We consider the fixed-budget best arm identification problem where the goal is to find the arm of the largest mean with a fixed number of samples. It is known that the probability of misidentifying the best arm is exponentially small to the number of rounds. However, limited characterizations have been discussed on the rate (exponent) of this value. In this paper, we characterize the minimax optimal rate as a result of an optimization over all possible parameters. We introduce two rates, Rgo and Rgo, corresponding to lower bounds on the probability of misidentification, each of which is associated with a proposed algorithm. The rate Rgo is associated with Rgo-tracking, which can be efficiently implemented by a neural network and is shown to outperform existing algorithms. However, this rate requires a nontrivial condition to be achievable. To address this issue, we introduce the second rate Rgo . We show that this rate is indeed achievable by introducing a conceptual algorithm called delayed optimal tracking (DOT).

Learning classifiers that are robust to adversarial examples has received a great deal of recent attention. A major drawback of the standard robust learning framework is there is an artificial robustness radius r that applies to all inputs. This ignores the fact that data may be highly heterogeneous, in which case it is plausible that robustness regions should be larger in some regions of data, and smaller in others. In this paper, we address this limitation by proposing a new limit classifier, called the neighborhood optimal classifier, that extends the Bayes optimal classifier outside its support by using the label of the closest in-support point. We then argue that this classifier maximizes the size of its robustness regions subject to the constraint of having accuracy equal to the Bayes optimal. We then present sufficient conditions under which general non-parametric methods that can be represented as weight functions converge towards this limit, and show that both nearest neighbors and kernel classifiers satisfy them under certain conditions.

The tremendous success of large models trained on extensive datasets demonstrates that scale is a key ingredient in achieving superior results. Therefore, the reflection on the rationality of designing knowledge distillation (KD) approaches for limited-capacity architectures solely based on small-scale datasets is now deemed imperative. In this paper, we identify the small data pitfall that presents in previous KD methods, which results in the underestimation of the power of vanilla KD framework on large-scale datasets such as ImageNet-1K. Specifically, we show that employing stronger data augmentation techniques and using larger datasets can directly decrease the gap between vanilla KD and other meticulously designed KD variants. This highlights the necessity of designing and evaluating KD approaches in the context of practical scenarios, casting off the limitations of small-scale datasets. Our investigation of the vanilla KD and its variants in more complex schemes, including stronger training strategies and different model capacities, demonstrates that vanilla KD is elegantly simple but astonishingly effective in large-scale scenarios. Without bells and whistles, we obtain state-of-the-art ResNet50, ViT-S, and ConvNeXtV2-T models for ImageNet, which achieve 83.1%, 84.3%, and 85.0% top-1 accuracy, respectively.

What can linearized neural networks actually say about generalization? As mentioned in the main text, all our models are trained using the same scheme which was selected without any hyperparameter tuning, besides ensuring a good performance on CIFAR2 for the neural networks. Namely, we train using stochastic gradient descent (SGD) to optimize a binary crossentropy loss, with a decaying learning rate starting at 0.05 and momentum set to 0.9. Furthermore, we use a batch size of 128and train for a 100epochs. This is enough to obtain close-to-zero training losses for the neural networks, and converge to a stable test accuracy in the case of the linearized models1.

For certain infinitely-wide neural networks, the neural tangent kernel (NTK) theory fully characterizes generalization, but for the networks used in practice, the empirical NTK only provides a rough first-order approximation. Still, a growing body of work keeps leveraging this approximation to successfully analyze important deep learning phenomena and design algorithms for new applications. In our work, we provide strong empirical evidence to determine the practical validity of such approximation by conducting a systematic comparison of the behavior of different neural networks and their linear approximations on different tasks. We show that the linear approximations can indeed rank the learning complexity of certain tasks for neural networks, even when they achieve very different performances. However, in contrast to what was previously reported, we discover that neural networks do not always perform better than their kernel approximations, and reveal that the performance gap heavily depends on architecture, dataset size and training task. We discover that networks overfit to these tasks mostly due to the evolution of their kernel during training, thus, revealing a new type of implicit bias.

Expressing universal semantics common to all languages is helpful in understanding the meanings of complex and culture-specific sentences. The research theme underlying this scenario focuses on learning universal representations across languages with the usage of massive parallel corpora. However, due to the sparsity and scarcity of parallel data, there is still a big challenge in learning authentic "universals" for any two languages. In this paper, we propose EMMA-X: an EM-like Multilingual pre-training Algorithm, to learn (X)Cross-lingual universals with the aid of excessive multilingual non-parallel data.

Pre-trained language models have been successful on text classification tasks, but are prone to learning spurious correlations from biased datasets, and are thus vulnerable when making inferences in a new domain. Prior work reveals such spurious patterns via post-hoc explanation algorithms which compute the importance of input features. Further, the model is regularized to align the importance scores with human knowledge, so that the unintended model behaviors are eliminated. However, such a regularization technique lacks flexibility and coverage, since only importance scores towards a pre-defined list of features are adjusted, while more complex human knowledge such as feature interaction and pattern generalization can hardly be incorporated. In this work, we propose to refine a learned language model for a target domain by collecting human-provided compositional explanations regarding observed biases. By parsing these explanations into executable logic rules, the human-specified refinement advice from a small set of explanations can be generalized to more training examples. We additionally introduce a regularization term allowing adjustments for both importance and interaction of features to better rectify model behavior. We demonstrate the effectiveness of the proposed approach on two text classification tasks by showing improved performance in target domain as well as improved model fairness after refinement1.