Real-world data universally confronts a severe class-imbalance problem and exhibits a long-tailed distribution, i.e., most labels are associated with limited instances. The naïve models supervised by such datasets would prefer dominant labels, encounter a serious generalization challenge and become poorly calibrated. We propose two novel methods from the prior perspective to alleviate this dilemma. First, we deduce a balance-oriented data augmentation named Uniform Mixup (UniMix) to promote mixup in long-tailed scenarios, which adopts advanced mixing factor and sampler in favor of the minority. Second, motivated by the Bayesian theory, we figure out the Bayes Bias (Bayias), an inherent bias caused by the inconsistency of prior, and compensate it as a modification on standard cross-entropy loss. We further prove that both the proposed methods ensure the classification calibration theoretically and empirically. Extensive experiments verify that our strategies contribute to a better-calibrated model and their combination achieves state-of-the-art performance on CIFAR-LT, ImageNet-LT, and iNaturalist 2018.

We revisit first-order optimization under local information constraints such as local privacy, gradient quantization, and computational constraints limiting access to a few coordinates of the gradient. In this setting, the optimization algorithm is not allowed to directly access the complete output of the gradient oracle, but only gets limited information about it subject to the local information constraints. We study the role of adaptivity in processing the gradient output to obtain this limited information from it. We consider optimization for both convex and strongly convex functions and obtain tight or nearly tight lower bounds for the convergence rate, when adaptive gradient processing is allowed. Prior work was restricted to convex functions and allowed only nonadaptive processing of gradients. For both of these function classes and for the three information constraints mentioned above, our lower bound implies that adaptive processing of gradients cannot outperform nonadaptive processing in most regimes of interest. We complement these results by exhibiting a natural optimization problem under information constraints for which adaptive processing of gradient strictly outperforms nonadaptive processing.

Current operator library with quantized operators is not feasible for vision transformer inference because of the specific operators including the GeLU activation and layer normalization. Layer normalization (LayerNorm) normalizes the activations of each layer in a neural network independently, reducing internal covariate shift and improving training stability as follows: LayerNorm(x) = γ p Var(x)+ϵ (x µ)+β, (1) where x is the input tensor. We construct surrogate equations with fixed-point interactive methods to calculate the output of the square root operators inspired by I-BERT[3]. We provide the details of how to approximate the square root operators in Algorithm.1. GeLU requires the cumulative distribution function (CDF) of Gaussian distribution, we approximate the activation function by Equation.2[1].

A structural equation model (SEM) is an effective framework to reason over causal relationships represented via a directed acyclic graph (DAG). Recent advances have enabled effective maximum-likelihood point estimation of DAGs from observational data. However, a point estimate may not accurately capture the uncertainty in inferring the underlying graph in practical scenarios, wherein the true DAG is non-identifiable and/or the observed dataset is limited. We propose Bayesian Causal Discovery Nets (BCD Nets), a variational inference framework for estimating a distribution over DAGs characterizing a linear-Gaussian SEM. Developing a full Bayesian posterior over DAGs is challenging due to the the discrete and combinatorial nature of graphs. We analyse key design choices for scalable VI over DAGs, such as 1) the parametrization of DAGs via an expressive variational family, 2) a continuous relaxation that enables low-variance stochastic optimization, and 3) suitable priors over the latent variables. We provide a series of experiments on real and synthetic data showing that BCDNets outperform maximum-likelihood methods on standard causal discovery metrics such as structural Hamming distance in low data regimes.