Srikumar Ramalingam

Maximilian Böther, Abraham Sebastian, Pranjal Awasthi et al.

Modern datasets span billions of samples, making training on all available data infeasible. Selecting a high quality subset helps in reducing training costs and enhancing model quality. Submodularity, a discrete analogue of convexity, is commonly used for solving such subset selection problems. However, existing algorithms for optimizing submodular functions are sequential, and the prior distributed methods require at least one central machine to fit the target subset in DRAM. At billion datapoint scale, even the subset may not fit a single machine, and the sequential algorithms are prohibitively slow. In this paper, we relax the requirement of having a central machine for the target subset by proposing a novel distributed bounding algorithm with provable approximation guarantees. The algorithm iteratively bounds the minimum and maximum utility values to select high quality points and discard the unimportant ones. When bounding does not find the complete subset, we use a multi-round, partition-based distributed greedy algorithm to identify the remaining subset. We discuss how to implement these algorithms in a distributed data processing framework and empirically analyze different configurations. We find high quality subsets on CIFAR-100 and ImageNet with marginal or no loss in quality compared to centralized methods, and scale to a dataset with 13 billion points.

Seungyeon Kim, Daniel Glasner, Srikumar Ramalingam et al.

It is generally believed that robust training of extremely large networks is critical to their success in real-world applications. However, when taken to the extreme, methods that promote robustness can hurt the model's sensitivity to rare or underrepresented patterns. In this paper, we discuss this trade-off between sensitivity and robustness to natural (non-adversarial) perturbations by introducing two notions: contextual feature utility and contextual feature sensitivity. We propose Feature Contrastive Learning (FCL) that encourages a model to be more sensitive to the features that have higher contextual utility. Empirical results demonstrate that models trained with FCL achieve a better balance of robustness and sensitivity, leading to improved generalization in the presence of noise on both vision and NLP datasets.

Srikumar Ramalingam, Daniel Glasner, Kaushal Patel et al.

Deep learning has yielded extraordinary results in vision and natural language processing, but this achievement comes at a cost. Most models require enormous resources during training, both in terms of computation and in human labeling effort. We show that we can identify informative and diverse subsets of data that lead to deep learning models with similar performance as the ones trained with the original dataset. Prior methods have exploited diversity and uncertainty in submodular objective functions for choosing subsets. In addition to these measures, we show that balancing constraints on predicted class labels and decision boundaries are beneficial. We propose a novel formulation of these constraints using matroids, an algebraic structure that generalizes linear independence in vector spaces, and present an efficient greedy algorithm with constant approximation guarantees. We outperform competing baselines on standard classification datasets such as CIFAR-10, CIFAR-100, ImageNet, as well as long-tailed datasets such as CIFAR-100-LT.

Sadeep Jayasumana, Srikumar Ramalingam, Sanjiv Kumar

We propose a kernelized classification layer for deep networks. Although conventional deep networks introduce an abundance of nonlinearity for representation (feature) learning, they almost universally use a linear classifier on the learned feature vectors. We advocate a nonlinear classification layer by using the kernel trick on the softmax cross-entropy loss function during training and the scorer function during testing. However, the choice of the kernel remains a challenge. To tackle this, we theoretically show the possibility of optimizing over all possible positive definite kernels applicable to our problem setting. This theory is then used to device a new kernelized classification layer that learns the optimal kernel function for a given problem automatically within the deep network itself. We show the usefulness of the proposed nonlinear classification layer on several datasets and tasks.

Abhinav Kumar, Thiago Serra, Srikumar Ramalingam

Two networks are equivalent if they produce the same output for any given input. In this paper, we study the possibility of transforming a deep neural network to another network with a different number of units or layers, which can be either equivalent, a local exact approximation, or a global linear approximation of the original network. On the practical side, we show that certain rectified linear units (ReLUs) can be safely removed from a network if they are always active or inactive for any valid input. If we only need an equivalent network for a smaller domain, then more units can be removed and some layers collapsed. On the theoretical side, we constructively show that for any feed-forward ReLU network, there exists a global linear approximation to a 2-hidden-layer shallow network with a fixed number of units. This result is a balance between the increasing number of units for arbitrary approximation with a single layer and the known upper bound of $\lceil log(n_0+1)\rceil +1$ layers for exact representation, where $n_0$ is the input dimension. While the transformed network may require an exponential number of units to capture the activation patterns of the original network, we show that it can be made substantially smaller by only accounting for the patterns that define linear regions. Based on experiments with ReLU networks on the MNIST dataset, we found that $l_1$-regularization and adversarial training reduces the number of linear regions significantly as the number of stable units increases due to weight sparsity. Therefore, we can also intentionally train ReLU networks to allow for effective loss-less compression and approximation.

Thiago Serra, Christian Tjandraatmadja, Srikumar Ramalingam

The holy grail of deep learning is to come up with an automatic method to design optimal architectures for different applications. In other words, how can we effectively dimension and organize neurons along the network layers based on the computational resources, input size, and amount of training data? We outline promising research directions based on polyhedral theory and mixed-integer representability that may offer an analytical approach to this question, in contrast to the empirical techniques often employed.

Xin Yu, Zhiding Yu, Srikumar Ramalingam

A family of super deep networks, referred to as residual networks or ResNet, achieved record-beating performance in various visual tasks such as image recognition, object detection, and semantic segmentation. The ability to train very deep networks naturally pushed the researchers to use enormous resources to achieve the best performance. Consequently, in many applications super deep residual networks were employed for just a marginal improvement in performance. In this paper, we propose epsilon-ResNet that allows us to automatically discard redundant layers, which produces responses that are smaller than a threshold epsilon, with a marginal or no loss in performance. The epsilon-ResNet architecture can be achieved using a few additional rectified linear units in the original ResNet. Our method does not use any additional variables nor numerous trials like other hyper-parameter optimization techniques. The layer selection is achieved using a single training process and the evaluation is performed on CIFAR-10, CIFAR-100, SVHN, and ImageNet datasets. In some instances, we achieve about 80% reduction in the number of parameters.

Varun Manjunatha, Srikumar Ramalingam, Tim K. Marks et al.

In recent years, it is common practice to extract fully-connected layer (fc) features that were learned while performing image classification on a source dataset, such as ImageNet, and apply them generally to a wide range of other tasks. The general usefulness of some large training datasets for transfer learning is not yet well understood, and raises a number of questions. For example, in the context of transfer learning, what is the role of a specific class in the source dataset, and how is the transferability of fc features affected when they are trained using various subsets of the set of all classes in the source dataset? In this paper, we address the question of how to select an optimal subset of the set of classes, subject to a budget constraint, that will more likely generate good features for other tasks. To accomplish this, we use a submodular set function to model the accuracy achievable on a new task when the features have been learned on a given subset of classes of the source dataset. An optimal subset is identified as the set that maximizes this submodular function. The maximization can be accomplished using an efficient greedy algorithm that comes with guarantees on the optimality of the solution. We empirically validate our submodular model by successfully identifying subsets of classes that produce good features for new tasks.

Thiago Serra, Christian Tjandraatmadja, Srikumar Ramalingam

We investigate the complexity of deep neural networks (DNN) that represent piecewise linear (PWL) functions. In particular, we study the number of linear regions, i.e. pieces, that a PWL function represented by a DNN can attain, both theoretically and empirically. We present (i) tighter upper and lower bounds for the maximum number of linear regions on rectifier networks, which are exact for inputs of dimension one; (ii) a first upper bound for multi-layer maxout networks; and (iii) a first method to perform exact enumeration or counting of the number of regions by modeling the DNN with a mixed-integer linear formulation. These bounds come from leveraging the dimension of the space defining each linear region. The results also indicate that a deep rectifier network can only have more linear regions than every shallow counterpart with same number of neurons if that number exceeds the dimension of the input.

Zhiding Yu, Chen Feng, Ming-Yu Liu et al.

Boundary and edge cues are highly beneficial in improving a wide variety of vision tasks such as semantic segmentation, object recognition, stereo, and object proposal generation. Recently, the problem of edge detection has been revisited and significant progress has been made with deep learning. While classical edge detection is a challenging binary problem in itself, the category-aware semantic edge detection by nature is an even more challenging multi-label problem. We model the problem such that each edge pixel can be associated with more than one class as they appear in contours or junctions belonging to two or more semantic classes. To this end, we propose a novel end-to-end deep semantic edge learning architecture based on ResNet and a new skip-layer architecture where category-wise edge activations at the top convolution layer share and are fused with the same set of bottom layer features. We then propose a multi-label loss function to supervise the fused activations. We show that our proposed architecture benefits this problem with better performance, and we outperform the current state-of-the-art semantic edge detection methods by a large margin on standard data sets such as SBD and Cityscapes.

Sudeep Pillai, Srikumar Ramalingam, John J. Leonard

Traditional stereo algorithms have focused their efforts on reconstruction quality and have largely avoided prioritizing for run time performance. Robots, on the other hand, require quick maneuverability and effective computation to observe its immediate environment and perform tasks within it. In this work, we propose a high-performance and tunable stereo disparity estimation method, with a peak frame-rate of 120Hz (VGA resolution, on a single CPU-thread), that can potentially enable robots to quickly reconstruct their immediate surroundings and maneuver at high-speeds. Our key contribution is a disparity estimation algorithm that iteratively approximates the scene depth via a piece-wise planar mesh from stereo imagery, with a fast depth validation step for semi-dense reconstruction. The mesh is initially seeded with sparsely matched keypoints, and is recursively tessellated and refined as needed (via a resampling stage), to provide the desired stereo disparity accuracy. The inherent simplicity and speed of our approach, with the ability to tune it to a desired reconstruction quality and runtime performance makes it a compelling solution for applications in high-speed vehicles.