Related papers: Conspiracies between Learning Algorithms, Circuit …

We introduce new combinatorial quantities for concept classes, and prove lower and upper bounds for learning complexity in several models of query learning in terms of various combinatorial quantities. Our approach is flexible and powerful…

We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…

Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…

We empirically evaluate common assumptions about neural networks that are widely held by practitioners and theorists alike. In this work, we: (1) prove the widespread existence of suboptimal local minima in the loss landscape of neural…

A pseudo independent (PI) model is a probabilistic domain model (PDM) where proper subsets of a set of collectively dependent variables display marginal independence. PI models cannot be learned correctly by many algorithms that rely on a…

We investigate the risk of overestimating the performance gain when applying neural network based receivers in systems with pseudo random bit sequences or with limited memory depths, resulting in repeated short patterns. We show that with…

We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…

We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set $\mathcal{G}$ up to the smallest possible additive term, called the convergence rate. When the…

Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…

It is already shown that a Boolean function for a NP-complete problem can be computed by a polynomial-sized circuit if its variables have enough number of automorphisms. Looking at this previous study from the different perspective gives us…

This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms. We present techniques for derandomising algorithms to decrease randomness resource requirements and improve efficiency. One key object in…

Pseudorandmness plays an important role in number theory, complexity theory and cryptography. Our aim is to use models of arithmetic to explain pseudorandomness by randomness. To this end we construct a set of models $\cal M$, a common…

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast…

This is a brief technical note to clarify the state of lower bounds on regret for reinforcement learning. In particular, this paper: - Reproduces a lower bound on regret for reinforcement learning, similar to the result of Theorem 5 in the…

The celebrated result of Kabanets and Impagliazzo (Computational Complexity, 2004) showed that PIT algorithms imply circuit lower bounds, and vice versa. Since then it has been a major challenge to understand the precise connections between…

Semi-supervised learning, i.e. jointly learning from labeled and unlabeled samples, is an active research topic due to its key role on relaxing human supervision. In the context of image classification, recent advances to learn from…

We propose a deep supervised learning algorithm based on low-discrepancy sequences as the training set. By a combination of theoretical arguments and extensive numerical experiments we demonstrate that the proposed algorithm significantly…

We present and discuss general techniques for proving inapproximability results for truthful mechanisms. We make use of these techniques to prove lower bounds on the approximability of several non-utilitarian multi-parameter problems. In…

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…