Related papers: A Generalized Framework for Virtual Substitution
Domain generalization aims to learn an invariant model that can generalize well to the unseen target domain. In this paper, we propose to tackle the problem of domain generalization by delivering an effective framework named Variational…
We give asymptotic sharp estimates for the cardinality of a set of residue classes with the property that the representation function is bounded by a prescribed number. We then use this to obtain an analogous result for sets of integers,…
This paper presents a program analysis method that generates program summaries involving polynomial arithmetic. Our approach builds on prior techniques that use solvable polynomial maps for summarizing loops. These techniques are able to…
Though there are some works on improving distributed word representations using lexicons, the improper overfitting of the words that have multiple meanings is a remaining issue deteriorating the learning when lexicons are used, which needs…
In this article, we study a calibrated version of Reifenberg theorem "with holes". In particular we study sets that are suitably approximable at all points and scales by calibrated planes and show that, without any additional hypotheses on…
Quantization replaces floating point arithmetic with integer arithmetic in deep neural network models, providing more efficient on-device inference with less power and memory. In this work, we propose a framework for formally verifying…
Probably Approximately Correct (PAC) bounds are widely used to derive probabilistic guarantees for the generalisation of machine learning models. They highlight the components of the model which contribute to its generalisation capacity.…
Elementary hybrid systems (EHSs) are those hybrid systems (HSs) containing elementary functions such as exp, ln, sin, cos, etc. EHSs are very common in practice, especially in safety-critical domains. Due to the non-polynomial expressions…
In this article we provide an experimental algorithm that in many cases gives us an upper bound of the global infimum of a real polynomial on $\R^{n}$. It is very well known that to find the global infimum of a real polynomial on $\R^{n}$,…
We give a quantifier elimination procedure for one-parametric Presburger arithmetic, the extension of Presburger arithmetic with the function $x \mapsto t \cdot x$, where $t$ is a fixed free variable ranging over the integers. This resolves…
We present a combination of the Mixed-Echelon-Hermite transformation and the Double-Bounded Reduction for systems of linear mixed arithmetic that preserve satisfiability and can be computed in polynomial time. Together, the two…
We study a matrix completion problem where both the ground truth $R$ matrix and the unknown sampling distribution $P$ over observed entries are low-rank matrices, and \textit{share a common subspace}. We assume that a large amount $M$ of…
We present a generalization of quantum error correction to infinite-dimensional Hilbert spaces. The generalization yields new classes of quantum error correcting codes that have no finite-dimensional counterparts. The error correction…
In this paper, we generalize the algorithm described by Rump and Graillat, as well as our previous work on certifying breadth-one singular solutions of polynomial systems, to compute verified and narrow error bounds such that a slightly…
We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing…
The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas--e.g., deductive databases, theorem proving, static…
Can we endow visuomotor robots with generalization capabilities to operate in diverse open-world scenarios? In this paper, we propose \textbf{Maniwhere}, a generalizable framework tailored for visual reinforcement learning, enabling the…
Evaluating a polynomial on a set of points is a fundamental task in computer algebra. In this work, we revisit a particular variant called trimmed multipoint evaluation: given an $n$-variate polynomial with bounded individual degree $d$ and…
We study the use of hypermodels to represent epistemic uncertainty and guide exploration. This generalizes and extends the use of ensembles to approximate Thompson sampling. The computational cost of training an ensemble grows with its…
We present effective procedures to calculate regular normal cones and other related objects using quantifier elimination. This method of normal cone calculations is complementary to computing Lagrangians and it works best at points where…