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The ultimate random number generators are those certified to be unpredictable -- including to an adversary. The use of simple quantum processes promises to provide numbers that no physical observer could predict but, in practice, unwanted…
To understand and engineer biological and artificial nucleic acid systems, algorithms are employed for prediction of secondary structures at thermodynamic equilibrium. Dynamic programming algorithms are used to compute the most favoured, or…
We develop the theory of cryptographic nondeterministic-secure pseudorandomness beyond the point reached by Rudich's original work (Rudich 1997), and apply it to draw new consequences in average-case complexity and proof complexity.…
Pseudorandom quantum states (PRS) are efficiently constructible states that are computationally indistinguishable from being Haar-random, and have recently found cryptographic applications. We explore new definitions, new properties and…
Period finding and phase estimation are fundamental in quantum computing. Prior work has established lower bounds on their success probabilities. Such quantum algorithms measure a state $|\hat\ell\rangle$ in an $n$-qubit computational…
We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and…
A large body of research has focused on theory and computation for variable selection techniques for high dimensional data. There has been substantially less work in the big tall data paradigm, where the number of variables may be large,…
The restarted primal-dual hybrid gradient method (rPDHG) is a first-order method that has recently received significant attention for its computational effectiveness in solving linear program (LP) problems. Despite its impressive practical…
We introduce a variant of PCPs, that we refer to as rectangular PCPs, wherein proofs are thought of as square matrices, and the random coins used by the verifier can be partitioned into two disjoint sets, one determining the row of each…
We initiate a systematic study of pseudo-deterministic quantum algorithms. These are quantum algorithms that, for any input, output a canonical solution with high probability. Focusing on the query complexity model, our main contributions…
Secure computation often benefits from the use of correlated randomness to achieve fast, non-cryptographic online protocols. A recent paradigm put forth by Boyle $\textit{et al.}$ (CCS 2018, Crypto 2019) showed how pseudorandom correlation…
This paper considers the computational hardness of computing expected outcomes and deciding (universal) (positive) almost-sure termination of probabilistic programs. It is shown that computing lower and upper bounds of expected outcomes is…
Random numbers are commonly used in many different fields, ranging from simulations in fundamental science to security applications. In some critical cases, as Bell's tests and cryptography, the random numbers are required to be both secure…
In the wake of the explosive growth in smartphones and cyberphysical systems, there has been an accelerating shift in how data is generated away from centralised data towards on-device generated data. In response, machine learning…
Proving complexity lower bounds remains a challenging task: we only know how to prove conditional uniform lower bounds and nonuniform lower bounds in restricted circuit models. Williams (STOC 2010) showed how to derive nonuniform lower…
Derandomization is one of the classic topics studied in the theory of parallel computations, dating back to the early 1980s. Despite much work, all known techniques lead to deterministic algorithms that are not work-efficient. For instance,…
The generation of certifiable randomness is the most fundamental information-theoretic task that meaningfully separates quantum devices from their classical counterparts. We propose a protocol for exponential certified randomness expansion…
Regression methods are fundamental for scientific and technological applications. However, fitted models can be highly unreliable outside of their training domain, and hence the quantification of their uncertainty is crucial in many of…
Probabilistic Circuits (PCs) offer a computationally scalable framework for generative modeling, supporting exact and efficient inference of a wide range of probabilistic queries. While recent advances have significantly improved the…
Although recent provable methods have been developed to compute preimage bounds for neural networks, their scalability is fundamentally limited by the #P-hardness of the problem. In this work, we adopt a novel probabilistic perspective,…