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Least squares method is one of the simplest and most popular techniques applied in data fitting, imaging processing and high dimension data analysis. The classic methods like QR and SVD decomposition for solving least squares problems has a…

Pretraining plays a pivotal role in acquiring generalized knowledge from large-scale data, achieving remarkable successes as evidenced by large models in CV and NLP. However, progress in the graph domain remains limited due to fundamental…

Universal graph pre-training has emerged as a key paradigm in graph representation learning, offering a promising way to train encoders to learn transferable representations from unlabeled graphs and to effectively generalize across a wide…

In this work, we are interested in adaptive and distributed estimation of graph filters from streaming data. We formulate this problem as a consensus estimation problem over graphs, which can be addressed with diffusion LMS strategies. Most…

Properties of Superiorized Preconditioned Conjugate Gradient (SupPCG) algorithms in image reconstruction from projections are examined. Least squares (LS) is usually chosen for measuring data-inconsistency in these inverse problems.…

This paper presents estimates of the convergence rate and complexity of an algebraic multilevel preconditioner based on piecewise constant coarse vector spaces applied to the graph Laplacian. A bound is derived on the energy norm of the…

Several recent works demonstrate that transformers can implement algorithms like gradient descent. By a careful construction of weights, these works show that multiple layers of transformers are expressive enough to simulate iterations of…

Neural preconditioners for real-time physics simulation offer promising data-driven priors, but they often fail to capture long-range couplings efficiently because they inherit local message passing or sparse-operator access patterns. We…

Layer-wise preconditioning methods are a family of memory-efficient optimization algorithms that introduce preconditioners per axis of each layer's weight tensors. These methods have seen a recent resurgence, demonstrating impressive…

Language model (LM) pre-training has resulted in impressive performance and sample efficiency on a variety of language understanding tasks. However, it remains unclear how to best use pre-trained LMs for generation tasks such as abstractive…

We consider effective preconditioners for solving Laplacians of general weighted graphs. Theoretically, spectral sparsifiers (SSs) provide preconditioners of optimal computational complexity. However, they are not easy to use for real-world…

We show theoretically and empirically that the linear Transformer, when applied to graph data, can implement algorithms that solve canonical problems such as electric flow and eigenvector decomposition. The Transformer has access to…

Medical image segmentation remains challenging in low-data regimes, where scarce annotations often yield poor generalization and ambiguous boundaries with missing fine structures. Recent self-supervised pretraining has improved…

Given the prevalence of JPEG compressed images, optimizing image reconstruction from the compressed format remains an important problem. Instead of simply reconstructing a pixel block from the centers of indexed DCT coefficient quantization…

We show that preconditioners constructed by random sampling can perform well without meeting the standard requirements of iterative methods. When applied to graph Laplacians, this leads to ultra-sparsifiers that in expectation behave as the…

Deep-learning (DL)-based precoding in multi-user multiple-input single-output (MU-MISO) systems involves training DL models to map features derived from channel coefficients to labels derived from precoding weights. Traditionally,…

Large linear systems are ubiquitous in modern computational science and engineering. The main recipe for solving them is the use of Krylov subspace iterative methods with well-designed preconditioners. Recently, GNNs have been shown to be a…

We investigate a scalable $M$-channel critically sampled filter bank for graph signals, where each of the $M$ filters is supported on a different subband of the graph Laplacian spectrum. For analysis, the graph signal is filtered on each…

Data dependent regularization is known to benefit a wide variety of problems in machine learning. Often, these regularizers cannot be easily decomposed into a sum over a finite number of terms, e.g., a sum over individual example-wise…

Transformers have achieved great success in several domains, including Natural Language Processing and Computer Vision. However, its application to real-world graphs is less explored, mainly due to its high computation cost and its poor…