Related papers: Data Complexity Estimates for Operator Learning

Neural operators (NOs) employ deep neural networks to learn mappings between infinite-dimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex…

Machine learning models have demonstrated substantial performance enhancements over non-learned alternatives in various fundamental data management operations, including indexing (locating items in an array), cardinality estimation…

As deep learning models are becoming larger and data-hungrier, there are growing ethical, legal and technical concerns over use of data: in practice, agreements on data use may change over time, rendering previously-used training data…

We present approximation theories and efficient training methods for derivative-informed Fourier neural operators (DIFNOs) with applications to PDE-constrained optimization. A DIFNO is an FNO trained by minimizing its prediction error…

An important question in data-driven control is how to obtain an informative dataset. In this work, we consider the problem of effective data acquisition of an unknown linear system with bounded disturbance for both open-loop and…

This dissertation considers Open-world Robot Manipulation, a manipulation problem where a robot must generalize or quickly adapt to new objects, scenes, or tasks for which it has not been pre-programmed or pre-trained. This dissertation…

Deep Neural Networks (DNNs) often rely on very large datasets for training. Given the large size of such datasets, it is conceivable that they contain certain samples that either do not contribute or negatively impact the DNN's…

The accuracy of deep learning, i.e., deep neural networks, can be characterized by dividing the total error into three main types: approximation error, optimization error, and generalization error. Whereas there are some satisfactory…

At its core, machine learning seeks to train models that reliably generalize beyond noisy observations; however, the theoretical vacuum in which state-of-the-art universal approximation theorems (UATs) operate isolates them from this goal,…

The problem of learning threshold functions is a fundamental one in machine learning. Classical learning theory implies sample complexity of $O(\xi^{-1} \log(1/\beta))$ (for generalization error $\xi$ with confidence $1-\beta$). The private…

Integrating machine learning into the internals of database management systems requires significant feature engineering, a human effort-intensive process to determine the best way to represent the pieces of information that are relevant to…

We consider the sample complexity of learning with adversarial robustness. Most prior theoretical results for this problem have considered a setting where different classes in the data are close together or overlapping. Motivated by some…

Let $\mathscr{F}_{n,d}$ be the class of all functions $f:\{-1,1\}^n\to[-1,1]$ on the $n$-dimensional discrete hypercube of degree at most $d$. In the first part of this paper, we prove that any (deterministic or randomized) algorithm which…

In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…

Deep learning's success has been attributed to the training of large, overparameterized models on massive amounts of data. As this trend continues, model training has become prohibitively costly, requiring access to powerful computing…

We define a measure for the complexity of Boolean functions related to their implementation in neural networks, and in particular close related to the generalization ability that could be obtained through the learning process. The measure…

Given a small training data set and a learning algorithm, how much more data is necessary to reach a target validation or test performance? This question is of critical importance in applications such as autonomous driving or medical…

Neural networks have emerged as effective tools for solving ill-posed inverse problems. In many scientific applications, however, observational training data are insufficient, and learned inverse operators must instead be trained on…

An overarching goal in machine learning is to build a generalizable model with few samples. To this end, overparameterization has been the subject of immense interest to explain the generalization ability of deep nets even when the size of…

Recognizing symmetries in data allows for significant boosts in neural network training, which is especially important where training data are limited. In many cases, however, the exact underlying symmetry is present only in an idealized…