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The problem of optimising a network of discretely firing neurons is addressed. An objective function is introduced which measures the average number of bits that are needed for the network to encode its state. When this is minimised, it is…
Understanding the inductive bias of neural networks is critical to explaining their ability to generalise. Here, for one of the simplest neural networks -- a single-layer perceptron with n input neurons, one output neuron, and no threshold…
A Boolean network (BN) with $n$ components is a discrete dynamical system described by the successive iterations of a function $f:\{0,1\}^n \to \{0,1\}^n$. This model finds applications in biology, where fixed points play a central role.…
We derive exact upper and lower bounds for the cumulative distribution function (cdf) of the output of a neural network (NN) over its entire support subject to noisy (stochastic) inputs. The upper and lower bounds converge to the true cdf…
A Boolean network (BN) is called observable if any initial state can be uniquely determined from the output sequence. In the existing literature on observability of BNs, there is almost no research on the relationship between the number of…
With a constant improvement in the network architectures and training methodologies, Neural Networks (NNs) are increasingly being deployed in real-world Machine Learning systems. However, despite their impressive performance on "known…
Deterministic and stochastic Boolean network models are build for the dynamics of negative feedback loops of the p53 pathways. It is shown that the main function of the negative feedback in the p53 pathways is to keep p53 at a low steady…
Computational models of biological processes provide one of the most powerful methods for a detailed analysis of the mechanisms that drive the behavior of complex systems. Logic-based modeling has enhanced our understanding and…
In supervised learning, it is known that overparameterized neural networks with one hidden layer provably and efficiently learn and generalize, when trained using stochastic gradient descent with a sufficiently small learning rate and…
The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides…
Antifragility is a property that enhances the capability of a system in response to external perturbations. Although the concept has been applied in many areas, a practical measure of antifragility has not been developed yet. Here we…
The stability of Boolean networks has attracted much attention due to its wide applications in describing the dynamics of biological systems. During the past decades, much effort has been invested in unveiling how network structure and…
We study two types of simplified Boolean dynamics over scale-free networks, both with synchronous update. Assigning only Boolean functions AND and XOR to the nodes with probability $1-p$ and $p$, respectively, we are able to analyze the…
Boolean networks have been proposed as potentially useful models for genetic control. An important aspect of these networks is the stability of their dynamics in response to small perturbations. Previous approaches to stability have assumed…
Acoustic scene classification and related tasks have been dominated by Convolutional Neural Networks (CNNs). Top-performing CNNs use mainly audio spectograms as input and borrow their architectural design primarily from computer vision. A…
Non-negative matrix factorization (NMF) is a new knowledge discovery method that is used for text mining, signal processing, bioinformatics, and consumer analysis. However, its basic property as a learning machine is not yet clarified, as…
It is a common assumption that the activation of different layers in neural networks follow Gaussian distribution. This distribution can be transformed using normalization techniques, such as batch-normalization, increasing convergence…
Despite their ability to represent highly expressive functions, deep learning models seem to find simple solutions that generalize surprisingly well. Spectral bias -- the tendency of neural networks to prioritize learning low frequency…
The noise sensitivity of a Boolean function $f: \{0,1\}^n \rightarrow \{0,1\}$ is one of its fundamental properties. A function of a positive noise parameter $\delta$, it is denoted as $NS_{\delta}[f]$. Here we study the algorithmic problem…
Control barrier functions (CBFs) enable guaranteed safe multi-agent navigation in the continuous domain. The resulting navigation performance, however, is highly sensitive to the underlying hyperparameters. Traditional approaches consider…