Related papers: General Interpolation and Strong Amalgamation for …

We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…

Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…

Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…

We develop a new approximation theory for linear and quadratic interpolation models, suitable for use in convex-constrained derivative-free optimization (DFO). Most existing model-based DFO methods for constrained problems assume the…

Linear algebra computations are foundational for neural networks and machine learning, often handled through arrays. While many functional programming languages feature lists and recursion, arrays in linear algebra demand constant-time…

In practice, deep neural networks are often able to easily interpolate their training data. To understand this phenomenon, many works have aimed to quantify the memorization capacity of a neural network architecture: the largest number of…

In this paper, we propose new deterministic and Monte Carlo interpolation algorithms for sparse multivariate polynomials represented by straight-line programs. Let $f$ be an $n$-variate polynomial given by a straight-line program, which has…

We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…

Formally verifying properties of programs that manipulate arrays in loops is computationally challenging. In this paper, we focus on a useful class of such programs, and present a novel property-driven verification method that first infers…

We propose Deep Feature Interpolation (DFI), a new data-driven baseline for automatic high-resolution image transformation. As the name suggests, it relies only on simple linear interpolation of deep convolutional features from pre-trained…

Fair and trustworthy AI is becoming ever more important in both machine learning and legal domains. One important consequence is that decision makers must seek to guarantee a 'fair', i.e., non-discriminatory, algorithmic decision procedure.…

Among all data augmentation techniques proposed so far, linear interpolation of training samples, also called Mixup, has found to be effective for a large panel of applications. Along with improved predictive performance, Mixup is also a…

In this paper we study possibilities of interpolation and symbol elimination in extensions of a theory $\mathcal{T}_0$ with additional function symbols whose properties are axiomatised using a set of clauses. We analyze situations in which…

We examine the necessity of interpolation in overparameterized models, that is, when achieving optimal predictive risk in machine learning problems requires (nearly) interpolating the training data. In particular, we consider simple…

We analyze the convergence of generalized kernel-based interpolation methods. This is done under minimalistic assumptions on both the kernel and the target function. On these grounds, we further prove convergence of popular greedy data…

We consider type inference for guarded recursive data types (GRDTs) -- a recent generalization of algebraic data types. We reduce type inference for GRDTs to unification under a mixed prefix. Thus, we obtain efficient type inference.…

We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…

Mixup is a widely adopted strategy for training deep networks, where additional samples are augmented by interpolating inputs and labels of training pairs. Mixup has shown to improve classification performance, network calibration, and…

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work…

Deep learning based methods have penetrated many image processing problems and become dominant solutions to these problems. A natural question raised here is "Is there any space for conventional methods on these problems?" In this paper,…