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Vector-symbolic architectures (VSAs) provide methods for computing which are highly flexible and carry unique advantages. Concepts in VSAs are represented by 'symbols,' long vectors of values which utilize properties of high-dimensional…

Traditional artificial neural networks consist of nodes with non-oscillatory dynamics. Biological neural networks, on the other hand, consist of oscillatory components embedded in an oscillatory environment. Motivated by this feature of…

Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…

Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators. Inspired by the ability of these systems to express a rich set of outputs while keeping (gradients of) state…

We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the…

In neural circuits, recurrent connectivity plays a crucial role in network function and stability. However, existing recurrent spiking neural networks (RSNNs) are often constructed by random connections without optimization. While RSNNs can…

We propose a new type of neural networks, Kronecker neural networks (KNNs), that form a general framework for neural networks with adaptive activation functions. KNNs employ the Kronecker product, which provides an efficient way of…

Deep convolutional neural networks demonstrate impressive results in the super-resolution domain. A series of studies concentrate on improving peak signal noise ratio (PSNR) by using much deeper layers, which are not friendly to constrained…

Existing information retrieval systems are largely constrained by their reliance on vector inner products to assess query-document relevance, which naturally limits the expressiveness of the relevance score they can produce. We propose a…

There remains an important need for the development of image reconstruction methods that can produce diagnostically useful images from undersampled measurements. In magnetic resonance imaging (MRI), for example, such methods can facilitate…

Low-rank tensor compression has been proposed as a promising approach to reduce the memory and compute requirements of neural networks for their deployment on edge devices. Tensor compression reduces the number of parameters required to…

To accommodate structured approaches of neural computation, we propose a class of recurrent neural networks for indexing and storing sequences of symbols or analog data vectors. These networks with randomized input weights and orthogonal…

We introduce Residue Hyperdimensional Computing, a computing framework that unifies residue number systems with an algebra defined over random, high-dimensional vectors. We show how residue numbers can be represented as high-dimensional…

This paper presents an exact and explicit tensor-network equation for the search of nontrivial divisors of a composite integer, together with an algorithm for its computation. The proposed method is based on the MeLoCoToN approach, which…

We introduce SCORES, a recursive neural network for shape composition. Our network takes as input sets of parts from two or more source 3D shapes and a rough initial placement of the parts. It outputs an optimized part structure for the…

Recurrent neural networks can learn complex transduction problems that require maintaining and actively exploiting a memory of their inputs. Such models traditionally consider memory and input-output functionalities indissolubly entangled.…

Differential network is an important tool to capture the changes of conditional correlations under two sample cases. In this paper, we introduce a fast iterative algorithm to recover the differential network for high-dimensional data. The…

Despite achieving state-of-the-art performance, deep learning methods generally require a large amount of labeled data during training and may suffer from overfitting when the sample size is small. To ensure good generalizability of deep…

Ability of deep networks to extract high level features and of recurrent networks to perform time-series inference have been studied. In view of universality of one hidden layer network at approximating functions under weak constraints, the…

Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…