Zhiqiu Xu

Zhuang Liu, Zhiqiu Xu, Joseph Jin et al.

Introduced by Hinton et al. in 2012, dropout has stood the test of time as a regularizer for preventing overfitting in neural networks. In this study, we demonstrate that dropout can also mitigate underfitting when used at the start of training. During the early phase, we find dropout reduces the directional variance of gradients across mini-batches and helps align the mini-batch gradients with the entire dataset's gradient. This helps counteract the stochasticity of SGD and limit the influence of individual batches on model training. Our findings lead us to a solution for improving performance in underfitting models - early dropout: dropout is applied only during the initial phases of training, and turned off afterwards. Models equipped with early dropout achieve lower final training loss compared to their counterparts without dropout. Additionally, we explore a symmetric technique for regularizing overfitting models - late dropout, where dropout is not used in the early iterations and is only activated later in training. Experiments on ImageNet and various vision tasks demonstrate that our methods consistently improve generalization accuracy. Our results encourage more research on understanding regularization in deep learning and our methods can be useful tools for future neural network training, especially in the era of large data. Code is available at https://github.com/facebookresearch/dropout.

Zhiqiu Xu, Yanjie Chen, Kirill Vishniakov et al.

Weight initialization plays an important role in neural network training. Widely used initialization methods are proposed and evaluated for networks that are trained from scratch. However, the growing number of pretrained models now offers new opportunities for tackling this classical problem of weight initialization. In this work, we introduce weight selection, a method for initializing smaller models by selecting a subset of weights from a pretrained larger model. This enables the transfer of knowledge from pretrained weights to smaller models. Our experiments demonstrate that weight selection can significantly enhance the performance of small models and reduce their training time. Notably, it can also be used together with knowledge distillation. Weight selection offers a new approach to leverage the power of pretrained models in resource-constrained settings, and we hope it can be a useful tool for training small models in the large-model era. Code is available at https://github.com/OscarXZQ/weight-selection.

Yida Yin, Zhiqiu Xu, Zhiyuan Li et al.

Stochastic Variance Reduced Gradient (SVRG), introduced by Johnson & Zhang (2013), is a theoretically compelling optimization method. However, as Defazio & Bottou (2019) highlight, its effectiveness in deep learning is yet to be proven. In this work, we demonstrate the potential of SVRG in optimizing real-world neural networks. Our empirical analysis finds that, for deeper neural networks, the strength of the variance reduction term in SVRG should be smaller and decrease as training progresses. Inspired by this, we introduce a multiplicative coefficient $α$ to control the strength and adjust it through a linear decay schedule. We name our method $α$-SVRG. Our results show $α$-SVRG better optimizes models, consistently reducing training loss compared to the baseline and standard SVRG across various model architectures and multiple image classification datasets. We hope our findings encourage further exploration into variance reduction techniques in deep learning. Code is available at github.com/davidyyd/alpha-SVRG.

Zhiqiu Xu, Shibo Jin, Shreya Arya et al.

As frontier language models attain near-ceiling performance on static mathematical benchmarks, existing evaluations are increasingly unable to differentiate model capabilities, largely because they cast models solely as solvers of fixed problem sets. We introduce MathDuels, a self-play benchmark in which models occupy dual roles: each authors math problems under adversarial prompting and solves problems authored by every other participant. Problems are produced through a three-stage generation pipeline (meta-prompting, problem generation, and difficulty amplification), and validated by an independent verifier that excludes ill-posed questions. A Rasch model (Rasch, 1993) jointly estimates solver abilities and problem difficulties; author quality is derived from the difficulties of each model's authored problems. Experiments across 19 frontier models reveal that authoring and solving capabilities are partially decoupled, and that dual-role evaluation reveals capability separations invisible in single-role benchmarks. As newer models enter the arena, they produce problems that defeat previously dominant solvers, so the benchmark's difficulty co-evolves with participant strength rather than saturating at a fixed ceiling. We host a public leaderboard that updates as new models are released.

Zhuang Liu, Zhiqiu Xu, Hung-Ju Wang et al.

Anytime inference requires a model to make a progression of predictions which might be halted at any time. Prior research on anytime visual recognition has mostly focused on image classification. We propose the first unified and end-to-end approach for anytime dense prediction. A cascade of "exits" is attached to the model to make multiple predictions. We redesign the exits to account for the depth and spatial resolution of the features for each exit. To reduce total computation, and make full use of prior predictions, we develop a novel spatially adaptive approach to avoid further computation on regions where early predictions are already sufficiently confident. Our full method, named anytime dense prediction with confidence (ADP-C), achieves the same level of final accuracy as the base model, and meanwhile significantly reduces total computation. We evaluate our method on Cityscapes semantic segmentation and MPII human pose estimation: ADP-C enables anytime inference without sacrificing accuracy while also reducing the total FLOPs of its base models by 44.4% and 59.1%. We compare with anytime inference by deep equilibrium networks and feature-based stochastic sampling, showing that ADP-C dominates both across the accuracy-computation curve. Our code is available at https://github.com/liuzhuang13/anytime .