CondenseNet: An Efficient DenseNet using Learned Group Convolutions

Deep neural networks are increasingly used on mobile devices, where computational resources are limited. In this paper we develop CondenseNet, a novel network architecture with unprecedented efficiency. It combines dense connectivity with a novel module called learned group convolution. The dense connectivity facilitates feature re-use in the network, whereas learned group convolutions remove connections between layers for which this feature re-use is superfluous. At test time, our model can be implemented using standard group convolutions, allowing for efficient computation in practice. Our experiments show that CondenseNets are far more efficient than state-of-the-art compact convolutional networks such as MobileNets and ShuffleNets.

Multi-Scale Dense Networks for Resource Efficient Image Classification

In this paper we investigate image classification with computational resource limits at test time. Two such settings are: 1. anytime classification, where the network's prediction for a test example is progressively updated, facilitating the output of a prediction at any time; and 2. budgeted batch classification, where a fixed amount of computation is available to classify a set of examples that can be spent unevenly across "easier" and "harder" inputs. In contrast to most prior work, such as the popular Viola and Jones algorithm, our approach is based on convolutional neural networks. We train multiple classifiers with varying resource demands, which we adaptively apply during test time. To maximally re-use computation between the classifiers, we incorporate them as early-exits into a single deep convolutional neural network and inter-connect them with dense connectivity. To facilitate high quality classification early on, we use a two-dimensional multi-scale network architecture that maintains coarse and fine level features all-throughout the network. Experiments on three image-classification tasks demonstrate that our framework substantially improves the existing state-of-the-art in both settings.

Product Kernel Interpolation for Scalable Gaussian Processes

Recent work shows that inference for Gaussian processes can be performed efficiently using iterative methods that rely only on matrix-vector multiplications (MVMs). Structured Kernel Interpolation (SKI) exploits these techniques by deriving approximate kernels with very fast MVMs. Unfortunately, such strategies suffer badly from the curse of dimensionality. We develop a new technique for MVM based learning that exploits product kernel structure. We demonstrate that this technique is broadly applicable, resulting in linear rather than exponential runtime with dimension for SKI, as well as state-of-the-art asymptotic complexity for multi-task GPs.

Densely Connected Convolutional Networks

Recent work has shown that convolutional networks can be substantially deeper, more accurate, and efficient to train if they contain shorter connections between layers close to the input and those close to the output. In this paper, we embrace this observation and introduce the Dense Convolutional Network (DenseNet), which connects each layer to every other layer in a feed-forward fashion. Whereas traditional convolutional networks with L layers have L connections - one between each layer and its subsequent layer - our network has L(L+1)/2 direct connections. For each layer, the feature-maps of all preceding layers are used as inputs, and its own feature-maps are used as inputs into all subsequent layers. DenseNets have several compelling advantages: they alleviate the vanishing-gradient problem, strengthen feature propagation, encourage feature reuse, and substantially reduce the number of parameters. We evaluate our proposed architecture on four highly competitive object recognition benchmark tasks (CIFAR-10, CIFAR-100, SVHN, and ImageNet). DenseNets obtain significant improvements over the state-of-the-art on most of them, whilst requiring less computation to achieve high performance. Code and pre-trained models are available at https://github.com/liuzhuang13/DenseNet .

On Fairness and Calibration

The machine learning community has become increasingly concerned with the potential for bias and discrimination in predictive models. This has motivated a growing line of work on what it means for a classification procedure to be "fair." In this paper, we investigate the tension between minimizing error disparity across different population groups while maintaining calibrated probability estimates. We show that calibration is compatible only with a single error constraint (i.e. equal false-negatives rates across groups), and show that any algorithm that satisfies this relaxation is no better than randomizing a percentage of predictions for an existing classifier. These unsettling findings, which extend and generalize existing results, are empirically confirmed on several datasets.

On Calibration of Modern Neural Networks

Confidence calibration -- the problem of predicting probability estimates representative of the true correctness likelihood -- is important for classification models in many applications. We discover that modern neural networks, unlike those from a decade ago, are poorly calibrated. Through extensive experiments, we observe that depth, width, weight decay, and Batch Normalization are important factors influencing calibration. We evaluate the performance of various post-processing calibration methods on state-of-the-art architectures with image and document classification datasets. Our analysis and experiments not only offer insights into neural network learning, but also provide a simple and straightforward recipe for practical settings: on most datasets, temperature scaling -- a single-parameter variant of Platt Scaling -- is surprisingly effective at calibrating predictions.

Memory-Efficient Implementation of DenseNets

The DenseNet architecture is highly computationally efficient as a result of feature reuse. However, a naive DenseNet implementation can require a significant amount of GPU memory: If not properly managed, pre-activation batch normalization and contiguous convolution operations can produce feature maps that grow quadratically with network depth. In this technical report, we introduce strategies to reduce the memory consumption of DenseNets during training. By strategically using shared memory allocations, we reduce the memory cost for storing feature maps from quadratic to linear. Without the GPU memory bottleneck, it is now possible to train extremely deep DenseNets. Networks with 14M parameters can be trained on a single GPU, up from 4M. A 264-layer DenseNet (73M parameters), which previously would have been infeasible to train, can now be trained on a single workstation with 8 NVIDIA Tesla M40 GPUs. On the ImageNet ILSVRC classification dataset, this large DenseNet obtains a state-of-the-art single-crop top-1 error of 20.26%.

Snapshot Ensembles: Train 1, get M for free

Ensembles of neural networks are known to be much more robust and accurate than individual networks. However, training multiple deep networks for model averaging is computationally expensive. In this paper, we propose a method to obtain the seemingly contradictory goal of ensembling multiple neural networks at no additional training cost. We achieve this goal by training a single neural network, converging to several local minima along its optimization path and saving the model parameters. To obtain repeated rapid convergence, we leverage recent work on cyclic learning rate schedules. The resulting technique, which we refer to as Snapshot Ensembling, is simple, yet surprisingly effective. We show in a series of experiments that our approach is compatible with diverse network architectures and learning tasks. It consistently yields lower error rates than state-of-the-art single models at no additional training cost, and compares favorably with traditional network ensembles. On CIFAR-10 and CIFAR-100 our DenseNet Snapshot Ensembles obtain error rates of 3.4% and 17.4% respectively.

Private Causal Inference

Causal inference deals with identifying which random variables "cause" or control other random variables. Recent advances on the topic of causal inference based on tools from statistical estimation and machine learning have resulted in practical algorithms for causal inference. Causal inference has the potential to have significant impact on medical research, prevention and control of diseases, and identifying factors that impact economic changes to name just a few. However, these promising applications for causal inference are often ones that involve sensitive or personal data of users that need to be kept private (e.g., medical records, personal finances, etc). Therefore, there is a need for the development of causal inference methods that preserve data privacy. We study the problem of inferring causality using the current, popular causal inference framework, the additive noise model (ANM) while simultaneously ensuring privacy of the users. Our framework provides differential privacy guarantees for a variety of ANM variants. We run extensive experiments, and demonstrate that our techniques are practical and easy to implement.

Deep Manifold Traversal: Changing Labels with Convolutional Features

Many tasks in computer vision can be cast as a "label changing" problem, where the goal is to make a semantic change to the appearance of an image or some subject in an image in order to alter the class membership. Although successful task-specific methods have been developed for some label changing applications, to date no general purpose method exists. Motivated by this we propose deep manifold traversal, a method that addresses the problem in its most general form: it first approximates the manifold of natural images then morphs a test image along a traversal path away from a source class and towards a target class while staying near the manifold throughout. The resulting algorithm is surprisingly effective and versatile. It is completely data driven, requiring only an example set of images from the desired source and target domains. We demonstrate deep manifold traversal on highly diverse label changing tasks: changing an individual's appearance (age and hair color), changing the season of an outdoor image, and transforming a city skyline towards nighttime.