Related papers: Size matters in the modal $\mu$-calculus
Recently, pre-trained language models like BERT have shown promising performance on multiple natural language processing tasks. However, the application of these models has been limited due to their huge size. To reduce its size, a popular…
Active learning parallelization is widely used, but typically relies on fixing the batch size throughout experimentation. This fixed approach is inefficient because of a dynamic trade-off between cost and speed -- larger batches are more…
To interpret uncertainty estimates from differentiable probabilistic models, recent work has proposed generating a single Counterfactual Latent Uncertainty Explanation (CLUE) for a given data point where the model is uncertain, identifying…
An enumerative invariant theory in Algebraic Geometry, Differential Geometry, or Representation Theory, is the study of invariants which 'count' $\tau$-(semi)stable objects $E$ with fixed topological invariants $[E]=\alpha$ in some…
We define a function, called s-multiplicity, that interpolates between Hilbert-Samuel multiplicity and Hilbert-Kunz multiplicity by comparing powers of ideals to the Frobenius powers of ideals. The function is continuous in s, and its value…
As a variant of the Area Under the ROC Curve (AUC), the partial AUC (PAUC) focuses on a specific range of false positive rate (FPR) and/or true positive rate (TPR) in the ROC curve. It is a pivotal evaluation metric in real-world scenarios…
The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function…
In this work, we study diversity-aware clustering problems where the data points are associated with multiple attributes resulting in intersecting groups. A clustering solution needs to ensure that the number of chosen cluster centers from…
Magnitude of a finite metric space and the related notion of magnitude functions on metric spaces is an active area of research in algebraic topology. Magnitude originally arose in the context of biology, where it represents the number of…
Classical complexity theory measures the cost of computing a function, but many computational tasks require committing to one valid output among several. We introduce determination depth -- the minimum number of sequential layers of…
We consider the problem of translating between irreducible closed sets and implicational bases in closure systems. To date, the complexity status of this problem is widely open, and it is further known to generalize the notorious hypergraph…
A $q$-analogue of the tau function of the modified KP hierarchy is defined by a change of independent variables. This tau function satisfies a system of bilinear $q$-difference equations. These bilinear equations are translated to the…
Diversity is an important principle in data selection and summarization, facility location, and recommendation systems. Our work focuses on maximizing diversity in data selection, while offering fairness guarantees. In particular, we offer…
We show that the principal types of the closed terms of the affine fragment of $\lambda$-calculus, with respect to a simple type discipline, are structurally isomorphic to their interpretations, as partial involutions, in a natural Geometry…
Separation bounds are a fundamental measure of the complexity of solving a zero-dimensional system as it measures how difficult it is to separate its zeroes. In the positive dimensional case, the notion of reach takes its place. In this…
We compute anomalous dimensions of higher spin operators in Conformal Field Theory at arbitrary space-time dimension by using the OPE inversion formula of \cite{Caron-Huot:2017vep}, both from the position space representation as well as…
We consider the random 2-satisfiability problem, in which each instance is a formula that is the conjunction of m clauses of the form (x or y), chosen uniformly at random from among all 2-clauses on n Boolean variables and their negations.…
For many quantum systems of interest, the classical computational cost of simulating their time evolution scales exponentially in the system size. At the same time, quantum computers have been shown to allow for simulations of some of these…
The algebraic $\lambda$-calculus is an extension of the ordinary $\lambda$-calculus with linear combinations of terms. We establish that two ordinary $\lambda$-terms are equivalent in the algebraic $\lambda$-calculus iff they are…
Majorization uncertainty relations are derived for arbitrary quantum operations acting on a finite-dimensional space. The basic idea is to consider submatrices of block matrices comprised of the corresponding Kraus operators. This is an…