Related papers: NIL: Learning Nonlinear Interpolants
The problem of computing Craig interpolants in SAT and SMT has recently received a lot of interest, mainly for its applications in formal verification. Efficient algorithms for interpolant generation have been presented for some theories of…
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
We propose Splinter, a new technique for proving properties of heap-manipulating programs that marries (1) a new separation logic-based analysis for heap reasoning with (2) an interpolation-based technique for refining heap-shape invariants…
Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated…
Due to the model aging problem, Deep Neural Networks (DNNs) need updates to adjust them to new data distributions. The common practice leverages incremental learning (IL), e.g., Class-based Incremental Learning (CIL) that updates output…
To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…
We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…
The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…
Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and…
Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…
As a prominent category of imitation learning methods, adversarial imitation learning (AIL) has garnered significant practical success powered by neural network approximation. However, existing theoretical studies on AIL are primarily…
This paper discusses a new method to solve definite integrals using artificial neural networks. The objective is to build a neural network that would be a novel alternative to pre-established numerical methods and with the help of a…
Class-incremental learning (CIL) with pre-trained models (PTMs) faces a critical trade-off between efficient adaptation and long-term stability. While analytic learning enables rapid, recursive closed-form updates, its efficacy is often…
We introduce proof nets for PiL, an extension of first-order multiplicative additive linear logic with new operators allowing a shallow encoding of processes in the {\pi}-calculus as formulas. We provide correctness criterion,…
This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…
This paper introduces the Non-linear Partition of Unity Method, a novel technique integrating Radial Basis Function interpolation and Weighted Essentially Non-Oscillatory algorithms. It addresses challenges in high-accuracy approximations,…
Provably correct software is one of the key challenges of our software-driven society. Program synthesis -- the task of constructing a program satisfying a given specification -- is one strategy for achieving this. The result of this task…
Partial label learning (PLL) is a typical weakly supervised learning, where each sample is associated with a set of candidate labels. Its basic assumption is that the ground-truth label must be in the candidate set, but this assumption may…
In this paper we present InterHorn, a solver for recursion-free Horn clauses. The main application domain of InterHorn lies in solving interpolation problems arising in software verification. We show how a range of interpolation problems,…
Complementary-label learning (CLL) is a weakly supervised learning paradigm for multiclass classification, where only complementary labels -- indicating classes an instance does not belong to -- are provided to the learning algorithm.…