Related papers: Efficient Interpolation for the Theory of Arrays
We present algorithms that run in linear time on pointer machines for a collection of problems, each of which either directly or indirectly requires the evaluation of a function defined on paths in a tree. These problems previously had…
We consider the well-known problem of enumerating all triangles of an undirected graph. Our focus is on determining the input/output (I/O) complexity of this problem. Let $E$ be the number of edges, $M<E$ the size of internal memory, and…
Model merging, typically on Instruct and Thinking models, has shown remarkable performance for efficient reasoning. In this paper, we systematically revisit the simplest merging method that interpolates two weights directly. Particularly,…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…
Classical wisdom suggests that estimators should avoid fitting noise to achieve good generalization. In contrast, modern overparameterized models can yield small test error despite interpolating noise -- a phenomenon often called "benign…
We have recently presented a general method of proving the fundamental logical properties of Craig and Lyndon Interpolation (IPs) by induction on derivations in a wide class of internal sequent calculi, including sequents, hypersequents,…
Deep Neural Networks (DNNs) and Large Language Models (LLMs) have revolutionized artificial intelligence, yet their deployment faces significant memory and computational challenges, especially in resource-constrained environments.…
In many applications one wants to identify identical subtrees of a program syntax tree. This identification should ideally be robust to alpha-renaming of the program, but no existing technique has been shown to achieve this with good…
Spanning tree modulus is a generalization of effective resistance that is closely related to graph strength and fractional arboricity. The optimal edge density associated with spanning tree modulus is known to produce two hierarchical…
Estimating camera geometry typically involves solving minimal problems formulated as systems of multivariate polynomial equations, which often pose computational challenges when using existing Gr\"obner-basis or resultant-based methods due…
In this work we study the interleaving distance between merge trees from a combinatorial point of view. We use a particular type of matching between trees to obtain a novel formulation of the distance. With such formulation, we tackle the…
Computationally expensive Radiative Transfer Models (RTMs) are widely used} to realistically reproduce the light interaction with the Earth surface and atmosphere. Because these models take long processing time, the common practice is to…
We revisit the problem of fair representation learning by proposing Fair Partial Least Squares (PLS) components. PLS is widely used in statistics to efficiently reduce the dimension of the data by providing representation tailored for the…
Constrained counting is a fundamental problem in artificial intelligence. A promising new algebraic approach to constrained counting makes use of tensor networks, following a reduction from constrained counting to the problem of…
A fast and reliable algorithm for the optimal interpolation of scattered data on the torus by multivariate trigonometric polynomials is presented. The algorithm is based on a variant of the conjugate gradient method in combination with the…
Learning on large graphs presents significant challenges, with traditional Message Passing Neural Networks suffering from computational and memory costs scaling linearly with the number of edges. We introduce the Intersecting Block Graph…
Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding function evaluations, or data values. This method has some…
We present a unified interpolation scheme that combines compactly-supported positive-definite kernels and multivariate polynomials. This unified framework generalizes interpolation with compactly-supported kernels and also classical…
In this paper, we study a posteriori error estimators which aid multilevel iterative solvers for linear systems with graph Laplacians. In earlier works such estimates were computed by solving global optimization problems, which could be…