It is widely believed that the success of deep convolutional networks is based on progressively discarding uninformative variability about the input with respect to the problem at hand. This is supported empirically by the difficulty of recovering images from their hidden representations, in most commonly used network architectures. In this paper we show via a one-to-one mapping that this loss of information is not a necessary condition to learn representations that generalize well on complicated problems, such as ImageNet. Via a cascade of homeomorphic layers, we build the i-RevNet, a network that can be fully inverted up to the final projection onto the classes, i.e. no information is discarded. Building an invertible architecture is difficult, for one, because the local inversion is ill-conditioned, we overcome this by providing an explicit inverse. An analysis of i-RevNets learned representations suggests an alternative explanation for the success of deep networks by a progressive contraction and linear separation with depth. To shed light on the nature of the model learned by the i-RevNet we reconstruct linear interpolations between natural image representations.
Our main inspiration for this work is the recent reversible residual network (RevNet), introduced in @cite_7 . RevNets are in turn closely related to NICE and Real-NVP architectures , which make use of constrained Jacobian determinants for generative modeling. All these architectures are similar to the lifting scheme and Feistel cipher diagrams , as we will show. RevNets illustrate how to build invertible ResNet-type blocks that avoid storing intermediate activations necessary for the backward pass. However, RevNets still employ multiple non-invertible operators like max-pooling and downsampling operators as part of the network. As such, RevNets are not invertible by construction. In this paper, we show how to build an invertible type of RevNet architecture that performs competitively with RevNets on Imagenet, which we call @math -RevNet for invertible RevNet.
@cite_7
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It is widely believed that the success of deep convolutional networks is based on progressively discarding uninformative variability about the input with respect to the problem at hand. This is supported empirically by the difficulty of recovering images from their hidden representations, in most commonly used network architectures. In this paper we show that this loss of information is not a necessary condition to learn representations that generalize well on complicated problems, such as ImageNet. Via a cascade of homeomorphic layers, we build the i-RevNet, a network that can be fully inverted up to the final projection onto the classes, i.e. no information is discarded. Building an invertible architecture is difficult, for example, because the local inversion is ill-conditioned, we overcome this by providing an explicit inverse. An analysis of i-RevNet’s learned representations suggests an explanation of the good accuracy by a progressive contraction and linear separation with depth. To shed light on the nature of the model learned by the i-RevNet we reconstruct linear interpolations between natural images representations. Residual Networks (ResNets) have demonstrated significant improvement over traditional Convolutional Neural Networks (CNNs) on image classification, increasing in performance as networks grow both deeper and wider. However, memory consumption becomes a bottleneck as one needs to store all the intermediate activations for calculating gradients using backpropagation. In this work, we present the Reversible Residual Network (RevNet), a variant of ResNets where each layer's activations can be reconstructed exactly from the next layer's. Therefore, the activations for most layers need not be stored in memory during backprop. We demonstrate the effectiveness of RevNets on CIFAR and ImageNet, establishing nearly identical performance to equally-sized ResNets, with activation storage requirements independent of depth. Deep residual networks (ResNets) have significantly pushed forward the state-of-the-art on image classification, increasing in performance as networks grow both deeper and wider. However, memory consumption becomes a bottleneck, as one needs to store the activations in order to calculate gradients using backpropagation. We present the Reversible Residual Network (RevNet), a variant of ResNets where each layer's activations can be reconstructed exactly from the next layer's. Therefore, the activations for most layers need not be stored in memory during backpropagation. We demonstrate the effectiveness of RevNets on CIFAR-10, CIFAR-100, and ImageNet, establishing nearly identical classification accuracy to equally-sized ResNets, even though the activation storage requirements are independent of depth. In our work, we bridge deep neural network design with numerical differential equations. We show that many effective networks, such as ResNet, PolyNet, FractalNet and RevNet, can be interpreted as different numerical discretizations of differential equations. This finding brings us a brand new perspective on the design of effective deep architectures. We can take advantage of the rich knowledge in numerical analysis to guide us in designing new and potentially more effective deep networks. As an example, we propose a linear multi-step architecture (LM-architecture) which is inspired by the linear multi-step method solving ordinary differential equations. The LM-architecture is an effective structure that can be used on any ResNet-like networks. In particular, we demonstrate that LM-ResNet and LM-ResNeXt (i.e. the networks obtained by applying the LM-architecture on ResNet and ResNeXt respectively) can achieve noticeably higher accuracy than ResNet and ResNeXt on both CIFAR and ImageNet with comparable numbers of trainable parameters. In particular, on both CIFAR and ImageNet, LM-ResNet LM-ResNeXt can significantly compress ( @math ) the original networks while maintaining a similar performance. This can be explained mathematically using the concept of modified equation from numerical analysis. Last but not least, we also establish a connection between stochastic control and noise injection in the training process which helps to improve generalization of the networks. Furthermore, by relating stochastic training strategy with stochastic dynamic system, we can easily apply stochastic training to the networks with the LM-architecture. As an example, we introduced stochastic depth to LM-ResNet and achieve significant improvement over the original LM-ResNet on CIFAR10. A promising class of generative models maps points from a simple distribution to a complex distribution through an invertible neural network. Likelihood-based training of these models requires restricting their architectures to allow cheap computation of Jacobian determinants. Alternatively, the Jacobian trace can be used if the transformation is specified by an ordinary differential equation. In this paper, we use Hutchinson's trace estimator to give a scalable unbiased estimate of the log-density. The result is a continuous-time invertible generative model with unbiased density estimation and one-pass sampling, while allowing unrestricted neural network architectures. We demonstrate our approach on high-dimensional density estimation, image generation, and variational inference, achieving the state-of-the-art among exact likelihood methods with efficient sampling. In this paper we describe a new mobile architecture, MobileNetV2, that improves the state of the art performance of mobile models on multiple tasks and benchmarks as well as across a spectrum of different model sizes. We also describe efficient ways of applying these mobile models to object detection in a novel framework we call SSDLite. Additionally, we demonstrate how to build mobile semantic segmentation models through a reduced form of DeepLabv3 which we call Mobile DeepLabv3. The MobileNetV2 architecture is based on an inverted residual structure where the input and output of the residual block are thin bottleneck layers opposite to traditional residual models which use expanded representations in the input an MobileNetV2 uses lightweight depthwise convolutions to filter features in the intermediate expansion layer. Additionally, we find that it is important to remove non-linearities in the narrow layers in order to maintain representational power. We demonstrate that this improves performance and provide an intuition that led to this design. Finally, our approach allows decoupling of the input output domains from the expressiveness of the transformation, which provides a convenient framework for further analysis. We measure our performance on Imagenet classification, COCO object detection, VOC image segmentation. We evaluate the trade-offs between accuracy, and number of operations measured by multiply-adds (MAdd), as well as the number of parameters In this work we compute lower Lipschitz bounds of @math pooling operators for @math as well as @math pooling operators preceded by half-rectification layers. These give sufficient conditions for the design of invertible neural network layers. Numerical experiments on MNIST and image patches confirm that pooling layers can be inverted with phase recovery algorithms. Moreover, the regularity of the inverse pooling, controlled by the lower Lipschitz constant, is empirically verified with a nearest neighbor regression. Deep residual networks have emerged as a family of extremely deep architectures showing compelling accuracy and nice convergence behaviors. In this paper, we analyze the propagation formulations behind the residual building blocks, which suggest that the forward and backward signals can be directly propagated from one block to any other block, when using identity mappings as the skip connections and after-addition activation. A series of ablation experiments support the importance of these identity mappings. This motivates us to propose a new residual unit, which makes training easier and improves generalization. We report improved results using a 1001-layer ResNet on CIFAR-10 (4.62 error) and CIFAR-100, and a 200-layer ResNet on ImageNet. Code is available at: this https URL Deep residual networks have emerged as a family of extremely deep architectures showing compelling accuracy and nice convergence behaviors. In this paper, we analyze the propagation formulations behind the residual building blocks, which suggest that the forward and backward signals can be directly propagated from one block to any other block, when using identity mappings as the skip connections and after-addition activation. A series of ablation experiments support the importance of these identity mappings. This motivates us to propose a new residual unit, which makes training easier and improves generalization. We report improved results using a 1001-layer ResNet on CIFAR-10 (4.62 error) and CIFAR-100, and a 200-layer ResNet on ImageNet. Code is available at: https: github.com KaimingHe resnet-1k-layers. Shayevitz and Feder proposed a capacity-achieving sequential transmission scheme for memoryless channels called posterior matching (PM). The proof of capacity achievability of PM is involved and requires invertibility of the PM kernel (also referred to as one-step invertibility). Recent work by the same authors provided a simpler proof but still requires PM kernel invertibility. This paper demonstrates a novel method to establish robust control and stability of microgrid connected with photovoltaic (PV) grid tie inverter, battery storage with bidirectional inverter, and diesel generator. The proposed control scheme enables optimum power sharing among the sources based on the changes in generation due to intermittent nature of PV source and level of energy stored in battery. Power flow control has been achieved by varying the active power generated by the PV inverter as a function of the system frequency in the islanded mode of operation. Detailed analysis has been carried out in MATLAB Simulink tool and the captured results are found to effective and same has been confirmed with hardware prototype setup with PV inverter and bidirectional battery charger. In this paper we describe a new mobile architecture, MobileNetV2, that improves the state of the art performance of mobile models on multiple tasks and benchmarks as well as across a spectrum of different model sizes. We also describe efficient ways of applying these mobile models to object detection in a novel framework we call SSDLite. Additionally, we demonstrate how to build mobile semantic segmentation models through a reduced form of DeepLabv3 which we call Mobile DeepLabv3. is based on an inverted residual structure where the shortcut connections are between the thin bottleneck layers. The intermediate expansion layer uses lightweight depthwise convolutions to filter features as a source of non-linearity. Additionally, we find that it is important to remove non-linearities in the narrow layers in order to maintain representational power. We demonstrate that this improves performance and provide an intuition that led to this design. Finally, our approach allows decoupling of the input output domains from the expressiveness of the transformation, which provides a convenient framework for further analysis. We measure our performance on ImageNet [1] classification, COCO object detection [2], VOC image segmentation [3]. We evaluate the trade-offs between accuracy, and number of operations measured by multiply-adds (MAdd), as well as actual latency, and the number of parameters. Embedded systems in safety-critical environments demand safety guarantees while providing many useful services that are too complex to formally verify or fully test. Existing application-level fault-tolerance methods, even if formally verified, leave the system vulnerable to errors in the real-time operating system (RTOS), middleware, and microprocessor. We introduce the System-Level Simplex Architecture, which uses hardware software co-design to provide fail-operational guarantees for both logical application-level faults, as well as faults in previously dependent layers including the RTOS and microprocessor. We also provide an end-to-end design process for the System-Level Simplex Architecture where the AADL architecture description is automatically constructed and checked and the VHDL hardware code is generated.To show the efficacy of System-Level Simplex design, we apply the approach to both a classic inverted pendulum and a cardiac pacemaker. We perform fault-injection tests on the inverted pendulum design which demonstrate robustness in spite of software controller and operating system faults. For the pacemaker, we contrast the provided safety guarantees with those of a previous-generation pacemaker. Inverting a function f at a given point y in its range involves finding any x in the domain such that f(x) = y. This is a general problem. We wish to find a heuristic for inverting those functions which satisfy certain statistical properties similar to those of random functions. As an example, we choose popular secure hash functions which are expected to be hard to invert and any successful strategy to do so will be quite useful. This provides an excellent challenge for SAT solvers. We first find the limits of inverting via direct encoding of these functions as SAT: for MD4 this is one round and twelve steps and for MD5 it is one round and ten steps. Then, we show that by adding customized constraints obtained by modifying an earlier attack by Dobbertin, we can invert MD4 up to 2 rounds and 7 steps in < 8 hours. Existing billion-scale nearest neighbor search systems have mostly been compared on a single dataset of a billion of SIFT vectors, where systems based on the Inverted Multi-Index (IMI) have been performing very well, achieving state-of-the-art recall in several milliseconds. SIFT-like descriptors, however, are quickly being replaced with descriptors based on deep neural networks (DNN) that provide better performance for many computer vision tasks. In this paper, we introduce a new dataset of one billion descriptors based on DNNs and reveal the relative inefficiency of IMI-based indexing for such descriptors compared to SIFT data. We then introduce two new indexing structures, the Non-Orthogonal Inverted Multi-Index (NO-IMI) and the Generalized Non-Orthogonal Inverted Multi-Index (GNO-IMI). We show that due to additional flexibility, the new structures are able to adapt to DNN descriptor distribution in a better way. In particular, extensive experiments on the new dataset demonstrate that these data structures provide considerably better trade-off between the speed of retrieval and recall, given similar amount of memory, as compared to the standard Inverted Multi-Index. In content-based image retrieval, inverted indexes allow fast access to database images and summarize all knowledge about the database. Indexing multiple clues of image contents allows retrieval algorithms search for relevant images from different perspectives, which is appealing to deliver satisfactory user experiences. However, when incorporating diverse image features during online retrieval, it is challenging to ensure retrieval efficiency and scalability. In this paper, for large-scale image retrieval, we propose a semantic-aware co-indexing algorithm to jointly embed two strong cues into the inverted indexes: 1) local invariant features that are robust to delineate low-level image contents, and 2) semantic attributes from large-scale object recognition that may reveal image semantic meanings. Specifically, for an initial set of inverted indexes of local features, we utilize semantic attributes to filter out isolated images and insert semantically similar images to this initial set. Encoding these two distinct and complementary cues together effectively enhances the discriminative capability of inverted indexes. Such co-indexing operations are totally off-line and introduce small computation overhead to online retrieval, because only local features but no semantic attributes are employed for the query. Hence, this co-indexing is different from existing image retrieval methods fusing multiple features or retrieval results. Extensive experiments and comparisons with recent retrieval methods manifest the competitive performance of our method. Abstract Invertible wavelet transforms that map integers to integers have important applications in lossless coding. In this paper we present two approaches to build integer to integer wavelet transforms. The first approach is to adapt the precoder of Laroiaet al,which is used in information transmission; we combine it with expansion factors for the high and low pass band in subband filtering. The second approach builds upon the idea of factoring wavelet transforms into so-called lifting steps. This allows the construction of an integer version of every wavelet transform. Finally, we use these approaches in a lossless image coder and compare the results to those given in the literature. Full-text information retrieval systems have traditionally been designed for archival environments. They often provide little or no support for adding new documents to an existing document collection, requiring instead that the entire collection be re-indexed. Modern applications, such as information filtering, operate in dynamic environments that require frequent additions to document collections. We provide this ability using a traditional inverted file index built on top of a persistent object store. The data management facilities of the persistent object store are used to produce efficient incremental update of the inverted lists. We describe our system and present experimental results showing superior incremental indexing and competitive query processing performance. The visual system must not only recognize and localize objects, but perform much richer inferences about the underlying causes in the world that give rise to observed sense data. Analyzing scenes by inverting causal generative models, also known as "analysis-by-synthesis", has a long history in computational vision, and these models have some behavioral support, but they are typically too slow to support online perception and have no known mapping to actual neural circuits. Here we present a neurally plausible model for efficiently inverting generative models of images and test it as a precise account of one aspect of high-level vision, the perception of faces. The model is based on a deep neural network that learns to invert a three-dimensional (3D) face graphics program in a single fast feedforward pass. It successfully explains both human behavioral data and multiple levels of neural processing in non-human primates, as well as a classic illusion, the "hollow face" effect. The model also fits qualitatively better than state-of-the-art computer vision models, and suggests an interpretable reverse-engineering account of how images are transformed into scene percepts in the primate ventral stream. A new data structure for efficient similarity search in very large datasets of high-dimensional vectors is introduced. This structure called the inverted multi-index generalizes the inverted index idea by replacing the standard quantization within inverted indices with product quantization. For very similar retrieval complexity and pre-processing time, inverted multi-indices achieve a much denser subdivision of the search space compared to inverted indices, while retaining their memory efficiency. Our experiments with large datasets of SIFT and GIST vectors demonstrate that because of the denser subdivision, inverted multi-indices are able to return much shorter candidate lists with higher recall. Augmented with a suitable reranking procedure, multi-indices were able to significantly improve the speed of approximate nearest neighbor search on the dataset of 1 billion SIFT vectors compared to the best previously published systems, while achieving better recall and incurring only few percent of memory overhead.