Related papers: Resolution Lower Bounds for Refutation Statements
We show new limits on the efficiency of using current techniques to make exact probabilistic inference for large classes of natural problems. In particular we show new lower bounds on knowledge compilation to SDD and DNNF forms. We give…
In generative communication, the transmitter sends a compact generative description, such as model parameters or a latent representation, rather than raw data. The receiver uses this description to form a posterior belief over the…
An extended formulation of a polytope P is a polytope Q which can be projected onto P. Extended formulations of small size (i.e., number of facets) are of interest, as they allow to model corresponding optimization problems as linear…
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…
Barren-plateau results have established exponential gradient suppression as a widely cited obstacle to the scalability of variational quantum algorithms. When and whether these results extend to a given objective has been addressed through…
We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…
Lower bounds against strong algebraic proof systems and specifically fragments of the Ideal Proof System (IPS), have been obtained in an ongoing line of work. All of these bounds, however, are proved only over large (or characteristic $0$)…
We prove a lower bound on the canonical height associated to polynomials over number fields evaluated at points with infinite forward orbit. The lower bound depends only on the degree of the polynomial, the degree of the number field, and…
In this paper we discuss contrastive explanations for formal argumentation - the question why a certain argument (the fact) can be accepted, whilst another argument (the foil) cannot be accepted under various extension-based semantics. The…
We prove, for a sufficiently small subset $\mathcal{A}$ of a prime residue field, an estimate on the number of solutions to the equation $(a_1-a_2)(a_3-a_4) = (a_5-a_6)(a_7-a_8)$ with all variables in $\mathcal{A}$. We then derive new…
The increasing deployment of machine learning as well as legal regulations such as EU's GDPR cause a need for user-friendly explanations of decisions proposed by machine learning models. Counterfactual explanations are considered as one of…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
This paper talks about difference between P and NP by using topological space that mean resolution principle. I pay attention to restrictions of antecedent and consequent in resolution, and show what kind of influence the restrictions have…
Lower bounds involving $f$-divergences between the underlying probability measures are proved for the minimax risk in estimation problems. Our proofs just use simple convexity facts. Special cases and straightforward corollaries of our…
This preliminary report addresses the expressive power of unit resolution regarding input data encoded with partial truth assignments of propositional variables. A characterization of the functions that are computable in this way, which we…
We consider sets $\Gamma(n,s,k)$ of narrow clauses expressing that no definition of a size $s$ circuit with $n$ inputs is refutable in resolution R in $k$ steps. We show that every CNF shortly refutable in Extended R, ER, can be easily…
We prove a lower bound of exp(-C (log(2/alpha))^7)N^{k-1} to the number of solutions of an invariant equation in k variables, contained in a set of density alpha. Moreover, we give a Behrend-type construction for the same problem with the…
We prove limiting absorption resolvent bounds for the semiclassical Schr\"odinger operator with a repulsive potential in dimension $n\ge 3$, which may have a singularity at the origin. As an application, we obtain time decay for the…
We establish the boundedness of solutions of reaction-diffusion systems with quadratic (in fact slightly super-quadratic) reaction terms that satisfy a natural entropy dissipation property, in any space dimension N>2. This bound imply the…