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Transformer-based self-supervised models are trained as feature extractors and have empowered many downstream speech tasks to achieve state-of-the-art performance. However, both the training and inference process of these models may…

Transformers achieve state-of-the-art performance for natural language processing tasks by pre-training on large-scale text corpora. They are extremely compute-intensive and have very high sample complexity. Memory replay is a mechanism…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…

The transformer has been shown to outperform recurrent neural network-based sequence-to-sequence models in various word-level NLP tasks. Yet for character-level transduction tasks, e.g. morphological inflection generation and historical…

There have been significant advancements made by large language models (LLMs) in various aspects of our daily lives. LLMs serve as a transformative force in natural language processing, finding applications in text generation, translation,…

Language models typically need to be trained or finetuned in order to acquire new knowledge, which involves updating their weights. We instead envision language models that can simply read and memorize new data at inference time, thus…

The Transformer translation model employs residual connection and layer normalization to ease the optimization difficulties caused by its multi-layer encoder/decoder structure. Previous research shows that even with residual connection and…

In this work we propose for the first time a transformer-based framework for unsupervised representation learning of multivariate time series. Pre-trained models can be potentially used for downstream tasks such as regression and…

Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…

This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and non-convex objective functions;…

We are concerned with the computation of the ${\mathcal L}_\infty$-norm for an ${\mathcal L}_\infty$-function of the form $H(s) = C(s) D(s)^{-1} B(s)$, where the middle factor is the inverse of a meromorphic matrix-valued function, and…

We describe an efficient hierarchical method to compute attention in the Transformer architecture. The proposed attention mechanism exploits a matrix structure similar to the Hierarchical Matrix (H-Matrix) developed by the numerical…

There is an ongoing debate on whether neural networks can grasp the quasi-regularities in languages like humans. In a typical quasi-regularity task, English past tense inflections, the neural network model has long been criticized that it…

This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or…

We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in $L^2([0,1))$ our…

Despite the widespread success of Transformers on NLP tasks, recent works have found that they struggle to model several formal languages when compared to recurrent models. This raises the question of why Transformers perform well in…

We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-H\"older smooth functions…

Transformer models cannot easily scale to long sequences due to their O(N^2) time and space complexity. This has led to Transformer variants seeking to lower computational complexity, such as Longformer and Performer. While such models have…

Transformers (Vaswani et al., 2017) have brought a remarkable improvement in the performance of neural machine translation (NMT) systems but they could be surprisingly vulnerable to noise. In this work, we try to investigate how noise…