https://arxiv.org/pdf/1701.04831v1.pdf On the Equivalence of Restricted Boltzmann Machines and Tensor Network States

Quantum Clustering and Gaussian Mixtures

The quest for a Quantum Neural Network Edit descriptiondl.acm.org

https://arxiv.org/pdf/1701.04831v1.pdf https://arxiv.org/abs/1408.7005 https://arxiv.org/pdf/1612.05695v2.pdf

https://arxiv.org/abs/1708.02918v1 The Tensor Memory Hypothesis

We discuss memory models which are based on tensor decompositions using latent representations of entities and events. We show how episodic memory and semantic memory can be realized and discuss how new memory traces can be generated from sensory input: Existing memories are the basis for perception and new memories are generated via perception. We relate our mathematical approach to the hippocampal memory indexing theory. We describe the first mathematical memory models that are truly declarative by generating explicit semantic triples describing both memory content and sensory inputs. Our main hypothesis is that perception includes an active semantic decoding process, which relies on latent representations of entities and predicates, and that episodic and semantic memories depend on the same decoding process.

https://arxiv.org/abs/1707.08308 Tensor Regression Networks

To date, most convolutional neural network architectures output predictions by flattening 3rd-order activation tensors, and applying fully-connected output layers. This approach has two drawbacks: (i) we lose rich, multi-modal structure during the flattening process and (ii) fully-connected layers require many parameters. We present the first attempt to circumvent these issues by expressing the output of a neural network directly as the the result of a multi-linear mapping from an activation tensor to the output. By imposing low-rank constraints on the regression tensor, we can efficiently solve problems for which existing solutions are badly parametrized. Our proposed tensor regression layer replaces flattening operations and fully-connected layers by leveraging multi-modal structure in the data and expressing the regression weights via a low rank tensor decomposition. Additionally, we combine tensor regression with tensor contraction to further increase efficiency. Augmenting the VGG and ResNet architectures, we demonstrate large reductions in the number of parameters with negligible impact on performance on the ImageNet dataset.

https://arxiv.org/pdf/1710.10248v2.pdf TENSOR NETWORK LANGUAGE MODEL

https://arxiv.org/abs/1802.08235v1 Vector Field Based Neural Networks

A novel Neural Network architecture is proposed using the mathematically and physically rich idea of vector fields as hidden layers to perform nonlinear transformations in the data. The data points are interpreted as particles moving along a flow defined by the vector field which intuitively represents the desired movement to enable classification. The architecture moves the data points from their original configuration to anew one following the streamlines of the vector field with the objective of achieving a final configuration where classes are separable. An optimization problem is solved through gradient descent to learn this vector field.