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We prove an impossibility result for conditional Probably Approximately Correct (PAC)-efficient reasoning in large language models. While recent work has established marginal PAC efficiency guarantees for composite models that switch…
We introduce and develop propositional continuous intuitionistic logic and propositional continuous affine logic via complete algebraic semantics. Our approach centres on AC-algebras, which are algebras $USC(\mathcal{L})$ of sup-preserving…
We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…
The minimization problem for propositional formulas is an important optimization problem in the second level of the polynomial hierarchy. In general, the problem is Sigma-2-complete under Turing reductions, but restricted versions are…
We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches. Our key idea is to parameterize a single potential in the…
A property $\Pi$ on a finite set $U$ is \emph{monotone} if for every $X \subseteq U$ satisfying $\Pi$, every superset $Y \subseteq U$ of $X$ also satisfies $\Pi$. Many combinatorial properties can be seen as monotone properties. The problem…
We discuss some results concerning fixed point equations in the setting of topological *-algebras of unbounded operators. In particular, an existence result is obtained for what we have called {\em weak $\tau$ strict contractions}, and some…
Predicting the value of a function $f$ at a new point given its values at old points is an ubiquitous scientific endeavor, somewhat less developed when $f$ produces multiple values that depend on one another, e.g. when it outputs…
We develop an idempotent version of probabilistic potential theory. The goal is to describe the set of max-plus harmonic functions, which give the stationary solutions of deterministic optimal control problems with additive reward. The…
For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering…
Estimating equations arise in a wide range of statistical applications, including longitudinal and clustered data analysis, survival analysis, econometrics, and semiparametric inference. In high-dimensional settings, adding…
Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…
We find many tight codes in compact spaces, i.e., optimal codes whose optimality follows from linear programming bounds. In particular, we show the existence (and abundance) of several hitherto unknown families of simplices in quaternionic…
In this paper we consider a broad class of infinite horizon discrete-time optimal control models that involve a nonnegative cost function and an affine mapping in their dynamic programming equation. They include as special cases classical…
Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depends on both the structure and the parametrization of the…
We propose a novel formulation for approximating reachable sets through a minimum discounted reward optimal control problem. The formulation yields a continuous solution that can be obtained by solving a Hamilton-Jacobi equation.…
The estimation of a random vector with independent components passed through a linear transform followed by a componentwise (possibly nonlinear) output map arises in a range of applications. Approximate message passing (AMP) methods, based…
A fixed point theorem is proved for inverse transducers, leading to an automata-theoretic proof of the fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated. If the endomorphism is…
Conditional independence is a crucial concept supporting adequate modelling and efficient reasoning in probabilistics. In knowledge representation, the idea of conditional independence has also been introduced for specific formalisms, such…
A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…