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Register a new userRethinking Numerical Representations for Deep Neural Networks
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With ever-increasing computational demand for deep learning, it is critical to investigate the implications of the numeric representation and precision of DNN model weights and activations on computational efficiency. In this work, we explore unconventional narrow-precision floating-point representations as it relates to inference accuracy and efficiency to steer the improved design of future DNN platforms. We show that inference using these custom numeric representations on production-grade DNNs, including GoogLeNet and VGG, achieves an average speedup of 7.6x with less than 1% degradation in inference accuracy relative to a state-of-the-art baseline platform representing the most sophisticated hardware using single-precision floating point. To facilitate the use of such customized precision, we also present a novel technique that drastically reduces the time required to derive the optimal precision configuration.
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The graph Laplacian regularization term is usually used in semi-supervised representation learning to provide graph structure information for a model $f(X)$. However, with the recent popularity of graph neural networks (GNNs), directly encoding graph structure $A$ into a model, i.e., $f(A, X)$, has become the more common approach. While we show that graph Laplacian regularization brings little-to-no benefit to existing GNNs, and propose a simple but non-trivial variant of graph Laplacian regularization, called Propagation-regularization (P-reg), to boost the performance of existing GNN models. We provide formal analyses to show that P-reg not only infuses extra information (that is not captured by the traditional graph Laplacian regularization) into GNNs, but also has the capacity equivalent to an infinite-depth graph convolutional network. We demonstrate that P-reg can effectively boost the performance of existing GNN models on both node-level and graph-level tasks across many different datasets.
The classical bias-variance trade-off predicts that bias decreases and variance increase with model complexity, leading to a U-shaped risk curve. Recent work calls this into question for neural networks and other over-parameterized models, for which it is often observed that larger models generalize better. We provide a simple explanation for this by measuring the bias and variance of neural networks: while the bias is monotonically decreasing as in the classical theory, the variance is unimodal or bell-shaped: it increases then decreases with the width of the network. We vary the network architecture, loss function, and choice of dataset and confirm that variance unimodality occurs robustly for all models we considered. The risk curve is the sum of the bias and variance curves and displays different qualitative shapes depending on the relative scale of bias and variance, with the double descent curve observed in recent literature as a special case. We corroborate these empirical results with a theoretical analysis of two-layer linear networks with random first layer. Finally, evaluation on out-of-distribution data shows that most of the drop in accuracy comes from increased bias while variance increases by a relatively small amount. Moreover, we find that deeper models decrease bias and increase variance for both in-distribution and out-of-distribution data.
In this work, we propose a novel technique to boost training efficiency of a neural network. Our work is based on an excellent idea that whitening the inputs of neural networks can achieve a fast convergence speed. Given the well-known fact that independent components must be whitened, we introduce a novel Independent-Component (IC) layer before each weight layer, whose inputs would be made more independent. However, determining independent components is a computationally intensive task. To overcome this challenge, we propose to implement an IC layer by combining two popular techniques, Batch Normalization and Dropout, in a new manner that we can rigorously prove that Dropout can quadratically reduce the mutual information and linearly reduce the correlation between any pair of neurons with respect to the dropout layer parameter $p$. As demonstrated experimentally, the IC layer consistently outperforms the baseline approaches with more stable training process, faster convergence speed and better convergence limit on CIFAR10/100 and ILSVRC2012 datasets. The implementation of our IC layer makes us rethink the common practices in the design of neural networks. For example, we should not place Batch Normalization before ReLU since the non-negative responses of ReLU will make the weight layer updated in a suboptimal way, and we can achieve better performance by combining Batch Normalization and Dropout together as an IC layer.
We propose a novel training method to integrate rules into deep learning, in a way their strengths are controllable at inference. Deep Neural Networks with Controllable Rule Representations (DeepCTRL) incorporates a rule encoder into the model coupled with a rule-based objective, enabling a shared representation for decision making. DeepCTRL is agnostic to data type and model architecture. It can be applied to any kind of rule defined for inputs and outputs. The key aspect of DeepCTRL is that it does not require retraining to adapt the rule strength -- at inference, the user can adjust it based on the desired operation point on accuracy vs. rule verification ratio. In real-world domains where incorporating rules is critical -- such as Physics, Retail and Healthcare -- we show the effectiveness of DeepCTRL in teaching rules for deep learning. DeepCTRL improves the trust and reliability of the trained models by significantly increasing their rule verification ratio, while also providing accuracy gains at downstream tasks. Additionally, DeepCTRL enables novel use cases such as hypothesis testing of the rules on data samples, and unsupervised adaptation based on shared rules between datasets.
Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although these networks involve the composition of simple arithmetic operations, it can be very challenging to verify whether a particular network satisfies certain input-output properties. This article surveys methods that have emerged recently for soundly verifying such properties. These methods borrow insights from reachability analysis, optimization, and search. We discuss fundamental differences and connections between existing algorithms. In addition, we provide pedagogical implementations of existing methods and compare them on a set of benchmark problems.
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