Machine unlearning is the process of updating machine learning models to remove the information of specific training data samples, in order to comply with data protection regulations that allow individuals to request the removal of their personal data. Despite the recent development of numerous unlearning algorithms, reliable evaluation of these algorithms remains an open research question. In this work, we focus on membership inference attack (MIA) based evaluation, one of the most common approaches for evaluating unlearning algorithms, and address various pitfalls of existing evaluation metrics that lack reliability. Specifically, we propose a game-theoretic framework that formalizes the evaluation process as a game between unlearning algorithms and MIA adversaries, measuring the data removal efficacy of unlearning algorithms by the capability of the MIA adversaries. Through careful design of the game, we demonstrate that the natural evaluation metric induced from the game enjoys provable guarantees that the existing evaluation metrics fail to satisfy. Furthermore, we propose a practical and efficient algorithm to estimate the evaluation metric induced from the game, and demonstrate its effectiveness through both theoretical analysis and empirical experiments. This work presents a novel and reliable approach to empirically evaluating unlearning algorithms, paving the way for the development of more effective unlearning techniques.

The rapid growth of machine learning has spurred legislative initiatives such as ``the Right to be Forgotten,'' allowing users to request data removal. In response, ``machine unlearning'' proposes the selective removal of unwanted data without the need for retraining from scratch. While the Neural-Tangent-Kernel-based (NTK-based) unlearning method excels in performance, it suffers from significant computational complexity, especially for large-scale models and datasets. Our work introduces ``Fast-NTK,'' a novel NTK-based unlearning algorithm that significantly reduces the computational complexity by incorporating parameter-efficient fine-tuning methods, such as fine-tuning batch normalization layers in a CNN or visual prompts in a vision transformer. Our experimental results demonstrate scalability to much larger neural networks and datasets (e.g., 88M parameters; 5k images), surpassing the limitations of previous full-model NTK-based approaches designed for smaller cases (e.g., 8M parameters; 500 images). Notably, our approach maintains a performance comparable to the traditional method of retraining on the retain set alone. Fast-NTK can thus enable for practical and scalable NTK-based unlearning in deep neural networks.

Singularities are ubiquitous in the parameter space of hierarchical models such as multilayer perceptrons. At singularities, the Fisher information matrix degenerates, and the Cramer-Rao paradigm does no more hold, implying that the classical model selection theory such as AIC and MDL cannot be applied. It is important to study the relation between the generalization error and the training error at singularities. The present paper demonstrates a method of analyzing these errors both for the maximum likelihood estimator and the Bayesian predictive distribution in terms of Gaussian random fields, by using simple models. 1 Introduction A neural network is specified by a number of parameters which are synaptic weights and biases. Learning takes place by modifying these parameters from observed input-output examples.

Singularities are ubiquitous in the parameter space of hierarchical models such as multilayer perceptrons. At singularities, the Fisher information matrix degenerates, and the Cramer-Rao paradigm does no more hold, implying that the classical model selection theory such as AIC and MDL cannot be applied. It is important to study the relation between the generalization error and the training error at singularities. The present paper demonstrates a method of analyzing these errors both for the maximum likelihood estimator and the Bayesian predictive distribution in terms of Gaussian random fields, by using simple models. 1 Introduction A neural network is specified by a number of parameters which are synaptic weights and biases. Learning takes place by modifying these parameters from observed input-output examples.

Singularities are ubiquitous in the parameter space of hierarchical models such as multilayer perceptrons. At singularities, the Fisher information matrix degenerates, and the Cramer-Rao paradigm does no more hold, implying that the classical model selection theory suchas AIC and MDL cannot be applied. It is important to study the relation between the generalization error and the training error at singularities. The present paper demonstrates a method of analyzing these errors both for the maximum likelihood estimator andthe Bayesian predictive distribution in terms of Gaussian random fields, by using simple models. 1 Introduction A neural network is specified by a number of parameters which are synaptic weights and biases. Learning takes place by modifying these parameters from observed input-output examples.

The method of Structural Risk Minimization refers to tuning the capacity of the classifier to the available amount of training data.

The method of Structural Risk Minimization refers to tuning the capacity of the classifier to the available amount of training data. This capacity is influenced by several factors, including: (1) properties of the input space, (2) nature and structure of the classifier, and (3) learning algorithm. Actions based on these three factors are combined here to control the capacity of linear classifiers and improve generalization on the problem of handwritten digit recognition.

The method of Structural Risk Minimization refers to tuning the capacity of the classifier to the available amount of training data. This capacity is influenced by several factors, including: (1) properties of the input space, (2) nature and structure of the classifier, and (3) learning algorithm. Actions based on these three factors are combined here to control the capacity of linear classifiers and improve generalization on the problem of handwritten digit recognition.