Related papers: NIL: Learning Nonlinear Interpolants

Class-incremental learning (CIL) has been widely studied under the setting of starting from a small number of classes (base classes). Instead, we explore an understudied real-world setting of CIL that starts with a strong model pre-trained…

We study the problem of $P$-interpolation, where $P$ is a set of binary predicate symbols, for certain classes of local extensions of a base theory. For computing the $P$-interpolating terms, we use a hierarchic approach: This allows us to…

Optimizing and certifying the positivity of polynomials are fundamental primitives across mathematics and engineering applications, from dynamical systems to operations research. However, solving these problems in practice requires large…

Automated verification of all members of a (potentially infinite) set of programs has the potential to be useful in program synthesis, as well as in verification of dynamically loaded code, concurrent code, and language properties. Existing…

The ability of transformers to perform precision tasks such as question answering, Natural Language Inference (NLI) or summarising, have enabled them to be ranked as one of the best paradigm to address Natural Language Processing (NLP)…

The paper deals with two fundamental types of trigonometric polynomials and splines on uniform grids, which allow us to construct interpolation approximations that depend linearly on the values of the interpolated function. Fundamental on…

Recent work has shown logical background knowledge can be used in learning systems to compensate for a lack of labeled training data. Many methods work by creating a loss function that encodes this knowledge. However, often the logic is…

We present FLINT (learning-based FLow estimation and temporal INTerpolation), a novel deep learning-based approach to estimate flow fields for 2D+time and 3D+time scientific ensemble data. FLINT can flexibly handle different types of…

For $m,n \in \mathbb{N}$, $m\geq 1$ and a given function $f : \mathbb{R}^m\longrightarrow \mathbb{R}$ the polynomial interpolation problem (PIP) is to determine a \emph{generic node set} $P \subseteq \mathbb{R}^m$ and the coefficients of…

Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address…

Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor neural network based machine learning method. This means…

We present an efficient algorithm for the least squares parameter fitting optimized for component separation in multi-frequency CMB experiments. We sidestep some of the problems associated with non-linear optimization by taking advantage of…

Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the…

We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and…

Despite the recent success on image classification, self-training has only achieved limited gains on structured prediction tasks such as neural machine translation (NMT). This is mainly due to the compositionality of the target space, where…

Craig interpolation has become a versatile algorithmic tool for improving software verification. Interpolants can, for instance, accelerate the convergence of fixpoint computations for infinite-state systems. They also help improve the…

Language models are aligned to the collective voice of many, resulting in generic outputs that do not align with specific users' styles. In this work, we present Trial-Error-Explain In-Context Learning (TICL), a tuning-free method that…

Class-incremental learning (CIL) enables models to learn new classes progressively while preserving knowledge of previously learned ones. Recent advances in this field have shifted towards parameter-efficient fine-tuning techniques, with…

While Mixed-integer linear programming (MILP) is NP-hard in general, practical MILP has received roughly 100--fold speedup in the past twenty years. Still, many classes of MILPs quickly become unsolvable as their sizes increase, motivating…

We address the predicate generation problem in the context of loop invariant inference. Motivated by the interpolation-based abstraction refinement technique, we apply the interpolation theorem to synthesize predicates implicitly implied by…