Related papers: Toward a Characterization of Simulation Between Ar…
We prove that the bounded arithmetic theory $S^1_2$ is consistent with EXP $\not\subseteq$ P/poly. More generally, we show that certain separations of $V^1_2$ from a theory $T$ imply the consistency of $T$ with EXP $\not\subseteq$ P/poly.…
We study interactions between Skolem Arithmetic and certain classes of Constraint Satisfaction Problems (CSPs). We revisit results of Glass er et al. in the context of CSPs and settle the major open question from that paper, finding a…
Explainable Artificial Intelligence (XAI) aims to make machine learning models transparent and trustworthy, yet most current approaches communicate explanations visually or through text. This paper introduces an information theoretic…
Simulation-Based Inference (SBI) is an approach to statistical inference where simulations from an assumed model are used to construct estimators and confidence sets. SBI is often used when the likelihood is intractable and to construct…
Recent legislative regulations have underlined the need for accountable and transparent artificial intelligence systems and have contributed to a growing interest in the Explainable Artificial Intelligence (XAI) field. Nonetheless, the lack…
For a finite relational structure A, let CSP(A) denote the CSP instances whose constraint relations are taken from A. The resulting family of problems CSP(A) has been considered heavily in a variety of computational contexts. In this…
We study the algebraic theory of computable functions, which can be viewed as arising from possibly non-halting computer programs or algorithms, acting on some state space, equipped with operations of composition, {\em if-then-else} and…
It is well known that the theory of coalgebras provides an abstract definition of behavioural equivalence that coincides with strong bisimulation across a wide variety of state-based systems. Unfortunately, the theory in the presence of…
This paper highlights a tension between semiparametric efficiency and bootstrap consistency in the context of a canonical semiparametric estimation problem, namely the problem of estimating the average density. It is shown that although…
Recent advances in computational cognitive science (i.e., simulation-based probabilistic programs) have paved the way for significant progress in formal, implementable models of pragmatics. Rather than describing a pragmatic reasoning…
A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness allows one to lift most good properties from finite Markov chains to denumerable…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
It is well known that the kind of P systems involved in the definition of the P conjecture is able to solve problems in the complexity class $\mathbf{P}$ by leveraging the uniformity condition. Here we show that these systems are indeed…
We report a proof of the quantum Sanov Theorem by elementary application of basic facts about representations of the symmetric group, together with a complete characterization of the optimal error exponent in a situation where the null…
The inner alignment problem, which asserts whether an arbitrary artificial intelligence (AI) model satisfices a non-trivial alignment function of its outputs given its inputs, is undecidable. This is rigorously proved by Rice's theorem,…
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…
Verifying the correctness of Bayesian computation is challenging. This is especially true for complex models that are common in practice, as these require sophisticated model implementations and algorithms. In this paper we introduce…
In mathematical logic there are two seemingly distinct kinds of principles called "reflection principles." Semantic reflection principles assert that if a formula holds in the whole universe, then it holds in a set-sized model. Syntactic…
Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…
Simulation-based Bayesian inference (SBI) methods are widely used for parameter estimation in complex models where evaluating the likelihood is challenging but generating simulations is relatively straightforward. However, these methods…