arXiv Machine Learning
Tensor Cookbook: Mastering Tensors through Diagrams
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arXiv AI
Jun 9
Deep Tree Tensor Networks
arXiv:2502. 09928v2 Announce Type: replace-cross Abstract: Originating in quantum physics, tensor networks (TNs) have been widely adopted as exponential machines and parametric decomposers for recognition tasks.
arXiv AI
Sep 1
Understanding Deep Learning via Notions of Rank
arXiv:2408.02111v4 Announce Type: replace-cross Abstract: Despite the extreme popularity of deep learning in science and industry, its formal understanding is limited. This thesis puts forth notions...
arXiv Machine Learning
Oct 23
Structured Unitary Tensor Network Representations for Circuit-Efficient Quantum Data Encoding
The paper introduces Tensor Network-based Quantum Data Encoding (TNQE), a framework that uses structured unitary tensor network representations to encode classical data into quantum states efficiently. TNQE decomposes each input into tensor cores and compiles them into encoding circuits via two core-to-circuit strategies, with learnable block unitaries ensuring trainability while maintaining unitarity. The method achieves significantly shallower circuits—down to 0.04× the depth of amplitude encoding—and scales to high‑resolution images, demonstrating practical feasibility on real quantum hardware.
arXiv Machine Learning
Sep 4
Parameterised graph theory for tensor networks: entanglement rerouting, structural simplification, and agnostic tomography
The paper applies parameterised graph theory to tensor networks, showing that cutwidth and tree‑cutwidth bound the bond‑dimension overhead needed to represent a tensor‑network state as a matrix product state or tree tensor network. It derives graph‑dependent upper bounds on the sample and computational complexity of tensor‑network tomography, introducing a new graph parameter called learning complexity. Finally, it extends the framework to an agnostic learner that approximates any state with a tensor‑network state of given bond dimension, providing explicit graph‑dependent complexity bounds.
arXiv Machine Learning
Aug 20
Quantum Tensor Network Learning with DMRG
The paper introduces a quantum tensor network learning framework that employs matrix product states (MPS) as a machine‑learning architecture, adding a global normalization condition to interpret the MPS as a quantum state. It compares two optimization strategies—gradient descent and a DMRG‑adapted method—to identify locally optimal tensors and evaluates their effectiveness.
arXiv Machine Learning
Sep 23
Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning
The paper presents a formal analysis of the quotient geometry of tree tensor networks (TTNs) and introduces efficient first- and second-order optimization algorithms that leverage this geometry. It also develops a backpropagation method for training TTNs in a kernel learning context. Numerical experiments on a digit classification task demonstrate a tradeoff between two horizontal distributions: one provides clearer geometric insights, while the other yields more efficient algorithms.