Related papers: Tensor formalism for predicting synaptic connectio…
A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…
Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…
Teaming is the process of establishing connections among agents within a system to enable collaboration toward achieving a collective goal. This paper examines teaming in the context of a network of agents learning to coordinate with…
Scientific problems require resolving multi-scale phenomena across different resolutions and learning solution operators in infinite-dimensional function spaces. Neural operators provide a powerful framework for this, using…
Neural symbolic processing aims to combine the generalization of logical learning approaches and the performance of neural networks. The Neural Theorem Proving (NTP) model by Rocktaschel et al (2017) learns embeddings for concepts and…
Training neural networks means solving a high-dimensional optimization problem. Normally the goal is to minimize a loss function that depends on what is called the network function, or in other words the function that gives the network…
Network alignment has extensive applications in comparative interactomics. Traditional approaches aim to simultaneously maximize the number of conserved edges and the underlying similarity of aligned entities. We propose a novel formulation…
Elasticities in depth, width, kernel size and resolution have been explored in compressing deep neural networks (DNNs). Recognizing that the kernels in a convolutional neural network (CNN) are 4-way tensors, we further exploit a new…
Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…
Tensor networks are a tool first employed in the context of many-body quantum physics that now have a wide range of uses across the computational sciences, from numerical methods to machine learning. Methods integrating tensor networks into…
In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…
In this paper, we introduce a tensor neural network based machine learning method for solving the elliptic partial differential equations with random coefficients in a bounded physical domain. With the help of tensor product structure, we…
Classical shortest-path methods rely on binary tropical semirings $(\min,+)$, whose dyadic structure limits them to pairwise cost interactions. However, many real-world systems, including logistics, supply chains, communication networks,…
We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…
We develop both first and second order numerical optimization methods to solve non-smooth optimization problems featuring a shared sparsity penalty, constrained by differential equations with uncertainty. To alleviate the curse of…
Why do neurons encode information the way they do? Normative answers to this question model neural activity as the solution to an optimisation problem; for example, the celebrated efficient coding hypothesis frames neural activity as the…
A method of simultaneously optimizing both the structure of neural networks and the connection weights in a single training loop can reduce the enormous computational cost of neural architecture search. We focus on the probabilistic…
Modeling the behavior of coupled networks is challenging due to their intricate dynamics. For example in neuroscience, it is of critical importance to understand the relationship between the functional neural processes and anatomical…
Automated model selection is often proposed to users to choose which machine learning model (or method) to apply to a given regression task. In this paper, we show that combining different regression models can yield better results than…
Efficient probabilistic inference by variable elimination in graphical models requires an optimal elimination order. However, finding an optimal order is a challenging combinatorial optimisation problem for models with a large number of…