Related papers: Simple yet Effective: Low-Rank Spatial Attention f…

In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of…

Neural operators have emerged as promising frameworks for learning mappings governed by partial differential equations (PDEs), serving as data-driven alternatives to traditional numerical methods. While methods such as the Fourier neural…

Neural operators effectively solve PDE problems from data without knowing the explicit equations, which learn the map from the input sequences of observed samples to the predicted values. Most existing works build the model in the original…

The low displacement rank (LDR) framework for structured matrices represents a matrix through two displacement operators and a low-rank residual. Existing use of LDR matrices in deep learning has applied fixed displacement operators…

Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To…

Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis. Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions. From a probabilistic perspective, these…

Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…

Weighted low rank approximation (WLRA) is an important yet computationally challenging primitive with applications ranging from statistical analysis, model compression, and signal processing. To cope with the NP-hardness of this problem,…

Sparse attention reduces the quadratic complexity of full self-attention but faces two challenges: (1) an attention gap, where applying sparse attention to full-attention-trained models causes performance degradation due to train-inference…

Block-wise sparse attention offers significant efficiency gains for long-context modeling, yet existing methods often suffer from low selection fidelity and cumulative contextual loss by completely discarding unselected blocks. To address…

Multi-label image recognition is a challenging computer vision task of practical use. Progresses in this area, however, are often characterized by complicated methods, heavy computations, and lack of intuitive explanations. To effectively…

Despite large neural networks demonstrating remarkable abilities to complete different tasks, they require excessive memory usage to store the optimization states for training. To alleviate this, the low-rank adaptation (LoRA) is proposed…

Factors that limit the size of the input and output of a neural network include memory requirements for the network states/activations to compute gradients, as well as memory for the convolutional kernels or other weights. The memory…

Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use the Generalized Multiscale Finite Element Method (GMsFEM) that…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

Spatial Pyramid Matching (SPM) and its variants have achieved a lot of success in image classification. The main difference among them is their encoding schemes. For example, ScSPM incorporates Sparse Code (SC) instead of Vector…

The scalability of deep learning models is fundamentally limited by computing resources, memory, and communication. Although methods like low-rank adaptation (LoRA) have reduced the cost of model finetuning, its application in model…

Low-Rank Representation (LRR) highly suffers from discarding the locality information of data points in subspace clustering, as it may not incorporate the data structure nonlinearity and the non-uniform distribution of observations over the…

Low-Rank Representation (LRR) is arguably one of the most powerful paradigms for Multi-view spectral clustering, which elegantly encodes the multi-view local graph/manifold structures into an intrinsic low-rank self-expressive data…

Long-form speech recognition is an application area of increasing research focus. ASR models based on multi-head attention (MHA) are ill-suited to long-form ASR because of their quadratic complexity in sequence length. We build on recent…