Related papers: Invariant Subspace Approach to Boolean (Control) N…

We consider the problem of distributing a control policy across a network of interconnected units. Distributing controllers in this way has a number of potential advantages, especially in terms of robustness, as the failure of a single unit…

Modeling natural phenomena with artificial neural networks (ANNs) often provides highly accurate predictions. However, ANNs often suffer from over-parameterization, complicating interpretation and raising uncertainty issues. Bayesian neural…

Recurrent neural networks (RNNs) are widely used in computational neuroscience and machine learning applications. In an RNN, each neuron computes its output as a nonlinear function of its integrated input. While the importance of RNNs,…

Networked systems display complex patterns of interactions between a large number of components. In physical networks, these interactions often occur along structural connections that link components in a hard-wired connection topology,…

Boolean networks, first developed in the late 1960s as a tool for studying complex disordered dynamical systems, consist of nodes governed by Boolean functions whose evolution is entirely deterministic in that the state of the network at a…

Controllable bosonic systems can provide post-classical computational power with sub-universal quantum computational capability. A network that consists of a number of bosons evolving through beam-splitters and phase-shifters between…

We investigate the expressive power of neural networks from the point of view of descriptive complexity. We study neural networks that use floating-point numbers and piecewise polynomial activation functions from two perspectives: 1) the…

Domains where supervised models are deployed often come with task-specific constraints, such as prior expert knowledge on the ground-truth function, or desiderata like safety and fairness. We introduce a novel probabilistic framework for…

Discrete modelling frameworks of Biological networks can be divided in two distinct categories: Boolean and Multi-valued. Although Multi-valued networks are more expressive for qualifying the regulatory behaviours modelled by more than two…

Intracellular networks process cellular-level information and control cell fate. They can be computationally modeled using Boolean networks, which are implicit-time causal models of discrete binary events. These networks can be embedded in…

The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…

Developing robust and interpretable vision systems is a crucial step towards trustworthy artificial intelligence. In this regard, a promising paradigm considers embedding task-required invariant structures, e.g., geometric invariance, in…

Nonlinear dynamical systems possessing an invariant subspace can display interesting dynamical behavior, such as on-off intermittency and bubbling. This letter shows that a class of such systems have amazing features of (1) supersensitivity…

Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…

Canalization is a key organizing principle in complex systems, particularly in gene regulatory networks. It describes how certain input variables exert dominant control over a function's output, thereby imposing hierarchical structure and…

Deep convolutional networks often append additive constant ("bias") terms to their convolution operations, enabling a richer repertoire of functional mappings. Biases are also used to facilitate training, by subtracting mean response over…

Binary Neural Networks (BNNs) have emerged as a promising solution for reducing the memory footprint and compute costs of deep neural networks, but they suffer from quality degradation due to the lack of freedom as activations and weights…

We present a general method for analysing novel computational substrates to determine which of their parameters can be manipulated to exhibit the complete set of 2-input boolean logical operations. We demonstrate this approach with an…

In this paper, we focus on mean-field variational Bayesian Neural Networks (BNNs) and explore the representation capacity of such BNNs by investigating which types of concepts are less likely to be encoded by the BNN. It has been observed…

Probabilistic Boolean Networks (PBNs) were introduced as a computational model for the study of complex dynamical systems, such as Gene Regulatory Networks (GRNs). Controllability in this context is the process of making strategic…