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Register a new userOn reaction network implementations of neural networks
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Added by
David Anderson
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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This paper is concerned with the utilization of deterministically modeled chemical reaction networks for the implementation of (feed-forward) neural networks. We develop a general mathematical framework and prove that the ordinary differential equations (ODEs) associated with certain reaction network implementations of neural networks have desirable properties including (i) existence of unique positive fixed points that are smooth in the parameters of the model (necessary for gradient descent), and (ii) fast convergence to the fixed point regardless of initial condition (necessary for efficient implementation). We do so by first making a connection between neural networks and fixed points for systems of ODEs, and then by constructing reaction networks with the correct associated set of ODEs. We demonstrate the theory by constructing a reaction network that implements a neural network with a smoothed ReLU activation function, though we also demonstrate how to generalize the construction to allow for other activation functions (each with the desirable properties listed previously). As there are multiple types of networks utilized in this paper, we also give a careful introduction to both reaction networks and neural networks, in order to disambiguate the overlapping vocabulary in the two settings and to clearly highlight the role of each networks properties.
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Koopman operator theory, a powerful framework for discovering the underlying dynamics of nonlinear dynamical systems, was recently shown to be intimately connected with neural network training. In this work, we take the first steps in making use of this connection. As Koopman operator theory is a linear theory, a successful implementation of it in evolving network weights and biases offers the promise of accelerated training, especially in the context of deep networks, where optimization is inherently a non-convex problem. We show that Koopman operator theoretic methods allow for accurate predictions of weights and biases of feedforward, fully connected deep networks over a non-trivial range of training time. During this window, we find that our approach is >10x faster than various gradient descent based methods (e.g. Adam, Adadelta, Adagrad), in line with our complexity analysis. We end by highlighting open questions in this exciting intersection between dynamical systems and neural network theory. We highlight additional methods by which our results could be expanded to broader classes of networks and larger training intervals, which shall be the focus of future work.
Performing analytical tasks over graph data has become increasingly interesting due to the ubiquity and large availability of relational information. However, unlike images or sentences, there is no notion of sequence in networks. Nodes (and edges) follow no absolute order, and it is hard for traditional machine learning (ML) algorithms to recognize a pattern and generalize their predictions on this type of data. Graph Neural Networks (GNN) successfully tackled this problem. They became popular after the generalization of the convolution concept to the graph domain. However, they possess a large number of hyperparameters and their design and optimization is currently hand-made, based on heuristics or empirical intuition. Neural Architecture Search (NAS) methods appear as an interesting solution to this problem. In this direction, this paper compares two NAS methods for optimizing GNN: one based on reinforcement learning and a second based on evolutionary algorithms. Results consider 7 datasets over two search spaces and show that both methods obtain similar accuracies to a random search, raising the question of how many of the search space dimensions are actually relevant to the problem.
Binarized neural networks, or BNNs, show great promise in edge-side applications with resource limited hardware, but raise the concerns of reduced accuracy. Motivated by the complex neural networks, in this paper we introduce complex representation into the BNNs and propose Binary complex neural network -- a novel network design that processes binary complex inputs and weights through complex convolution, but still can harvest the extraordinary computation efficiency of BNNs. To ensure fast convergence rate, we propose novel BCNN based batch normalization function and weight initialization function. Experimental results on Cifar10 and ImageNet using state-of-the-art network models (e.g., ResNet, ResNetE and NIN) show that BCNN can achieve better accuracy compared to the original BNN models. BCNN improves BNN by strengthening its learning capability through complex representation and extending its applicability to complex-valued input data. The source code of BCNN will be released on GitHub.
We introduce a method to train Quantized Neural Networks (QNNs) --- neural networks with extremely low precision (e.g., 1-bit) weights and activations, at run-time. At train-time the quantized weights and activations are used for computing the parameter gradients. During the forward pass, QNNs drastically reduce memory size and accesses, and replace most arithmetic operations with bit-wise operations. As a result, power consumption is expected to be drastically reduced. We trained QNNs over the MNIST, CIFAR-10, SVHN and ImageNet datasets. The resulting QNNs achieve prediction accuracy comparable to their 32-bit counterparts. For example, our quantized version of AlexNet with 1-bit weights and 2-bit activations achieves $51%$ top-1 accuracy. Moreover, we quantize the parameter gradients to 6-bits as well which enables gradients computation using only bit-wise operation. Quantized recurrent neural networks were tested over the Penn Treebank dataset, and achieved comparable accuracy as their 32-bit counterparts using only 4-bits. Last but not least, we programmed a binary matrix multiplication GPU kernel with which it is possible to run our MNIST QNN 7 times faster than with an unoptimized GPU kernel, without suffering any loss in classification accuracy. The QNN code is available online.
To reduce random access memory (RAM) requirements and to increase speed of recognition algorithms we consider a weight discretization problem for trained neural networks. We show that an exponential discretization is preferable to a linear discretization since it allows one to achieve the same accuracy when the number of bits is 1 or 2 less. The quality of the neural network VGG-16 is already satisfactory (top5 accuracy 69%) in the case of 3 bit exponential discretization. The ResNet50 neural network shows top5 accuracy 84% at 4 bits. Other neural networks perform fairly well at 5 bits (top5 accuracies of Xception, Inception-v3, and MobileNet-v2 top5 were 87%, 90%, and 77%, respectively). At less number of bits, the accuracy decreases rapidly.
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