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We recall some of the history of the information-theoretic approach to deriving core results in probability theory and indicate parts of the recent resurgence of interest in this area with current progress along several interesting…

Recent advances have demonstrated the possibility of solving the deconvolution problem without prior knowledge of the noise distribution. In this paper, we study the repeated measurements model, where information is derived from multiple…

We reconsider the concept of multi-prover commitments, as introduced in the late eighties in the seminal work by Ben-Or et al. As was recently shown by Cr\'{e}peau et al., the security of known two-prover commitment schemes not only relies…

We introduce a theorem proving algorithm that uses practically no domain heuristics for guiding its connection-style proof search. Instead, it runs many Monte-Carlo simulations guided by reinforcement learning from previous proof attempts.…

A new finite form of de Finetti's representation theorem is established using elementary information-theoretic tools. The distribution of the first $k$ random variables in an exchangeable vector of $n\geq k$ random variables is close to a…

Pimentel et al. (2020) recently analysed probing from an information-theoretic perspective. They argue that probing should be seen as approximating a mutual information. This led to the rather unintuitive conclusion that representations…

We prove a multiple recurrence result for arbitrary measure-preserving transformations along polynomials in two variables of the form $m+p_i(n)$, with rationally independent $p_i$'s with zero constant term. This is in contrast to the single…

Using multisets, we develop novel techniques for mechanizing the proofs of the synthesis conjectures for list-sorting algorithms, and we demonstrate them in the Theorema system. We use the classical principle of extracting the algorithm as…

A finite form of de Finetti's representation theorem is established using elementary information-theoretic tools: The distribution of the first $k$ random variables in an exchangeable binary vector of length $n\geq k$ is close to a mixture…

These notes pose a "proof challenge": a proof, or disproof, of the proposition that "For any given body of information, I, expressed as a one-dimensional sequence of atomic symbols, a multiple alignment concept, described in the document,…

We consider a class of two-prover interactive proof systems where each prover returns a single bit to the verifier and the verifier's verdict is a function of the XOR of the two bits received. We show that, when the provers are allowed to…

We prove a tight parallel repetition theorem for $3$-message computationally-secure quantum interactive protocols between an efficient challenger and an efficient adversary. We also prove under plausible assumptions that the security of…

We consider rank-one non-symmetric tensor estimation and derive simple formulas for the mutual information. We start by the order 2 problem, namely matrix factorization. We treat it completely in a simpler fashion than previous proofs using…

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

We present upper and lower bounds of the computational complexity of the two-way communication model of multiple-prover quantum interactive proof systems whose verifiers are limited to measure-many two-way quantum finite automata. We prove…

We propose nonparametric identification and semiparametric estimation of joint potential outcome distributions in the presence of confounding. First, in settings with observed confounding, we derive tighter, covariate-informed bounds on the…

We introduce a task consisting in matching a proof to a given mathematical statement. The task fits well within current research on Mathematical Information Retrieval and, more generally, mathematical article analysis (Mathematical…

Motivated by the simultaneous association analysis with the presence of latent confounders, this paper studies the large-scale hypothesis testing problem for the high-dimensional confounded linear models with both non-asymptotic and…

We prove a version of the quantum de Finetti theorem: permutation-invariant quantum states are well approximated as a probabilistic mixture of multi-fold product states. The approximation is measured by distinguishability under fully…

Models that learn spurious correlations from training data often fail when deployed in new environments. While many methods aim to learn invariant representations to address this, they often underperform standard empirical risk minimization…