Many tasks in AI require the collaboration of multiple agents. Typically, the communication protocol between agents is manually specified and not altered during training. In this paper we explore a simple neural model, called CommNet, that uses continuous communication for fully cooperative tasks. The model consists of multiple agents and the communication between them is learned alongside their policy. We apply this model to a diverse set of tasks, demonstrating the ability of the agents to learn to communicate amongst themselves, yielding improved performance over non-communicative agents and baselines. In some cases, it is possible to interpret the language devised by the agents, revealing simple but effective strategies for solving the task at hand.
The Neural GPU @cite_19 has similarities to our model but differs in that a 1-D ordering on the input is assumed and it employs convolution, as opposed to the global pooling in our approach (thus permitting unstructured inputs). Our model can be regarded as an instantiation of the GNN construction of Scarselli al @cite_9 , as expanded on by Li al @cite_37 . In particular, in @cite_9 , the output of the model is the fixed point of iterating equations and to convergence, using recurrent models. In @cite_37 , these recurrence equations are unrolled a fixed number of steps and the model trained via backprop through time. In this work, we do not require the model to be recurrent, neither do we aim to reach steady state. Additionally, we regard Eqn. as a pooling operation, conceptually making our model a single feed-forward network with local connections.
@cite_19 @cite_9 @cite_37
2963187627 2173051530 2962761264 2866343820 1922658220 2773850766 1934184906 2574952845 2798598284 2765985261 2953061907 2798858969 2762473905 2963484342 2964265128 2623629680 2603221039 2139906443 1498932870 2952436057
Abstract: Learning an algorithm from examples is a fundamental problem that has been widely studied. Recently it has been addressed using neural networks, in particular by Neural Turing Machines (NTMs). These are fully differentiable computers that use backpropagation to learn their own programming. Despite their appeal NTMs have a weakness that is caused by their sequential nature: they are not parallel and are are hard to train due to their large depth when unfolded. We present a neural network architecture to address this problem: the Neural GPU. It is based on a type of convolutional gated recurrent unit and, like the NTM, is computationally universal. Unlike the NTM, the Neural GPU is highly parallel which makes it easier to train and efficient to run. An essential property of algorithms is their ability to handle inputs of arbitrary size. We show that the Neural GPU can be trained on short instances of an algorithmic task and successfully generalize to long instances. We verified it on a number of tasks including long addition and long multiplication of numbers represented in binary. We train the Neural GPU on numbers with upto 20 bits and observe no errors whatsoever while testing it, even on much longer numbers. To achieve these results we introduce a technique for training deep recurrent networks: parameter sharing relaxation. We also found a small amount of dropout and gradient noise to have a large positive effect on learning and generalization. Learning an algorithm from examples is a fundamental problem that has been widely studied. Recently it has been addressed using neural networks, in particular by Neural Turing Machines (NTMs). These are fully differentiable computers that use backpropagation to learn their own programming. Despite their appeal NTMs have a weakness that is caused by their sequential nature: they are not parallel and are are hard to train due to their large depth when unfolded. We present a neural network architecture to address this problem: the Neural GPU. It is based on a type of convolutional gated recurrent unit and, like the NTM, is computationally universal. Unlike the NTM, the Neural GPU is highly parallel which makes it easier to train and efficient to run. An essential property of algorithms is their ability to handle inputs of arbitrary size. We show that the Neural GPU can be trained on short instances of an algorithmic task and successfully generalize to long instances. We verified it on a number of tasks including long addition and long multiplication of numbers represented in binary. We train the Neural GPU on numbers with upto 20 bits and observe no errors whatsoever while testing it, even on much longer numbers. To achieve these results we introduce a technique for training deep recurrent networks: parameter sharing relaxation. We also found a small amount of dropout and gradient noise to have a large positive effect on learning and generalization. Global covariance pooling in convolutional neural networks has achieved impressive improvement over the classical first-order pooling. Recent works have shown matrix square root normalization plays a central role in achieving state-of-the-art performance. However, existing methods depend heavily on eigendecomposition (EIG) or singular value decomposition (SVD), suffering from inefficient training due to limited support of EIG and SVD on GPU. Towards addressing this problem, we propose an iterative matrix square root normalization method for fast end-to-end training of global covariance pooling networks. At the core of our method is a meta-layer designed with loop-embedded directed graph structure. The meta-layer consists of three consecutive nonlinear structured layers, which perform pre-normalization, coupled matrix iteration and post-compensation, respectively. Our method is much faster than EIG or SVD based ones, since it involves only matrix multiplications, suitable for parallel implementation on GPU. Moreover, the proposed network with ResNet architecture can converge in much less epochs, further accelerating network training. On large-scale ImageNet, we achieve competitive performance superior to existing counterparts. By finetuning our models pre-trained on ImageNet, we establish state-of-the-art results on three challenging fine-grained benchmarks. The source code and network models will be available at http: www.peihuali.org iSQRT-COV. Recurrent neural networks (RNNs) sequentially process data by updating their state with each new data point, and have long been the de facto choice for sequence modeling tasks. However, their inherently sequential computation makes them slow to train. Feed-forward and convolutional architectures have recently been shown to achieve superior results on some sequence modeling tasks such as machine translation, with the added advantage that they concurrently process all inputs in the sequence, leading to easy parallelization and faster training times. Despite these successes, however, popular feed-forward sequence models like the Transformer fail to generalize in many simple tasks that recurrent models handle with ease, e.g. copying strings or even simple logical inference when the string or formula lengths exceed those observed at training time. We propose the Universal Transformer (UT), a parallel-in-time self-attentive recurrent sequence model which can be cast as a generalization of the Transformer model and which addresses these issues. UTs combine the parallelizability and global receptive field of feed-forward sequence models like the Transformer with the recurrent inductive bias of RNNs. We also add a dynamic per-position halting mechanism and find that it improves accuracy on several tasks. In contrast to the standard Transformer, under certain assumptions, UTs can be shown to be Turing-complete. Our experiments show that UTs outperform standard Transformers on a wide range of algorithmic and language understanding tasks, including the challenging LAMBADA language modeling task where UTs achieve a new state of the art, and machine translation where UTs achieve a 0.9 BLEU improvement over Transformers on the WMT14 En-De dataset. In existing convolutional neural networks (CNNs), both convolution and pooling are locally performed for image regions separately, no contextual dependencies between different image regions have been taken into consideration. Such dependencies represent useful spatial structure information in images. Whereas recurrent neural networks (RNNs) are designed for learning contextual dependencies among sequential data by using the recurrent (feedback) connections. In this work, we propose the convolutional recurrent neural network (C-RNN), which learns the spatial dependencies between image regions to enhance the discriminative power of image representation. The C-RNN is trained in an end-to-end manner from raw pixel images. CNN layers are firstly processed to generate middle level features. RNN layer is then learned to encode spatial dependencies. The C-RNN can learn better image representation, especially for images with obvious spatial contextual dependencies. Our method achieves competitive performance on ILSVRC 2012, SUN 397, and MIT indoor. We introduce a model-based image reconstruction framework with a convolution neural network (CNN) based regularization prior. The proposed formulation provides a systematic approach for deriving deep architectures for inverse problems with the arbitrary structure. Since the forward model is explicitly accounted for, a smaller network with fewer parameters is sufficient to capture the image information compared to black-box deep learning approaches, thus reducing the demand for training data and training time. Since we rely on end-to-end training, the CNN weights are customized to the forward model, thus offering improved performance over approaches that rely on pre-trained denoisers. The main difference of the framework from existing end-to-end training strategies is the sharing of the network weights across iterations and channels. Our experiments show that the decoupling of the number of iterations from the network complexity offered by this approach provides benefits including lower demand for training data, reduced risk of overfitting, and implementations with significantly reduced memory footprint. We propose to enforce data-consistency by using numerical optimization blocks such as conjugate gradients algorithm within the network; this approach offers faster convergence per iteration, compared to methods that rely on proximal gradients steps to enforce data consistency. Our experiments show that the faster convergence translates to improved performance, especially when the available GPU memory restricts the number of iterations. In recent years, the convolutional neural network (CNN) has achieved great success in many computer vision tasks. Partially inspired by neuroscience, CNN shares many properties with the visual system of the brain. A prominent difference is that CNN is typically a feed-forward architecture while in the visual system recurrent connections are abundant. Inspired by this fact, we propose a recurrent CNN (RCNN) for object recognition by incorporating recurrent connections into each convolutional layer. Though the input is static, the activities of RCNN units evolve over time so that the activity of each unit is modulated by the activities of its neighboring units. This property enhances the ability of the model to integrate the context information, which is important for object recognition. Like other recurrent neural networks, unfolding the RCNN through time can result in an arbitrarily deep network with a fixed number of parameters. Furthermore, the unfolded network has multiple paths, which can facilitate the learning process. The model is tested on four benchmark object recognition datasets: CIFAR-10, CIFAR-100, MNIST and SVHN. With fewer trainable parameters, RCNN outperforms the state-of-the-art models on all of these datasets. Increasing the number of parameters leads to even better performance. These results demonstrate the advantage of the recurrent structure over purely feed-forward structure for object recognition. In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the past few decades. These methods produce excellent results, but can be challenging to deploy in practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyperparameter selection. The starting point of this paper is the observation that unrolled iterative methods have the form of a CNN (filtering followed by pointwise non-linearity) when the normal operator ( @math , where @math is the adjoint of the forward imaging operator, @math ) of the forward model is a convolution. Based on this observation, we propose using direct inversion followed by a CNN to solve normal-convolutional inverse problems. The direct inversion encapsulates the physical model of the system, but leads to artifacts when the problem is ill posed; the CNN combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure. We demonstrate the performance of the proposed network in sparse-view reconstruction (down to 50 views) on parallel beam X-ray computed tomography in synthetic phantoms as well as in real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a @math image on the GPU. Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and reinterprets pooling as a possibly nonlinear subsampling stage where nearby nodes pool their information in a set of preselected sample nodes. A key component of the architecture is to remember the position of sampled nodes to permit computation of convolutional features at deeper layers. The second architecture, dubbed aggregation GNN, diffuses the signal through the graph and stores the sequence of diffused components observed by a designated node. This procedure effectively aggregates all components into a stream of information having temporal structure to which the convolution and pooling stages of regular CNNs can be applied. A multinode version of aggregation GNNs is further introduced for operation in large-scale graphs. An important property of selection and aggregation GNNs is that they reduce to conventional CNNs when particularized to time signals reinterpreted as graph signals in a circulant graph. Comparative numerical analyses are performed in a source localization application over synthetic and real-world networks. Performance is also evaluated for an authorship attribution problem and text category classification. Multinode aggregation GNNs are consistently the best-performing GNN architecture. We propose a new framework for parallelizing deep neural network training that maximize the amount of data that is ingested by the training algorithm. Our proposed framework called Livermore Tournament Fast Batch Learning (LTFB) targets large-scale data problems. The LTFB approach creates a set of Deep Neural Network (DNN) models and trains each instance of these models independently and in parallel. Periodically each model selects another model to pair with, exchanges models, and then run a local tournament against held-out tournament datasets. The winning model is will continue training on the local training datasets. This new approach maximizes computation and minimizes amount of synchronization required in training deep neural network, a major bottleneck in existing synchronous deep learning algorithms. We evaluate our proposed algorithm on two HPC machines at Lawrence Livermore National Laboratory including an early access IBM Power8+ with NVIDIA Tesla P100 GPUs machine. Experimental evaluations of the LTFB framework on two popular image classification benchmark: CIFAR10 [18] and ImageNet [19], show significant speed up compared to the sequential baseline. In this work, we propose a novel recurrent neural network (RNN) architecture. The proposed RNN, gated-feedback RNN (GF-RNN), extends the existing approach of stacking multiple recurrent layers by allowing and controlling signals flowing from upper recurrent layers to lower layers using a global gating unit for each pair of layers. The recurrent signals exchanged between layers are gated adaptively based on the previous hidden states and the current input. We evaluated the proposed GF-RNN with different types of recurrent units, such as tanh, long short-term memory and gated recurrent units, on the tasks of character-level language modeling and Python program evaluation. Our empirical evaluation of different RNN units, revealed that in both tasks, the GF-RNN outperforms the conventional approaches to build deep stacked RNNs. We suggest that the improvement arises because the GF-RNN can adaptively assign different layers to different timescales and layer-to-layer interactions (including the top-down ones which are not usually present in a stacked RNN) by learning to gate these interactions. Current end-to-end machine reading and question answering (Q &A) models are primarily based on recurrent neural networks (RNNs) with attention. Despite their success, these models are often slow for both training and inference due to the sequential nature of RNNs. We propose a new Q &A architecture called QANet, which does not require recurrent networks: Its encoder consists exclusively of convolution and self-attention, where convolution models local interactions and self-attention models global interactions. On the SQuAD dataset, our model is 3x to 13x faster in training and 4x to 9x faster in inference, while achieving equivalent accuracy to recurrent models. The speed-up gain allows us to train the model with much more data. We hence combine our model with data generated by backtranslation from a neural machine translation model. On the SQuAD dataset, our single model, trained with augmented data, achieves 84.6 F1 score on the test set, which is significantly better than the best published F1 score of 81.8. Optimizing deep neural networks (DNNs) often suffers from the ill-conditioned problem. We observe that the scaling-based weight space symmetry property in rectified nonlinear network will cause this negative effect. Therefore, we propose to constrain the incoming weights of each neuron to be unit-norm, which is formulated as an optimization problem over Oblique manifold. A simple yet efficient method referred to as projection based weight normalization (PBWN) is also developed to solve this problem. PBWN executes standard gradient updates, followed by projecting the updated weight back to Oblique manifold. This proposed method has the property of regularization and collaborates well with the commonly used batch normalization technique. We conduct comprehensive experiments on several widely-used image datasets including CIFAR-10, CIFAR-100, SVHN and ImageNet for supervised learning over the state-of-the-art convolutional neural networks, such as Inception, VGG and residual networks. The results show that our method is able to improve the performance of DNNs with different architectures consistently. We also apply our method to Ladder network for semi-supervised learning on permutation invariant MNIST dataset, and our method outperforms the state-of-the-art methods: we obtain test errors as 2.52 , 1.06 , and 0.91 with only 20, 50, and 100 labeled samples, respectively. Convolutional neural nets (CNNs) have demonstrated remarkable performance in recent history. Such approaches tend to work in a "unidirectional" bottom-up feed-forward fashion. However, practical experience and biological evidence tells us that feedback plays a crucial role, particularly for detailed spatial understanding tasks. This work explores "bidirectional" architectures that also reason with top-down feedback: neural units are influenced by both lower and higher-level units. We do so by treating units as rectified latent variables in a quadratic energy function, which can be seen as a hierarchical Rectified Gaussian model (RGs) [39]. We show that RGs can be optimized with a quadratic program (QP), that can in turn be optimized with a recurrent neural network (with rectified linear units). This allows RGs to be trained with GPU-optimized gradient descent. From a theoretical perspective, RGs help establish a connection between CNNs and hierarchical probabilistic models. From a practical perspective, RGs are well suited for detailed spatial tasks that can benefit from top-down reasoning. We illustrate them on the challenging task of keypoint localization under occlusions, where local bottom-up evidence may be misleading. We demonstrate state-of-the-art results on challenging benchmarks. The prevalent approach to sequence to sequence learning maps an input sequence to a variable length output sequence via recurrent neural networks. We introduce an architecture based entirely on convolutional neural networks. Compared to recurrent models, computations over all elements can be fully parallelized during training to better exploit the GPU hardware and optimization is easier since the number of non-linearities is fixed and independent of the input length. Our use of gated linear units eases gradient propagation and we equip each decoder layer with a separate attention module. We outperform the accuracy of the deep LSTM setup of (2016) on both WMT'14 English-German and WMT'14 English-French translation at an order of magnitude faster speed, both on GPU and CPU.* Convolutional neural networks (CNNs) have become the dominant neural network architecture for solving many state-of-the-art (SOA) visual processing tasks. Even though graphical processing units are most often used in training and deploying CNNs, their power efficiency is less than 10 GOp s W for single-frame runtime inference. We propose a flexible and efficient CNN accelerator architecture called NullHop that implements SOA CNNs useful for low-power and low-latency application scenarios. NullHop exploits the sparsity of neuron activations in CNNs to accelerate the computation and reduce memory requirements. The flexible architecture allows high utilization of available computing resources across kernel sizes ranging from @math to @math . NullHop can process up to 128 input and 128 output feature maps per layer in a single pass. We implemented the proposed architecture on a Xilinx Zynq field-programmable gate array (FPGA) platform and presented the results showing how our implementation reduces external memory transfers and compute time in five different CNNs ranging from small ones up to the widely known large VGG16 and VGG19 CNNs. Postsynthesis simulations using Mentor Modelsim in a 28-nm process with a clock frequency of 500 MHz show that the VGG19 network achieves over 450 GOp s. By exploiting sparsity, NullHop achieves an efficiency of 368 , maintains over 98 utilization of the multiply–accumulate units, and achieves a power efficiency of over 3 TOp s W in a core area of 6.3 mm2. As further proof of NullHop’s usability, we interfaced its FPGA implementation with a neuromorphic event camera for real-time interactive demonstrations. Previous theoretical work on deep learning and neural network optimization tend to focus on avoiding saddle points and local minima. However, the practical observation is that, at least in the case of the most successful Deep Convolutional Neural Networks (DCNNs), practitioners can always increase the network size to fit the training data (an extreme example would be [1]). The most successful DCNNs such as VGG and ResNets are best used with a degree of "overparametrization". In this work, we characterize with a mix of theory and experiments, the landscape of the empirical risk of overparametrized DCNNs. We first prove in the regression framework the existence of a large number of degenerate global minimizers with zero empirical error (modulo inconsistent equations). The argument that relies on the use of Bezout theorem is rigorous when the RELUs are replaced by a polynomial nonlinearity (which empirically works as well). As described in our Theory III [2] paper, the same minimizers are degenerate and thus very likely to be found by SGD that will furthermore select with higher probability the most robust zero-minimizer. We further experimentally explored and visualized the landscape of empirical risk of a DCNN on CIFAR-10 during the entire training process and especially the global minima. Finally, based on our theoretical and experimental results, we propose an intuitive model of the landscape of DCNN's empirical loss surface, which might not be as complicated as people commonly believe. This paper presents a new approach for learning in structured domains (SDs) using a constructive neural network for graphs (NN4G). The new model allows the extension of the input domain for supervised neural networks to a general class of graphs including both acyclic cyclic, directed undirected labeled graphs. In particular, the model can realize adaptive contextual transductions, learning the mapping from graphs for both classification and regression tasks. In contrast to previous neural networks for structures that had a recursive dynamics, NN4G is based on a constructive feedforward architecture with state variables that uses neurons with no feedback connections. The neurons are applied to the input graphs by a general traversal process that relaxes the constraints of previous approaches derived by the causality assumption over hierarchical input data. Moreover, the incremental approach eliminates the need to introduce cyclic dependencies in the definition of the system state variables. In the traversal process, the NN4G units exploit (local) contextual information of the graphs vertices. In spite of the simplicity of the approach, we show that, through the compositionality of the contextual information developed by the learning, the model can deal with contextual information that is incrementally extended according to the graphs topology. The effectiveness and the generality of the new approach are investigated by analyzing its theoretical properties and providing experimental results. Ability of deep networks to extract high level features and of recurrent networks to perform time-series inference have been studied. In view of universality of one hidden layer network at approximating functions under weak constraints, the benefit of multiple layers is to enlarge the space of dynamical systems approximated or, given the space, reduce the number of units required for a certain error. Traditionally shallow networks with manually engineered features are used, back-propagation extent is limited to one and attempt to choose a large number of hidden units to satisfy the Markov condition is made. In case of Markov models, it has been shown that many systems need to be modeled as higher order. In the present work, we present deep recurrent networks with longer backpropagation through time extent as a solution to modeling systems that are high order and to predicting ahead. We study epileptic seizure suppression electro-stimulator. Extraction of manually engineered complex features and prediction employing them has not allowed small low-power implementations as, to avoid possibility of surgery, extraction of any features that may be required has to be included. In this solution, a recurrent neural network performs both feature extraction and prediction. We prove analytically that adding hidden layers or increasing backpropagation extent increases the rate of decrease of approximation error. A Dynamic Programming (DP) training procedure employing matrix operations is derived. DP and use of matrix operations makes the procedure efficient particularly when using data-parallel computing. The simulation studies show the geometry of the parameter space, that the network learns the temporal structure, that parameters converge while model output displays same dynamic behavior as the system and greater than .99 Average Detection Rate on all real seizure data tried. Recurrent neural networks are a powerful tool for modeling sequential data, but the dependence of each timestep's computation on the previous timestep's output limits parallelism and makes RNNs unwieldy for very long sequences. We introduce quasi-recurrent neural networks (QRNNs), an approach to neural sequence modeling that alternates convolutional layers, which apply in parallel across timesteps, and a minimalist recurrent pooling function that applies in parallel across channels. Despite lacking trainable recurrent layers, stacked QRNNs have better predictive accuracy than stacked LSTMs of the same hidden size. Due to their increased parallelism, they are up to 16 times faster at train and test time. Experiments on language modeling, sentiment classification, and character-level neural machine translation demonstrate these advantages and underline the viability of QRNNs as a basic building block for a variety of sequence tasks.