Thus, one important question one can ask here is how welldFnn(ˆµn,ˆνm)approximatesdFnn(µ,ν).

An important class of distance metrics proposed for training generative adversarial networks (GANs) is the integral probability metric (IPM), in which the neural net distance captures the practical GAN training via two neural networks. This paper investigates the minimax estimation problem of the neural net distance based on samples drawn from the distributions. We develop the first known minimax lower bound on the estimation error of the neural net distance, and an upper bound tighter than an existing bound on the estimator error for the empirical neural net distance. Our lower and upper bounds match not only in the order of the sample size but also in terms of the norm of the parameter matrices of neural networks, which justifies the empirical neural net distance as a good approximation of the true neural net distance for training GANs in practice.

Section 2.2 for the precise formulation) and to address issue (b) by developing a tighter upper bound

As language models (LMs) approach human-level performance, a comprehensive understanding of their behavior becomes crucial. This includes evaluating capabilities, biases, task performance, and alignment with societal values. Extensive initial evaluations, including red teaming and diverse benchmarking, can establish a model's behavioral profile. However, subsequent fine-tuning or deployment modifications may alter these behaviors in unintended ways. We present a method for continual Behavioral Shift Auditing (BSA) in LMs. Our test compares model generations from a baseline model to those of the model under scrutiny and provides theoretical guarantees for change detection while controlling false positives. The test features a configurable tolerance parameter that adjusts sensitivity to behavioral changes for different use cases. We evaluate our approach using two case studies: monitoring changes in (a) toxicity and (b) translation performance. We find that the test is able to detect meaningful changes in behavior distributions using just hundreds of examples. Language models (LMs) can now achieve human-level performance in a wide range of tasks, including text summarization, machine translation, coding and even acting as AI scientists: generating hypotheses and designing experiments (Achiam et al., 2023; Katz et al., 2024; Lu et al., 2024; Zhang et al., 2024). Because of this, many sectors are looking for ways to use them to improve existing systems (Kasneci et al., 2023; Felten et al., 2023).

This paper considers the minimax estimation problem of neural net distance. The problem originates from the generative adversarial networks (GANs). In particular, the paper established the lower bound on the minimax estimation for neural net distance which seems to the first result of this kind. The authors then derived an upper bound on the estimation error which matches the minimax lower bound in terms of the order of sample size, and the norm of the parameter matrices. However, there is a gap of \sqrt{d} or \sqrt{d h} which remains as an open question.

An important class of distance metrics proposed for training generative adversarial networks (GANs) is the integral probability metric (IPM), in which the neural net distance captures the practical GAN training via two neural networks. This paper investigates the minimax estimation problem of the neural net distance based on samples drawn from the distributions. We develop the first known minimax lower bound on the estimation error of the neural net distance, and an upper bound tighter than an existing bound on the estimator error for the empirical neural net distance. Our lower and upper bounds match not only in the order of the sample size but also in terms of the norm of the parameter matrices of neural networks, which justifies the empirical neural net distance as a good approximation of the true neural net distance for training GANs in practice. Papers published at the Neural Information Processing Systems Conference.

An important class of distance metrics proposed for training generative adversarial networks (GANs) is the integral probability metric (IPM), in which the neural net distance captures the practical GAN training via two neural networks. This paper investigates the minimax estimation problem of the neural net distance based on samples drawn from the distributions. We develop the first known minimax lower bound on the estimation error of the neural net distance, and an upper bound tighter than an existing bound on the estimator error for the empirical neural net distance. Our lower and upper bounds match not only in the order of the sample size but also in terms of the norm of the parameter matrices of neural networks, which justifies the empirical neural net distance as a good approximation of the true neural net distance for training GANs in practice.

An important class of distance metrics proposed for training generative adversarial networks (GANs) is the integral probability metric (IPM), in which the neural net distance captures the practical GAN training via two neural networks. This paper investigates the minimax estimation problem of the neural net distance based on samples drawn from the distributions. We develop the first known minimax lower bound on the estimation error of the neural net distance, and an upper bound tighter than an existing bound on the estimator error for the empirical neural net distance. Our lower and upper bounds match not only in the order of the sample size but also in terms of the norm of the parameter matrices of neural networks, which justifies the empirical neural net distance as a good approximation of the true neural net distance for training GANs in practice.

An important class of distance metrics proposed for training generative adversarial networks (GANs) is the integral probability metric (IPM), in which the neural net distance captures the practical GAN training via two neural networks. This paper investigates the minimax estimation problem of the neural net distance based on samples drawn from the distributions. We develop the first known minimax lower bound on the estimation error of the neural net distance, and an upper bound tighter than an existing bound on the estimator error for the empirical neural net distance. Our lower and upper bounds match not only in the order of the sample size but also in terms of the norm of the parameter matrices of neural networks, which justifies the empirical neural net distance as a good approximation of the true neural net distance for training GANs in practice.