Related papers: On Known APNs
We compute the equation of the 7-secant variety to the Veronese variety (P^4,O(3)), its degree is 15. This is the last missing invariant in the Alexander-Hirschowitz classification. It gives the condition to express a homogeneous cubic…
While known algorithms for sensitivity analysis and parameter tuning in probabilistic networks have a running time that is exponential in the size of the network, the exact computational complexity of these problems has not been established…
In this paper, we are interested in the number of fixed points of functions $f:A^n\to A^n$ over a finite alphabet $A$ defined on a given signed digraph $D$. We first use techniques from network coding to derive some lower bounds on the…
A class of diamond networks are studied where the broadcast component is modelled by two independent bit-pipes. New upper and low bounds are derived on the capacity which improve previous bounds. The upper bound is in the form of a max-min…
Probabilistic Neural Network (PNN) is a feed-forward artificial neural network developed for solving classification problems. This paper proposes a hardware implementation of an approximated PNN (APNN) algorithm in which the conventional…
Conventional Convolutional Neural Networks (CNNs) in the real domain have been widely used for audio classification. However, their convolution operations process multi-channel inputs independently, limiting the ability to capture…
Let A be an idempotent algebra on a finite domain. We combine results of Chen 2008 and Zhuk 2015 to argue that if Inv(A) satisfies the polynomially generated powers property (PGP), then QCSP(Inv(A)) is in NP. We then use the result of Zhuk…
Although convolutional neural networks (CNNs) are now widely used in various computer vision applications, its huge resource demanding on parameter storage and computation makes the deployment on mobile and embedded devices difficult.…
While classical convolutional neural networks (CNNs) have revolutionized image classification, the emergence of quantum computing presents new opportunities for enhancing neural network architectures. Quantum CNNs (QCNNs) leverage quantum…
Neural network (NN) designed for challenging machine learning tasks is in general a highly nonlinear mapping that contains massive variational parameters. High complexity of NN, if unbounded or unconstrained, might unpredictably cause…
Recent results by Chen et al. and Polyanskiy et al. explore using feedback to approach capacity with short blocklengths. This paper explores Chernoff bounding techniques to extend the rate-compatible sphere-packing (RCSP) analysis proposed…
Subshifts are sets of colorings of $\mathbb{Z}^d$ defined by families of forbidden patterns. In a given subshift, the extender set of a finite pattern is the set of all its admissible completions. Since soficity of $\mathbb{Z}$ subshifts is…
We define a class of "algebraic" random matrix channels for which one can generically compute the limiting Shannon transform using numerical techniques and often enumerate the low SNR series expansion coefficients in closed form. We…
Understanding the behavior of Artificial Neural Networks is one of the main topics in the field recently, as black-box approaches have become usual since the widespread of deep learning. Such high-dimensional models may manifest…
The paper deals with planar polynomial vector fields. We aim to estimate the number of orbital topological equivalence classes for the fields of degree n. An evident obstacle for this is the second part of Hilbert's 16th problem. To…
Convolutional neural networks (CNNs) have been used in many machine learning fields. In practical applications, the computational cost of convolutional neural networks is often high with the deepening of the network and the growth of data…
Two important problems on almost perfect nonlinear (APN) functions are the enumeration and equivalence problems. In this paper, we solve these two problems for any biprojective APN function family by introducing a strong group theoretic…
We consider the power of Boolean circuits with MOD$_{6}$ gates. First, we introduce a few basic notions of computational complexity, and describe the standard models with which we study the complexity of problems. We then define the model…
We present an algorithmic framework for computing generators for the ring of invariants of an Artin-Schreier curve. We give explicit invariants for almost all Artin-Schreier curves of genus up to~8 in standard form, and for a handful of…
Quantum neural networks (QNNs) have emerged as a leading strategy to establish applications in machine learning, chemistry, and optimization. While the applications of QNN have been widely investigated, its theoretical foundation remains…