Related papers: Unifying vectors and matrices of different dimensi…
Word embeddings resulting from neural language models have been shown to be successful for a large variety of NLP tasks. However, such architecture might be difficult to train and time-consuming. Instead, we propose to drastically simplify…
Very recently, the Neural Cellular Automata (NCA) has been proposed to simulate the morphogenesis process with deep networks. NCA learns to grow an image starting from a fixed single pixel. In this work, we show that the neural network (NN)…
The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering…
We extend the concept of dual unitary quantum gates to quantum lattice models in $2 + 1$ dimensions, by introducing and studying ternary unitary four-particle gates, which are unitary in time and both spatial dimensions. When used as…
We investigate the state space reconstruction from multiple time series derived from continuous and discrete systems and propose a method for building embedding vectors progressively using information measure criteria regarding past,…
Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to…
Conference matrices are used to define complex structures on real vector spaces. Certain lattices in these spaces become modules for rings of quadratic integers. Multiplication of these lattices by non-principal ideals yields simple…
This tutorial covers a few recent papers in the field of network embedding. Network embedding is a collective term for techniques for mapping graph nodes to vectors of real numbers in a multidimensional space. To be useful, a good embedding…
Accurate spatiotemporal calibration is a prerequisite for multisensor fusion. However, sensors are typically asynchronous, and there is no overlap between the fields of view of cameras and LiDARs, posing challenges for intrinsic and…
Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…
Inspired by recent advances in multimodal learning and machine translation, we introduce an encoder-decoder pipeline that learns (a): a multimodal joint embedding space with images and text and (b): a novel language model for decoding…
Convolutional Neural Networks (CNNs) have been widely applied. But as the CNNs grow, the number of arithmetic operations and memory footprint also increase. Furthermore, typical non-linear activation functions do not allow associativity of…
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
Photonics has unlocked the potential for energy-efficient acceleration of deep learning. Most approaches toward photonic deep learning have diligently reproduced traditional deep learning architectures using photonic platforms, separately…
To address the issue of computational efficiency related to the modelling of blood flow in complex networks, we derive a family of nonlinear lumped-parameter models for blood flow in compliant vessels departing from a well-established…
Lifting is an efficient technique to scale up graphical models generalized to relational domains by exploiting the underlying symmetries. Concurrently, neural models are continuously expanding from grid-like tensor data into structured…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
Tabular data in relational databases represents a significant portion of industrial data. Hence, analyzing and interpreting tabular data is of utmost importance. Application tasks on tabular data are manifold and are often not specified…
Global dynamics of a non-linear Cellular Automata is, in general irregular, asymmetric and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable. In the past efforts have been made to systematize…
The problem of determining nonlinear neutral inclusions in (electrical or thermal)conductivity is considered. Neutral inclusions, inserted in a matrix containing a uniform applied electric field, do not disturb the field outside the…