Conditional computation aims to increase the size and accuracy of a network, at a small increase in inference cost. Previous hard-routing models explicitly route the input to a subset of experts. We propose soft conditional computation, which, in contrast, utilizes all experts while still permitting efficient inference through parameter routing. Concretely, for a given convolutional layer, we wish to compute a linear combination of @math experts @math , where @math are functions of the input learned through gradient descent. A straightforward evaluation requires @math convolutions. We propose an equivalent form of the above computation, @math , which requires only a single convolution. We demonstrate the efficacy of our method, named CondConv, by scaling up the MobileNetV1, MobileNetV2, and ResNet-50 model architectures to achieve higher accuracy while retaining efficient inference. On the ImageNet classification dataset, CondConv improves the top-1 validation accuracy of the MobileNetV1(0.5x) model from 63.8 to 71.6 while only increasing inference cost by 27 . On COCO object detection, CondConv improves the minival mAP of a MobileNetV1(1.0x) SSD model from 20.3 to 22.4 with just a 4 increase in inference cost.
Hydranets @cite_13 is a hard-routing approach for vision that can also be trained with gradient descent, but requires an unsupervised clustering-based method to partition examples to perform well. Increasing the number of experts evaluated at inference time improves performance of Hydranets, but results in increased inference cost. does not require auxiliary loss functions for learning the routing functions, and allows for the use of all experts at a small inference cost.
@cite_13
2798722023
There is growing interest in improving the design of deep network architectures to be both accurate and low cost. This paper explores semantic specialization as a mechanism for improving the computational efficiency (accuracy-per-unit-cost) of inference in the context of image classification. Specifically, we propose a network architecture template called HydraNet, which enables state-of-the-art architectures for image classification to be transformed into dynamic architectures which exploit conditional execution for efficient inference. HydraNets are wide networks containing distinct components specialized to compute features for visually similar classes, but they retain efficiency by dynamically selecting only a small number of components to evaluate for any one input image. This design is made possible by a soft gating mechanism that encourages component specialization during training and accurately performs component selection during inference. We evaluate the HydraNet approach on both the CIFAR-100 and ImageNet classification tasks. On CIFAR, applying the HydraNet template to the ResNet and DenseNet family of models reduces inference cost by 2-4A— while retaining the accuracy of the baseline architectures. On ImageNet, applying the HydraNet template improves accuracy up to 2.5 when compared to an efficient baseline architecture with similar inference cost. Many computer vision problems can be formulated in a Bayesian framework with Markov Random Field (MRF) or Conditional Random Field (CRF) priors. Usually, the model assumes that a full Maximum A Posteriori (MAP) estimation will be performed for inference, which can be really slow in practice. In this paper, we argue that through appropriate training, a MRF CRF model can be trained to perform very well on a suboptimal inference algorithm. The model is trained together with a fast inference algorithm through an optimization of a loss function on a training set containing pairs of input images and desired outputs. A validation set can be used in this approach to estimate the generalization performance of the trained system. We apply the proposed method to an image denoising application, training a Fields of Experts MRF together with a 1-4 iteration gradient descent inference algorithm. Experimental validation on unseen data shows that the proposed training approach obtains an improved benchmark performance as well as a 1000-3000 times speedup compared to the Fields of Experts MRF trained with contrastive divergence. Using the new approach, image denoising can be performed in real-time, at 8 fps on a single CPU for a 256 × 256 image sequence, with close to state-of-the-art accuracy. Many machine learning systems are built to solve the hardest examples of a particular task, which often makes them large and expensive to run---especially with respect to the easier examples, which might require much less computation. For an agent with a limited computational budget, this "one-size-fits-all" approach may result in the agent wasting valuable computation on easy examples, while not spending enough on hard examples. Rather than learning a single, fixed policy for solving all instances of a task, we introduce a metacontroller which learns to optimize a sequence of "imagined" internal simulations over predictive models of the world in order to construct a more informed, and more economical, solution. The metacontroller component is a model-free reinforcement learning agent, which decides both how many iterations of the optimization procedure to run, as well as which model to consult on each iteration. The models (which we call "experts") can be state transition models, action-value functions, or any other mechanism that provides information useful for solving the task, and can be learned on-policy or off-policy in parallel with the metacontroller. When the metacontroller, controller, and experts were trained with "interaction networks" (, 2016) as expert models, our approach was able to solve a challenging decision-making problem under complex non-linear dynamics. The metacontroller learned to adapt the amount of computation it performed to the difficulty of the task, and learned how to choose which experts to consult by factoring in both their reliability and individual computational resource costs. This allowed the metacontroller to achieve a lower overall cost (task loss plus computational cost) than more traditional fixed policy approaches. These results demonstrate that our approach is a powerful framework for using... Many machine learning systems are built to solve the hardest examples of a particular task, which often makes them large and expensive to run---especially with respect to the easier examples, which might require much less computation. For an agent with a limited computational budget, this "one-size-fits-all" approach may result in the agent wasting valuable computation on easy examples, while not spending enough on hard examples. Rather than learning a single, fixed policy for solving all instances of a task, we introduce a metacontroller which learns to optimize a sequence of "imagined" internal simulations over predictive models of the world in order to construct a more informed, and more economical, solution. The metacontroller component is a model-free reinforcement learning agent, which decides both how many iterations of the optimization procedure to run, as well as which model to consult on each iteration. The models (which we call "experts") can be state transition models, action-value functions, or any other mechanism that provides information useful for solving the task, and can be learned on-policy or off-policy in parallel with the metacontroller. When the metacontroller, controller, and experts were trained with "interaction networks" (, 2016) as expert models, our approach was able to solve a challenging decision-making problem under complex non-linear dynamics. The metacontroller learned to adapt the amount of computation it performed to the difficulty of the task, and learned how to choose which experts to consult by factoring in both their reliability and individual computational resource costs. This allowed the metacontroller to achieve a lower overall cost (task loss plus computational cost) than more traditional fixed policy approaches. These results demonstrate that our approach is a powerful framework for using rich forward models for efficient model-based reinforcement learning. Our first contribution in this paper is a theoretical investigation of curriculum learning in the context of stochastic gradient descent when optimizing the least squares loss function. We prove that the rate of convergence of an ideal curriculum learning method in monotonically increasing with the difficulty of the examples, and that this increase in convergence rate is monotonically decreasing as training proceeds. In our second contribution we analyze curriculum learning in the context of training a CNN for image classification. Here one crucial problem is the means to achieve a curriculum. We describe a method which infers the curriculum by way of transfer learning from another network, pre-trained on a different task. While this approach can only approximate the ideal curriculum, we observe empirically similar behavior to the one predicted by the theory, namely, a significant boost in convergence speed at the beginning of training. When the task is made more difficult, improvement in generalization performance is observed. Finally, curriculum learning exhibits robustness against unfavorable conditions such as strong regularization. Over the past decade there has been considerable interest in spectral algorithms for learning Predictive State Representations (PSRs). Spectral algorithms have appealing theoretical guarantees; however, the resulting models do not always perform well on inference tasks in practice. One reason for this behavior is the mismatch between the intended task (accurate filtering or prediction) and the loss function being optimized by the algorithm (estimation error in model parameters). A natural idea is to improve performance by refining PSRs using an algorithm such as EM. Unfortunately it is not obvious how to apply apply an EM style algorithm in the context of PSRs as the Log Likelihood is not well defined for all PSRs. We show that it is possible to overcome this problem using ideas from Predictive State Inference Machines. We combine spectral algorithms for PSRs as a consistent and efficient initialization with PSIM-style updates to refine the resulting model parameters. By combining these two ideas we develop Inference Gradients, a simple, fast, and robust method for practical learning of PSRs. Inference Gradients performs gradient descent in the PSR parameter space to optimize an inference-based loss function like PSIM. Because Inference Gradients uses a spectral initialization we get the same consistency benefits as PSRs. We show that Inference Gradients outperforms both PSRs and PSIMs on real and synthetic data sets. Imitation learning of sequential, goal-directed behavior by standard supervised techniques is often difficult. We frame learning such behaviors as a maximum margin structured prediction problem over a space of policies. In this approach, we learn mappings from features to cost so an optimal policy in an MDP with these cost mimics the expert's behavior. Further, we demonstrate a simple, provably efficient approach to structured maximum margin learning, based on the subgradient method, that leverages existing fast algorithms for inference. Although the technique is general, it is particularly relevant in problems where A* and dynamic programming approaches make learning policies tractable in problems beyond the limitations of a QP formulation. We demonstrate our approach applied to route planning for outdoor mobile robots, where the behavior a designer wishes a planner to execute is often clear, while specifying cost functions that engender this behavior is a much more difficult task. It is possible to combine multiple latent-variable models of the same data by multiplying their probability distributions together and then renormalizing. This way of combining individual "expert" models makes it hard to generate samples from the combined model but easy to infer the values of the latent variables of each expert, because the combination rule ensures that the latent variables of different experts are conditionally independent when given the data. A product of experts (PoE) is therefore an interesting candidate for a perceptual system in which rapid inference is vital and generation is unnecessary. Training a PoE by maximizing the likelihood of the data is difficult because it is hard even to approximate the derivatives of the renormalization term in the combination rule. Fortunately, a PoE can be trained using a different objective function called "contrastive divergence" whose derivatives with regard to the parameters can be approximated accurately and efficiently. Examples are presented of contrastive divergence learning using several types of expert on several types of data. A challenge for statistical learning is to deal with large data sets, e.g. in data mining. The training time of ordinary Support Vector Machines is at least quadratic, which raises a serious research challenge if we want to deal with data sets of millions of examples. We propose a "hard parallelizable mixture" methodology which yields significantly reduced training time through modularization and parallelization: the training data is iteratively partitioned by a "gater" model in such a way that it becomes easy to learn an "expert" model separately in each region of the partition. A probabilistic extension and the use of a set of generative models allows representing the gater so that all pieces of the model are locally trained. For SVMs, time complexity appears empirically to local growth linearly with the number of examples, while generalization performance can be enhanced. For the probabilistic version of the algorithm, the iterative algorithm probably goes down in a cost function that is an upper bound on the negative log-likelihood. There is an increasing interest on accelerating neural networks for real-time applications. We study the student-teacher strategy, in which a small and fast student network is trained with the auxiliary information learned from a large and accurate teacher network. We propose to use conditional adversarial networks to learn the loss function to transfer knowledge from teacher to student. The proposed method is particularly effective for relatively small student networks. Moreover, experimental results show the effect of network size when the modern networks are used as student. We empirically study the trade-off between inference time and classification accuracy, and provide suggestions on choosing a proper student network. We consider the problem of imitation learning where the examples, demonstrated by an expert, cover only a small part of a large state space. Inverse Reinforcement Learning (IRL) provides an ecient tool for generalizing the demonstration, based on the assumption that the expert is optimally acting in a Markov Decision Process (MDP). Most of the past work on IRL requires that a (near)optimal policy can be computed for dierent reward functions. However, this requirement can hardly be satised in systems with a large, or continuous, state space. In this paper, we propose a model-free IRL algorithm, where the relative entropy between the empirical distribution of the state-action trajectories under a baseline policy and their distribution under the learned policy is minimized by stochastic gradient descent. We compare this new approach to well-known IRL algorithms using learned MDP models. Empirical results on simulated car racing, gridworld and ball-in-a-cup problems show that our approach is able to learn good policies from a small number of demonstrations. We generalize the recent relative loss bounds for on-line algorithms where the additional loss of the algorithm on the whole sequence of examples over the loss of the best expert is bounded. The generalization allows the sequence to be partitioned into segments, and the goal is to bound the additional loss of the algorithm over the sum of the losses of the best experts for each segment. This is to model situations in which the examples change and different experts are best for certain segments of the sequence of examples. In the single segment case, the additional loss is proportional to log n, where n is the number of experts and the constant of proportionality depends on the loss function. Our algorithms do not produce the best partition; however the loss bound shows that our predictions are close to those of the best partition. When the number of segments is k+1 and the sequence is of length e, we can bound the additional loss of our algorithm over the best partition by O(k n+k (e k)). For the case when the loss per trial is bounded by one, we obtain an algorithm whose additional loss over the loss of the best partition is independent of the length of the sequence. The additional loss becomes O(k n+ k (L k)), where L is the loss of the best partitionwith k+1 segments. Our algorithms for tracking the predictions of the best expert aresimple adaptations of Vovk's original algorithm for the single best expert case. As in the original algorithms, we keep one weight per expert, and spend O(1) time per weight in each trial. We introduce collaborative learning in which multiple classifier heads of the same network are simultaneously trained on the same training data to improve generalization and robustness to label noise with no extra inference cost. It acquires the strengths from auxiliary training, multi-task learning and knowledge distillation. There are two important mechanisms involved in collaborative learning. First, the consensus of multiple views from different classifier heads on the same example provides supplementary information as well as regularization to each classifier, thereby improving generalization. Second, intermediate-level representation (ILR) sharing with backpropagation rescaling aggregates the gradient flows from all heads, which not only reduces training computational complexity, but also facilitates supervision to the shared layers. The empirical results on CIFAR and ImageNet datasets demonstrate that deep neural networks learned as a group in a collaborative way significantly reduce the generalization error and increase the robustness to label noise. We propose a novel method called deep convolutional decision jungle (CDJ) and its learning algorithm for image classification. The CDJ maintains the structure of standard convolutional neural networks (CNNs), i.e. multiple layers of multiple response maps fully connected. Each response map-or node-in both the convolutional and fully-connected layers selectively respond to class labels s.t. each data sample travels via a specific soft route of those activated nodes. The proposed method CDJ automatically learns features, whereas decision forests and jungles require pre-defined feature sets. Compared to CNNs, the method embeds the benefits of using data-dependent discriminative functions, which better handles multi-modal heterogeneous data; further,the method offers more diverse sparse network responses, which in turn can be used for cost-effective learning classification. The network is learnt by combining conventional softmax and proposed entropy losses in each layer. The entropy loss,as used in decision tree growing, measures the purity of data activation according to the class label distribution. The back-propagation rule for the proposed loss function is derived from stochastic gradient descent (SGD) optimization of CNNs. We show that our proposed method outperforms state-of-the-art methods on three public image classification benchmarks and one face verification dataset. We also demonstrate the use of auxiliary data labels, when available, which helps our method to learn more discriminative routing and representations and leads to improved classification. Machine learning models are often used at test-time subject to constraints and trade-offs not present at training-time. For example, a computer vision model operating on an embedded device may need to perform real-time inference, or a translation model operating on a cell phone may wish to bound its average compute time in order to be power-efficient. In this work we describe a mixture-of-experts model and show how to change its test-time resource-usage on a per-input basis using reinforcement learning. We test our method on a small MNIST-based example. While Gaussian processes (GPs) are the method of choice for regression tasks, they also come with practical difficulties, as inference cost scales cubic in time and quadratic in memory. In this paper, we introduce a natural and expressive way to tackle these problems, by incorporating GPs in sum-product networks (SPNs), a recently proposed tractable probabilistic model allowing exact and efficient inference. In particular, by using GPs as leaves of an SPN we obtain a novel flexible prior over functions, which implicitly represents an exponentially large mixture of local GPs. Exact and efficient posterior inference in this model can be done in a natural interplay of the inference mechanisms in GPs and SPNs. Thereby, each GP is -- similarly as in a mixture of experts approach -- responsible only for a subset of data points, which effectively reduces inference cost in a divide and conquer fashion. We show that integrating GPs into the SPN framework leads to a promising probabilistic regression model which is: (1) computational and memory efficient, (2) allows efficient and exact posterior inference, (3) is flexible enough to mix different kernel functions, and (4) naturally accounts for non-stationarities in time series. In a variate of experiments, we show that the SPN-GP model can learn input dependent parameters and hyper-parameters and is on par with or outperforms the traditional GPs as well as state of the art approximations on real-world data. In this paper we propose an approach to holistic scene understanding that reasons jointly about regions, location, class and spatial extent of objects, presence of a class in the image, as well as the scene type. Learning and inference in our model are efficient as we reason at the segment level, and introduce auxiliary variables that allow us to decompose the inherent high-order potentials into pairwise potentials between a few variables with small number of states (at most the number of classes). Inference is done via a convergent message-passing algorithm, which, unlike graph-cuts inference, has no submodularity restrictions and does not require potential specific moves. We believe this is very important, as it allows us to encode our ideas and prior knowledge about the problem without the need to change the inference engine every time we introduce a new potential. Our approach outperforms the state-of-the-art on the MSRC-21 benchmark, while being much faster. Importantly, our holistic model is able to improve performance in all tasks. Increasing depth and complexity in convolutional neural networks has enabled significant progress in visual perception tasks. However, incremental improvements in accuracy are often accompanied by exponentially deeper models that push the computational limits of modern hardware. These incremental improvements in accuracy imply that only a small fraction of the inputs require the additional model complexity. As a consequence, for any given image it is possible to bypass multiple stages of computation to reduce the cost of forward inference without affecting accuracy. We exploit this simple observation by learning to dynamically route computation through a convolutional network. We introduce dynamically routed networks (SkipNets) by adding gating layers that route images through existing convolutional networks and formulate the routing problem in the context of sequential decision making. We propose a hybrid learning algorithm which combines supervised learning and reinforcement learning to address the challenges of inherently non-differentiable routing decisions. We show SkipNet reduces computation by 30 - 90 while preserving the accuracy of the original model on four benchmark datasets. We compare SkipNet with SACT and ACT to show SkipNet achieves better accuracy with lower computation. We propose a neural language model capable of unsupervised syntactic structure induction. The model leverages the structure information to form better semantic representations and better language modeling. Standard recurrent neural networks are limited by their structure and fail to efficiently use syntactic information. On the other hand, tree-structured recursive networks usually require additional structural supervision at the cost of human expert annotation. In this paper, We propose a novel neural language model, called the Parsing-Reading-Predict Networks (PRPN), that can simultaneously induce the syntactic structure from unannotated sentences and leverage the inferred structure to learn a better language model. In our model, the gradient can be directly back-propagated from the language model loss into the neural parsing network. Experiments show that the proposed model can discover the underlying syntactic structure and achieve state-of-the-art performance on word character-level language model tasks. The Internet consists of rapidly increasing number of hosts interconnected by constantly evolving networks of links and routers. Interdomain routing in the Internet is coordinated by the Border Gateway Protocol (BGP). The BGP allows each autonomous system (AS) to choose its own administrative policy in selecting routes and propagating reachability information to others. These routing policies are constrained by the contractual commercial agreements between administrative domains. For example, an AS sets its policy so that it does not provide transit services between its providers. Such policies imply that AS relationships are an important aspect of the Internet structure. We propose an augmented AS graph representation that classifies AS relationships into customer-provider, peering, and sibling relationships. We classify the types of routes that can appear in BGP routing tables based on the relationships between the ASs in the path and present heuristic algorithms that infer AS relationships from BGP routing tables. The algorithms are tested on publicly available BGP routing tables. We verify our inference results with AT&T internal information on its relationship with neighboring ASs. As much as 99.1 of our inference results are confirmed by the AT&T internal information. We also verify our inferred sibling relationships with the information acquired from the WHOIS lookup service. More than half of our inferred sibling-to-sibling relationships are confirmed by the WHOIS lookup service. To the best of our knowledge, there has been no publicly available information about AS relationships and this is the first attempt in understanding and inferring AS relationships in the Internet. We show evidence that some routing table entries stem from router misconfigurations.