Related papers: Abstraction based Output Range Analysis for Neural…
We introduce switched linear projections for expressing the activity of a neuron in a deep neural network in terms of a single linear projection in the input space. The method works by isolating the active subnetwork, a series of linear…
Implicit Neural representations (INRs) are widely used for scientific data reduction and visualization by modeling the function that maps a spatial location to a data value. Without any prior knowledge about the spatial distribution of…
This is paper for the smooth function approximation by neural networks (NN). Mathematical or physical functions can be replaced by NN models through regression. In this study, we get NNs that generate highly accurate and highly smooth…
It is commonly recognized that the expressiveness of deep neural networks is contingent upon a range of factors, encompassing their depth, width, and other relevant considerations. Currently, the practical performance of the majority of…
In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…
The abstraction tasks are challenging for multi- modal sequences as they require a deeper semantic understanding and a novel text generation for the data. Although the recurrent neural networks (RNN) can be used to model the context of the…
Deep Neural Networks (DNNs) are rapidly being applied to safety-critical domains such as drone and airplane control, motivating techniques for verifying the safety of their behavior. Unfortunately, DNN verification is NP-hard, with current…
This paper presents a novel approach for the output range estimation problem in Deep Neural Networks (DNNs) by integrating a Simulated Annealing (SA) algorithm tailored to operate within constrained domains and ensure convergence towards…
In this chapter, an integer linear programming formulation for the problem of obtaining task-relevant, multi-resolution, environment abstractions for resource-constrained autonomous agents is presented. The formulation leverages concepts…
Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning…
Reasoning requires going beyond pattern matching or memorization of solutions to identify and implement "algorithmic procedures" that can be used to deduce answers to hard problems. Doing so requires realizing the most relevant primitives,…
Whereas distributed computing research has been very successful in exploring the solvability/impossibility border of distributed computing problems like consensus in representative classes of computing models with respect to model…
We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs). INNs are a class of implicit learning models that use implicit equations as layers and have been shown to exhibit several notable…
Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…
To verify safety and robustness of neural networks, researchers have successfully applied abstract interpretation, primarily using the interval abstract domain. In this paper, we study the theoretical power and limits of the interval domain…
We present a methodology for formulating simplifying abstractions in machine learning systems by identifying and harnessing the utility structure of decisions. Machine learning tasks commonly involve high-dimensional output spaces (e.g.,…
Neural implicit representations, which encode a surface as the level set of a neural network applied to spatial coordinates, have proven to be remarkably effective for optimizing, compressing, and generating 3D geometry. Although these…
In this paper, a mixed-integer linear programming formulation for the problem of obtaining task-relevant, multi-resolution, graph abstractions for resource-constrained agents is presented. The formulation leverages concepts from…
The number of linear regions is one of the distinct properties of the neural networks using piecewise linear activation functions such as ReLU, comparing with those conventional ones using other activation functions. Previous studies showed…
We derive upper bounds on the complexity of ReLU neural networks approximating the solution of a linear system given the matrix and the right-hand side. We focus on matrices which are symmetric positive definite and sparse, as they appear…