Search Results for author: Spencer Frei

Found 9 papers, 1 papers with code

Random Feature Amplification: Feature Learning and Generalization in Neural Networks

no code implementations15 Feb 2022 Spencer Frei, Niladri S. Chatterji, Peter L. Bartlett

We consider data with binary labels that are generated by an XOR-like function of the input features.

Benign Overfitting without Linearity: Neural Network Classifiers Trained by Gradient Descent for Noisy Linear Data

no code implementations11 Feb 2022 Spencer Frei, Niladri S. Chatterji, Peter L. Bartlett

Benign overfitting, the phenomenon where interpolating models generalize well in the presence of noisy data, was first observed in neural network models trained with gradient descent.

Proxy Convexity: A Unified Framework for the Analysis of Neural Networks Trained by Gradient Descent

no code implementations NeurIPS 2021 Spencer Frei, Quanquan Gu

We further show that many existing guarantees for neural networks trained by gradient descent can be unified through proxy convexity and proxy PL inequalities.

Self-training Converts Weak Learners to Strong Learners in Mixture Models

no code implementations25 Jun 2021 Spencer Frei, Difan Zou, Zixiang Chen, Quanquan Gu

We show that there exists a universal constant $C_{\mathrm{err}}>0$ such that if a pseudolabeler $\boldsymbol{\beta}_{\mathrm{pl}}$ can achieve classification error at most $C_{\mathrm{err}}$, then for any $\varepsilon>0$, an iterative self-training algorithm initialized at $\boldsymbol{\beta}_0 := \boldsymbol{\beta}_{\mathrm{pl}}$ using pseudolabels $\hat y = \mathrm{sgn}(\langle \boldsymbol{\beta}_t, \mathbf{x}\rangle)$ and using at most $\tilde O(d/\varepsilon^2)$ unlabeled examples suffices to learn the Bayes-optimal classifier up to $\varepsilon$ error, where $d$ is the ambient dimension.

Provable Robustness of Adversarial Training for Learning Halfspaces with Noise

no code implementations19 Apr 2021 Difan Zou, Spencer Frei, Quanquan Gu

To the best of our knowledge, this is the first work to show that adversarial training provably yields robust classifiers in the presence of noise.

Classification General Classification +1

Provable Generalization of SGD-trained Neural Networks of Any Width in the Presence of Adversarial Label Noise

1 code implementation4 Jan 2021 Spencer Frei, Yuan Cao, Quanquan Gu

We consider a one-hidden-layer leaky ReLU network of arbitrary width trained by stochastic gradient descent (SGD) following an arbitrary initialization.

Agnostic Learning of Halfspaces with Gradient Descent via Soft Margins

no code implementations1 Oct 2020 Spencer Frei, Yuan Cao, Quanquan Gu

We analyze the properties of gradient descent on convex surrogates for the zero-one loss for the agnostic learning of linear halfspaces.

General Classification

Agnostic Learning of a Single Neuron with Gradient Descent

no code implementations NeurIPS 2020 Spencer Frei, Yuan Cao, Quanquan Gu

In the agnostic PAC learning setting, where no assumption on the relationship between the labels $y$ and the input $x$ is made, if the optimal population risk is $\mathsf{OPT}$, we show that gradient descent achieves population risk $O(\mathsf{OPT})+\epsilon$ in polynomial time and sample complexity when $\sigma$ is strictly increasing.

PAC learning

Algorithm-Dependent Generalization Bounds for Overparameterized Deep Residual Networks

no code implementations NeurIPS 2019 Spencer Frei, Yuan Cao, Quanquan Gu

The skip-connections used in residual networks have become a standard architecture choice in deep learning due to the increased training stability and generalization performance with this architecture, although there has been limited theoretical understanding for this improvement.

Generalization Bounds

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