Empirical works show that for ReLU neural networks (NNs) with small initialization, input weights of hidden neurons (the input weight of a hidden neuron consists of the weight from its input layer to the hidden neuron and its bias term) condense onto isolated orientations. The condensation dynamics implies that the training implicitly regularizes a NN towards one with much smaller effective size. In this work, we illustrate the formation of the condensation in multi-layer fully connected NNs and show that the maximal number of condensed orientations in the initial training stage is twice the multiplicity of the activation function, where "multiplicity" indicates the multiple roots of activation function at origin. Our theoretical analysis confirms experiments for two cases, one is for the activation function of multiplicity one with arbitrary dimension input, which contains many common activation functions, and the other is for the layer with one-dimensional input and arbitrary multiplicity. This work makes a step towards understanding how small initialization leads NNs to condensation at the initial training stage.

Having similar behavior at training time and test time--what we call a "What You See Is What You Get" (WYSIWYG) property--is desirable in machine learning. Models trained with standard stochastic gradient descent (SGD), however, do not necessarily have this property, as their complex behaviors such as robustness or subgroup performance can differ drastically between training and test time. In contrast, we show that Differentially-Private (DP) training provably ensures the high-level WYSIWYG property, which we quantify using a notion of distributional generalization. Applying this connection, we introduce new conceptual tools for designing deep-learning methods by reducing generalization concerns to optimization ones: to mitigate unwanted behavior at test time, it is provably sufficient to mitigate this behavior on the training data. By applying this novel design principle, which bypasses "pathologies" of SGD, we construct simple algorithms that are competitive with SOTA in several distributional-robustness applications, significantly improve the privacy vs. disparate impact trade-off of DP-SGD, and mitigate robust overfitting in adversarial training. Finally, we also improve on theoretical bounds relating DP, stability, and distributional generalization.

Training large models from scratch usually costs a substantial amount of resources. Towards this problem, recent studies such as bert2BERT and LiGO have reused small pretrained models to initialize a large model (termed the "target model"), leading to a considerable acceleration in training. Despite the successes of these previous studies, they grew pretrained models by mapping partial weights only, ignoring potential correlations across the entire model. As we show in this paper, there are inter-and intra-interactions among the weights of both the pretrained and the target models. As a result, the partial mapping may not capture the complete information and lead to inadequate growth. In this paper, we propose a method that linearly correlates each weight of the target model to all the weights of the pretrained model to further enhance acceleration ability. We utilize multi-linear operators to reduce computational and spacial complexity, enabling acceptable resource requirements. Experiments demonstrate that our method can save 76% computational costs on DeiT-base transferred from DeiT-small, which outperforms bert2BERT by +12.0% and LiGO by +20.7%, respectively.

Prior studies [18, 12] show that GAN often experiences generation failures with severely degraded generation performance when only limited training data is available. Specifically, with limited training data, the discriminator tends to discriminate via meaningless shortcuts by merely focusing on easy-to-discriminate image locations and spectra instead of holistic understanding of images. This can be viewed clearly in Figure 1, where the Gini Coefficient [4] of discriminator's spatial attentions increases quickly along the training iteration (when only limited training data is available). Note that the Gini coefficient [4] is negatively correlated with equality, i.e., the discriminator will pay more unevenly distributed attention to each spatial location while the Gini coefficient increases from '0' to '1'. For image generation with GAN, the large Gini coefficient (of discriminator's spatial attentions) thus means that the discriminator starts to focus on certain spatial locations (easy to discriminate) while ignoring other spatial locations (hard to discriminate), ultimately leading to an over-confident discriminator and training collapse. In another word, the Gini coefficient [4] of '0' expresses perfect equality where all values are the same (i.e., where the discriminator pays the same attention to every spatial location) while '1' expresses maximal inequality among values (i.e., the discriminator focuses on only one location while all others are ignored).

Incrementality, which measures the causal effect of showing an ad to a potential customer (e.g. a user in an internet platform) versus not, is a central object for advertisers in online advertising platforms. This paper investigates the problem of how an advertiser can learn to optimize the bidding sequence in an online manner without knowing the incrementality parameters in advance. We formulate the offline version of this problem as a specially structured episodic Markov Decision Process (MDP) and then, for its online learning counterpart, propose a novel reinforcement learning (RL) algorithm with regret at most eO(H2 T), which depends on the number of rounds H and number of episodes T, but does not depend on the number of actions (i.e., possible bids). A fundamental difference between our learning problem from standard RL problems is that the realized reward feedback from conversion incrementality is mixed and delayed. To handle this difficulty we propose and analyze a novel pairwise moment-matching algorithm to learn the conversion incrementality, which we believe is of independent interest.