to-point channel, achieving the same rates as independent, identically distributed (i.i.d.) random Gaussian codebooks. Lattice codes are also known to outperform random codes…
Frequency estimation in data streams is one of the classical problems in streaming algorithms. Following much research, there are now almost matching upper and lower bounds for the trade-off needed between the number of samples and the…
Label smoothing is a regularization technique for neural networks. Normally neural models are trained to an output distribution that is a vector with a single 1 for the correct prediction, and 0 for all other elements. Label smoothing…
This paper studies the cardinality of codes correcting insertions and deletions. We give improved upper and lower bounds on code size. Our upper bound is obtained by utilizing the asymmetric property of list decoding for insertions and…
In this paper, we present an improved union bound on the Linear Programming (LP) decoding performance of the binary linear codes transmitted over an additive white Gaussian noise channels. The bounding technique is based on the second-order…
We analyze gradient descent with randomly weighted data points in a linear regression model, under a generic weighting distribution. This includes various forms of stochastic gradient descent, importance sampling, but also extends to…