Pre-Trained Low-Rank Tensor Decomposition for Multi-Dimensional Image Recovery
Read the original on arXiv Computer Vision →The Flow has not summarised this story yet — read it at arXiv Computer Vision.
The Flow has not summarised this story yet — read it at arXiv Computer Vision.
The paper introduces DiffTR, an unsupervised framework that unifies tensor completion, denoising, and hyperspectral super‑resolution using coordinate‑conditioned diffusion. Shared factors indexed by tensor coordinates condition a compact score network, allowing the model to learn both the factors and an implicit tensor representation from observations. The framework separates representation learning from task‑specific observation modeling, enabling reverse diffusion for missing‑value recovery, Tweedie‑based denoising, and measurement‑guided sampling for high‑resolution reconstruction, all while supporting multiple tensor modalities and corruption models.
The paper introduces a new semi‑tensor product for third‑order tensors that relaxes the dimensional constraints of the standard t‑product while preserving the closed‑form nature of T‑SVD. It builds a multi‑term semi‑tensor product singular value decomposition (MSTP‑SVD) that improves low‑rank approximation accuracy, and further accelerates it with randomized projection and power iteration to create the MRSTP‑SVD algorithm. Experiments on image and video compression and completion show that this method balances reconstruction accuracy and computational efficiency.
arXiv:2606. 25975v1 Announce Type: new Abstract: Common first-order optimizers, such as Adam, implicitly treat each parameter block as an unstructured vector, which disregards the multilinear weight structure present in many modern machine learning models.
Common first-order optimizers, such as Adam, implicitly treat each parameter block as an unstructured vector, which disregards the multilinear weight structure present in many modern machine learning models. Recent work has shown that exploiting matrix structure can improve optimization dynamics.
The paper proposes that super‑resolution should be performed in a latent space that is close to the manifold of high‑resolution images, rather than in reconstruction‑oriented or pixel spaces. By using the latent space of 23 fused layers of a frozen DINOv3‑L model, degraded images are embedded near this manifold, enabling a 415M decoder (RAESR) to map them back and decode to pixels in a single pass. RAESR achieves the best fidelity–perception trade‑off on several benchmarks while running at 37 ms per 512×512 image on a single H20 GPU, outperforming models that use a VAE latent substrate.
This survey reviews tensor methods applied to large language models, framing them through a seven‑stage lifecycle (tokenization, embeddings, pre‑training, adaptation, compression, inference, interpretability) and a component view (embeddings, attention, feed‑forward networks). It offers unified notation, theoretical foundations, and comparative analyses of tensorization strategies for Transformer components, while highlighting evaluation protocol differences and model scale effects. The paper also introduces a new metric, ρ_gap, to quantify the gap between theoretical memory savings and actual system‑level speedup, and connects tensor techniques to related efficiency and probabilistic methods.