相关论文: From multivalued to Boolean functions: preservatio…

We prove that nested canalizing functions are the minimum-sensitivity Boolean functions for any given activity ratio and we characterize the sensitivity boundary which has a nontrivial fractal structure. We further observe, on an extensive…

In this paper, we obtain complete characterization for nested canalyzing functions (NCFs) by obtaining its unique algebraic normal form (polynomial form). We introduce a new concept, LAYER NUMBER for NCF. Based on this, we obtain explicit…

Inferring dynamic biochemical networks is one of the main challenges in systems biology. Given experimental data, the objective is to identify the rules of interaction among the different entities of the network. However, the number of…

Canalizing functions have important applications in physics and biology. For example, they represent a mechanism capable of stabilizing chaotic behavior in Boolean network models of discrete dynamical systems. When comparing the class of…

Based on a recent characterization of nested canalyzing function (NCF), we obtain the formula of the sensitivity of any NCF. Hence we find that any sensitivity of NCF is between $\frac{n+1}{2}$ and $n$. Both lower and upper bounds are…

The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is…

Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by…

Canalization is a classic concept in Developmental Biology that is thought to be an important feature of evolving systems. In a Boolean network it is a form of network robustness in which a subset of the input signals control the behavior…

Convolutional neural networks (CNNs) are widely used for high-stakes applications like medicine, often surpassing human performance. However, most explanation methods rely on post-hoc attribution, approximating the decision-making process…

Empirical evidence has revealed that biological regulatory systems are controlled by high-level coordination between topology and Boolean rules. In this study, we study the joint effects of degree and Boolean functions on the stability of…

Convolutional neural networks (CNNs) are similar to "ordinary" neural networks in the sense that they are made up of hidden layers consisting of neurons with "learnable" parameters. These neurons receive inputs, performs a dot product, and…

A first step is taken towards understanding often observed non-robustness phenomena of deep neural net (DNN) classifiers. This is done from the perspective of Boolean functions by asking if certain sequences of Boolean functions represented…

Boolean networks with canalizing functions are used to model gene regulatory networks. In order to learn how such networks may behave under evolutionary forces, we simulate the evolution of a single Boolean network by means of an adaptive…

Network Functions Virtualization (NFV) and Network Coding (NC) have attracted much attention in recent years as key concepts for providing 5G networks with flexibility and differentiated reliability, respectively. In this paper, we present…

NPN classification is an essential problem in the design and verification of digital circuits. Most existing works explored variable symmetries and cofactor signatures to develop their classification methods. However, cofactor signatures…

Convolutional Neural Networks (CNNs) use pooling to decrease the size of activation maps. This process is crucial to increase the receptive fields and to reduce computational requirements of subsequent convolutions. An important feature of…

We propose a convolutional neural network (CNN) architecture for image classification based on subband decomposition of the image using wavelets. The proposed architecture decomposes the input image spectra into multiple critically sampled…

Deep neural networks are renowned for their ability to generalise well across diverse tasks, even when heavily overparameterized. Existing works offer only partial explanations (for example, the NTK-based task-model alignment explanation…

Convolutional Neural Networks (CNNs) are powerful models that achieve impressive results for image classification. In addition, pre-trained CNNs are also useful for other computer vision tasks as generic feature extractors. This paper aims…

Neural collapse (NC) describes the structured geometry that emerges in the features and weights of trained classifiers. Recent theory suggests NC can be suboptimal in deep architectures, attributing this to an explicit low-rank bias from L2…