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Register a new userLearning Activation Functions: A new paradigm for understanding Neural Networks
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Added by
Mohit Goyal
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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The scope of research in the domain of activation functions remains limited and centered around improving the ease of optimization or generalization quality of neural networks (NNs). However, to develop a deeper understanding of deep learning, it becomes important to look at the non linear component of NNs more carefully. In this paper, we aim to provide a generic form of activation function along with appropriate mathematical grounding so as to allow for insights into the working of NNs in future. We propose Self-Learnable Activation Functions (SLAF), which are learned during training and are capable of approximating most of the existing activation functions. SLAF is given as a weighted sum of pre-defined basis elements which can serve for a good approximation of the optimal activation function. The coefficients for these basis elements allow a search in the entire space of continuous functions (consisting of all the conventional activations). We propose various training routines which can be used to achieve performance with SLAF equipped neural networks (SLNNs). We prove that SLNNs can approximate any neural network with lipschitz continuous activations, to any arbitrary error highlighting their capacity and possible equivalence with standard NNs. Also, SLNNs can be completely represented as a collections of finite degree polynomial upto the very last layer obviating several hyper parameters like width and depth. Since the optimization of SLNNs is still a challenge, we show that using SLAF along with standard activations (like ReLU) can provide performance improvements with only a small increase in number of parameters.
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Achieving transparency in black-box deep learning algorithms is still an open challenge. High dimensional features and decisions given by deep neural networks (NN) require new algorithms and methods to expose its mechanisms. Current state-of-the-art NN interpretation methods (e.g. Saliency maps, DeepLIFT, LIME, etc.) focus more on the direct relationship between NN outputs and inputs rather than the NN structure and operations itself. In current deep NN operations, there is uncertainty over the exact role played by neurons with fixed activation functions. In this paper, we achieve partially explainable learning model by symbolically explaining the role of activation functions (AF) under a scalable topology. This is carried out by modeling the AFs as adaptive Gaussian Processes (GP), which sit within a novel scalable NN topology, based on the Kolmogorov-Arnold Superposition Theorem (KST). In this scalable NN architecture, the AFs are generated by GP interpolation between control points and can thus be tuned during the back-propagation procedure via gradient descent. The control points act as the core enabler to both local and global adjustability of AF, where the GP interpolation constrains the intrinsic autocorrelation to avoid over-fitting. We show that there exists a trade-off between the NNs expressive power and interpretation complexity, under linear KST topology scaling. To demonstrate this, we perform a case study on a binary classification dataset of banknote authentication. By quantitatively and qualitatively investigating the mapping relationship between inputs and output, our explainable model can provide interpretation over each of the one-dimensional attributes. These early results suggest that our model has the potential to act as the final interpretation layer for deep neural networks.
The machine learning community has become increasingly interested in the energy efficiency of neural networks. The Spiking Neural Network (SNN) is a promising approach to energy-efficient computing, since its activation levels are quantized into temporally sparse, one-bit values (i.e., spike events), which additionally converts the sum over weight-activity products into a simple addition of weights (one weight for each spike). However, the goal of maintaining state-of-the-art (SotA) accuracy when converting a non-spiking network into an SNN has remained an elusive challenge, primarily due to spikes having only a single bit of precision. Adopting tools from signal processing, we cast neural activation functions as quantizers with temporally-diffused error, and then train networks while smoothly interpolating between the non-spiking and spiking regimes. We apply this technique to the Legendre Memory Unit (LMU) to obtain the first known example of a hybrid SNN outperforming SotA recurrent architectures -- including the LSTM, GRU, and NRU -- in accuracy, while reducing activities to at most 3.74 bits on average with 1.26 significant bits multiplying each weight. We discuss how these methods can significantly improve the energy efficiency of neural networks.
The past few years have witnessed the fast development of different regularization methods for deep learning models such as fully-connected deep neural networks (DNNs) and Convolutional Neural Networks (CNNs). Most of previous methods mainly consider to drop features from input data and hidden layers, such as Dropout, Cutout and DropBlocks. DropConnect select to drop connections between fully-connected layers. By randomly discard some features or connections, the above mentioned methods control the overfitting problem and improve the performance of neural networks. In this paper, we proposed two novel regularization methods, namely DropFilter and DropFilter-PLUS, for the learning of CNNs. Different from the previous methods, DropFilter and DropFilter-PLUS selects to modify the convolution filters. For DropFilter-PLUS, we find a suitable way to accelerate the learning process based on theoretical analysis. Experimental results on MNIST show that using DropFilter and DropFilter-PLUS may improve performance on image classification tasks.
Training activation quantized neural networks involves minimizing a piecewise constant function whose gradient vanishes almost everywhere, which is undesirable for the standard back-propagation or chain rule. An empirical way around this issue is to use a straight-through estimator (STE) (Bengio et al., 2013) in the backward pass only, so that the gradient through the modified chain rule becomes non-trivial. Since this unusual gradient is certainly not the gradient of loss function, the following question arises: why searching in its negative direction minimizes the training loss? In this paper, we provide the theoretical justification of the concept of STE by answering this question. We consider the problem of learning a two-linear-layer network with binarized ReLU activation and Gaussian input data. We shall refer to the unusual gradient given by the STE-modifed chain rule as coarse gradient. The choice of STE is not unique. We prove that if the STE is properly chosen, the expected coarse gradient correlates positively with the population gradient (not available for the training), and its negation is a descent direction for minimizing the population loss. We further show the associated coarse gradient descent algorithm converges to a critical point of the population loss minimization problem. Moreover, we show that a poor choice of STE leads to instability of the training algorithm near certain local minima, which is verified with CIFAR-10 experiments.
Binarization of neural network models is considered as one of the promising methods to deploy deep neural network models on resource-constrained environments such as mobile devices. However, Binary Neural Networks (BNNs) tend to suffer from severe accuracy degradation compared to the full-precision counterpart model. Several techniques were proposed to improve the accuracy of BNNs. One of the approaches is to balance the distribution of binary activations so that the amount of information in the binary activations becomes maximum. Based on extensive analysis, in stark contrast to previous work, we argue that unbalanced activation distribution can actually improve the accuracy of BNNs. We also show that adjusting the threshold values of binary activation functions results in the unbalanced distribution of the binary activation, which increases the accuracy of BNN models. Experimental results show that the accuracy of previous BNN models (e.g. XNOR-Net and Bi-Real-Net) can be improved by simply shifting the threshold values of binary activation functions without requiring any other modification.
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