相关论文: FAVOR#: Sharp Attention Kernel Approximations via …

Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend…

Transformers are a class of autoregressive deep learning architectures which have recently achieved state-of-the-art performance in various vision, language, and robotics tasks. We revisit the problem of Kalman Filtering in linear dynamical…

This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…

While the Transformer architecture has achieved remarkable success across various domains, a thorough theoretical foundation explaining its optimization dynamics is yet to be fully developed. In this study, we aim to bridge this…

Feature selection is the problem of selecting a subset of features for a machine learning model that maximizes model quality subject to a budget constraint. For neural networks, prior methods, including those based on $\ell_1$…

Transformers have achieved remarkable performance in a myriad of fields including natural language processing and computer vision. However, when it comes to the graph mining area, where graph neural network (GNN) has been the dominant…

Randomized algorithms exploit stochasticity to reduce computational complexity. One important example is random feature regression (RFR) that accelerates Gaussian process regression (GPR). RFR approximates an unknown function with a random…

Robust parameter estimation is a crucial task in several 3D computer vision pipelines such as Structure from Motion (SfM). State-of-the-art algorithms for robust estimation, however, still suffer from difficulties in converging to…

Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…

We present a simple and intuitive Focus-and-eXpand (\fax) method to guide the training process of a neural network towards a specific solution. Optimizing a neural network is a highly non-convex problem. Typically, the space of solutions is…

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…

Self-attention networks have shown remarkable progress in computer vision tasks such as image classification. The main benefit of the self-attention mechanism is the ability to capture long-range feature interactions in attention-maps.…

Compared with voxel-based grid prediction, in the field of 3D semantic occupation prediction for autonomous driving, GaussianFormer proposed using 3D Gaussian to describe scenes with sparse 3D semantic Gaussian based on objects is another…

Factorization machines (FM) are a popular model class to learn pairwise interactions by a low-rank approximation. Different from existing FM-based approaches which use a fixed rank for all features, this paper proposes a Rank-Aware FM…

In the context of Gaussian conditioning, greedy algorithms iteratively select the most informative measurements, given an observed Gaussian random variable. However, the convergence analysis for conditioning Gaussian random variables…

Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…

Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the…

We show how the notion of message passing can be used to streamline the algebra and computer coding for fast approximate inference in large Bayesian semiparametric regression models. In particular, this approach is amenable to handling…

We show the formal equivalence of linearised self-attention mechanisms and fast weight controllers from the early '90s, where a ``slow" neural net learns by gradient descent to program the ``fast weights" of another net through sequences of…

We provide guarantees for approximate Gaussian Process (GP) regression resulting from two common low-rank kernel approximations: based on random Fourier features, and based on truncating the kernel's Mercer expansion. In particular, we…