AVITECH Seminar: Nguyen Thi Ngoc Lan (VNU-UET, Tensor Group)

Tensor decompositions have become a standard tool across many fields over recent years, with signal processing and machine learning among the most active. As the dimensionality of modern datasets keeps growing, finding compact yet expressive representations for higher-order tensors has turned into a pressing need. This talk introduces a new tensor network, the Triangular Network (TriNet), which aims at a favourable balance between representation power and computational cost in higher-order tensor decomposition and completion.

The talk will describe how TriNet organises tensor contractions so that the resulting network is built entirely from third-order factors. Adjacent factors are linked locally: every three neighbouring cores are tied together through a relay factor, which gives rise to localised subnetworks inside the overall architecture. The outcome is a lightweight model that stays computationally tractable on higher-order tensor data and scales more gracefully than existing tensor network designs.

Convergence guarantees will also be discussed, established under the alternating direction method of multipliers as well as the proximal alternating minimisation framework. The talk closes with experimental results comparing TriNet against state-of-the-art tensor decomposition methods.