相关论文: Minimax Rates for Learning Pairwise Interactions i…

We study nonparametric regression under covariate shift with structured data, where a small amount of labeled target data is supplemented by a large labeled source dataset. In many real-world settings, the covariates in the target domain…

State-of-the-art transformer models use pairwise dot-product based self-attention, which comes at a computational cost quadratic in the input sequence length. In this paper, we investigate the global structure of attention scores computed…

Attention mechanisms are ubiquitous components in neural architectures applied to natural language processing. In addition to yielding gains in predictive accuracy, attention weights are often claimed to confer interpretability, purportedly…

Attention mechanisms have been extensively employed in various applications, including time series modeling, owing to their capacity to capture intricate dependencies; however, their utility is often constrained by quadratic computational…

We derive minimax adaptive rates for a new, broad class of Tikhonov-regularized learning problems in Hilbert scales under general source conditions. Our analysis does not require the regression function to be contained in the hypothesis…

Policy evaluation in reinforcement learning is often conducted using two-timescale stochastic approximation, which results in various gradient temporal difference methods such as GTD(0), GTD2, and TDC. Here, we provide convergence rate…

Neural networks using transformer-based architectures have recently demonstrated great power and flexibility in modeling sequences of many types. One of the core components of transformer networks is the attention layer, which allows…

We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related…

The linear-in-means model is widely used to study peer influence in social networks. We consider estimation in the linear-in-means model when a randomized treatment is applied to nodes in a network. We show that even when peer effects are…

In the context of statistical supervised learning, the noiseless linear model assumes that there exists a deterministic linear relation $Y = \langle \theta_*, X \rangle$ between the random output $Y$ and the random feature vector $\Phi(U)$,…

We present a theoretical analysis of the performance of transformer with softmax attention in in-context learning with linear regression tasks. While the existing literature predominantly focuses on the convergence of transformers with…

In-context learning is a remarkable property of transformers and has been the focus of recent research. An attention mechanism is a key component in transformers, in which an attention matrix encodes relationships between words in a…

Polythetic classifications, based on shared patterns of features that need neither be universal nor constant among members of a class, are common in the natural world and greatly outnumber monothetic classifications over a set of features.…

The Transformer architecture aggregates input information through the self-attention mechanism, but there is no clear understanding of how this information is mixed across the entire model. Additionally, recent works have demonstrated that…

This paper considers sparse spiked covariance matrix models in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minimax rank detection. The optimal rate of…

In this paper we study minimax and adaptation rates in general isotonic regression. For uniform deterministic and random designs in $[0,1]^d$ with $d\ge 2$ and $N(0,1)$ noise, the minimax rate for the $\ell_2$ risk is known to be bounded…

Consider the standard linear regression model $\y = \Xmat \betastar + w$, where $\y \in \real^\numobs$ is an observation vector, $\Xmat \in \real^{\numobs \times \pdim}$ is a design matrix, $\betastar \in \real^\pdim$ is the unknown…

Aligning Large Language Models (LLMs) and Large Multimodal Models (LMMs) to human preferences is a central challenge in improving the quality of the models' generative outputs for real-world applications. A common approach is to use reward…

We propose a rate equation approach to compute two vertex correlations in scale-free growing network models based in the preferential attachment mechanism. The formalism, based on previous work of Szab\'o \textit{et al.} [Phys. Rev. E…

Dynamical systems across many disciplines are modeled as interacting particles or agents, with interaction rules that depend on a very small number of variables (e.g. pairwise distances, pairwise differences of phases, etc...), functions of…