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Register a new userSGD on Neural Networks Learns Functions of Increasing Complexity
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Added by
Preetum Nakkiran
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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We perform an experimental study of the dynamics of Stochastic Gradient Descent (SGD) in learning deep neural networks for several real and synthetic classification tasks. We show that in the initial epochs, almost all of the performance improvement of the classifier obtained by SGD can be explained by a linear classifier. More generally, we give evidence for the hypothesis that, as iterations progress, SGD learns functions of increasing complexity. This hypothesis can be helpful in explaining why SGD-learned classifiers tend to generalize well even in the over-parameterized regime. We also show that the linear classifier learned in the initial stages is retained throughout the execution even if training is continued to the point of zero training error, and complement this with a theoretical result in a simplified model. Key to our work is a new measure of how well one classifier explains the performance of another, based on conditional mutual information.
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Deep neural networks are the state-of-the-art methods for many real-world tasks, such as computer vision, natural language processing and speech recognition. For all its popularity, deep neural networks are also criticized for consuming a lot of memory and draining battery life of devices during training and inference. This makes it hard to deploy these models on mobile or embedded devices which have tight resource constraints. Quantization is recognized as one of the most effective approaches to satisfy the extreme memory requirements that deep neural network models demand. Instead of adopting 32-bit floating point format to represent weights, quantized representations store weights using more compact formats such as integers or even binary numbers. Despite a possible degradation in predictive performance, quantization provides a potential solution to greatly reduce the model size and the energy consumption. In this survey, we give a thorough review of different aspects of quantized neural networks. Current challenges and trends of quantized neural networks are also discussed.
Recurrent neural networks (RNNs) are notoriously difficult to train. When the eigenvalues of the hidden to hidden weight matrix deviate from absolute value 1, optimization becomes difficult due to the well studied issue of vanishing and exploding gradients, especially when trying to learn long-term dependencies. To circumvent this problem, we propose a new architecture that learns a unitary weight matrix, with eigenvalues of absolute value exactly 1. The challenge we address is that of parametrizing unitary matrices in a way that does not require expensive computations (such as eigendecomposition) after each weight update. We construct an expressive unitary weight matrix by composing several structured matrices that act as building blocks with parameters to be learned. Optimization with this parameterization becomes feasible only when considering hidden states in the complex domain. We demonstrate the potential of this architecture by achieving state of the art results in several hard tasks involving very long-term dependencies.
We consider functions defined by deep neural networks as definable objects in an o-miminal expansion of the real field, and derive an almost linear (in the number of weights) bound on sample complexity of such networks.
Deep Neural Network (DNN) is powerful but computationally expensive and memory intensive, thus impeding its practical usage on resource-constrained front-end devices. DNN pruning is an approach for deep model compression, which aims at eliminating some parameters with tolerable performance degradation. In this paper, we propose a novel momentum-SGD-based optimization method to reduce the network complexity by on-the-fly pruning. Concretely, given a global compression ratio, we categorize all the parameters into two parts at each training iteration which are updated using different rules. In this way, we gradually zero out the redundant parameters, as we update them using only the ordinary weight decay but no gradients derived from the objective function. As a departure from prior methods that require heavy human works to tune the layer-wise sparsity ratios, prune by solving complicated non-differentiable problems or finetune the model after pruning, our method is characterized by 1) global compression that automatically finds the appropriate per-layer sparsity ratios; 2) end-to-end training; 3) no need for a time-consuming re-training process after pruning; and 4) superior capability to find better winning tickets which have won the initialization lottery.
We examine the influence of input data representations on learning complexity. For learning, we posit that each model implicitly uses a candidate model distribution for unexplained variations in the data, its noise model. If the model distribution is not well aligned to the true distribution, then even relevant variations will be treated as noise. Crucially however, the alignment of model and true distribution can be changed, albeit implicitly, by changing data representations. Better representations can better align the model to the true distribution, making it easier to approximate the input-output relationship in the data without discarding useful data variations. To quantify this alignment effect of data representations on the difficulty of a learning task, we make use of an existing task complexity score and show its connection to the representation-dependent information coding length of the input. Empirically we extract the necessary statistics from a linear regression approximation and show that these are sufficient to predict relative learning performance outcomes of different data representations and neural network types obtained when utilizing an extensive neural network architecture search. We conclude that to ensure better learning outcomes, representations may need to be tailored to both task and model to align with the implicit distribution of model and task.
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