Related papers: Symmetry Properties of Nested Canalyzing Functions
The level of a function f on an n-dimensional space encloses a region. The volume of a region between two such levels depends on both levels. Fixing one of them the volume becomes a function of the remaining level. We show that if the…
It has long been recognized that the invariance and equivariance properties of a representation are critically important for success in many vision tasks. In this paper we present Steerable Convolutional Neural Networks, an efficient and…
We study the symmetry properties in the dynamics of quantum correlations for two-qubit systems in one-sided noisy channels, with respect to a switch in the location of noise from one qubit to the other. We consider four different channel…
We formalize and study a phenomenon called feature collapse that makes precise the intuitive idea that entities playing a similar role in a learning task receive similar representations. As feature collapse requires a notion of task, we…
Accurate simulations of thermalization in open quantum systems require a reliable representation of the bath correlation function (BCF). Numerical approaches, such as the hierarchical equations of motion and the pseudomode method,…
The field of network synchronization has seen tremendous growth following the introduction of the master stability function (MSF) formalism, which enables the efficient stability analysis of synchronization in large oscillator networks.…
Normalizing flows are exact-likelihood generative neural networks which approximately transform samples from a simple prior distribution to samples of the probability distribution of interest. Recent work showed that such generative models…
Let $m$ be an even positive integer. A Boolean bent function $f$ on $\GF{m-1} \times \GF {}$ is called a \emph{cyclic bent function} if for any $a\neq b\in \GF {m-1}$ and $\epsilon \in \GF{}$, $f(ax_1,x_2)+f(bx_1,x_2+\epsilon)$ is always…
We describe the emergence of a Convolution Bottleneck (CBN) structure in CNNs, where the network uses its first few layers to transform the input representation into a representation that is supported only along a few frequencies and…
Most of the research related to Non Functional Requirements (NFRs) have presented NFRs frameworks by integrating non functional requirements with functional requirements while we proposed that measurement of NFRs is possible e.g. cost and…
Biological network alignment identifies topologically and functionally conserved regions between networks of different species. It encompasses two algorithmic steps: node cost function (NCF), which measures similarities between nodes in…
Synchronization of network-coupled dynamical units is important to a variety of natural and engineered processes including circadian rhythms, cardiac function, neural processing, and power grids. Despite this ubiquity, it remains poorly…
Normalizing flows have emerged as an important family of deep neural networks for modelling complex probability distributions. In this note, we revisit their coupling and autoregressive transformation layers as probabilistic graphical…
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
Asymmetric lineshapes are experimentally observed in Raman spectra of different classes of condensed matter. Determination of the peak parameters, typically done with symmetric pseudo-Voigt functions, in such situations yields unreliable…
Modeling and synthesizing image noise is an important aspect in many computer vision applications. The long-standing additive white Gaussian and heteroscedastic (signal-dependent) noise models widely used in the literature provide only a…
Symmetry is present in nature and science. In image processing, kernels for spatial filtering possess some symmetry (e.g. Sobel operators, Gaussian, Laplacian). Convolutional layers in artificial feed-forward neural networks have typically…
Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic…
Flow models have rapidly become the go-to method for training and deploying large-scale generators, owing their success to inference-time flexibility via adjustable integration steps. A crucial ingredient in flow training is the choice of…
The probabilistic degree of a Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is defined to be the smallest $d$ such that there is a random polynomial $\mathbf{P}$ of degree at most $d$ that agrees with $f$ at each point with high…