The inverse of an invertible convolution is an important operation that comes up in Normalizing Flows, Image Deblurring, etc. The naive algorithm for backpropagation of this operation using Gaussian elimination has running time $O(n^3)$ where $n$ is the number of pixels in the image. We give a fast parallel backpropagation algorithm with running time $O(\sqrt{n})$ for a square image and provide a GPU implementation of the same. Inverse of Convolutions are usually used in Normalizing Flows in the sampling pass, making them slow. We propose to use Inverse of Convolutions in the forward (image to latent vector) pass of the Normalizing flow. Since the sampling pass is the inverse of the forward pass, it will use convolutions only, resulting in efficient sampling times. We use our parallel backpropagation algorithm for optimizing the inverse of convolution layer, resulting in fast training times also. We implement this approach in various Normalizing Flow backbones, resulting in our Inverse-Flow models. We benchmark Inverse-Flow on standard datasets and show significantly improved sampling times with similar bits per dimension compared to previous models.

Large-scale deployment of fully autonomous vehicles requires a very high degree of robustness to unstructured traffic, weather conditions, and should prevent unsafe mispredictions. While there are several datasets and benchmarks focusing on segmentation for drive scenes, they are not specifically focused on safety and robustness issues. We introduce the IDD-AW dataset, which provides 5000 pairs of high-quality images with pixel-level annotations, captured under rain, fog, low light, and snow in unstructured driving conditions. As compared to other adverse weather datasets, we provide i.) more annotated images, ii.) paired Near-Infrared (NIR) image for each frame, iii.) larger label set with a 4-level label hierarchy to capture unstructured traffic conditions. We benchmark state-of-the-art models for semantic segmentation in IDD-AW. We also propose a new metric called "Safe mean Intersection over Union (Safe mIoU)" for hierarchical datasets which penalizes dangerous mispredictions that are not captured in the traditional definition of mean Intersection over Union (mIoU). The results show that IDD-AW is one of the most challenging datasets to date for these tasks. The dataset and code will be available here: http://iddaw.github.io.

A significant cause of air pollution in urban areas worldwide is the high volume of road traffic. Long-term exposure to severe pollution can cause serious health issues. One approach towards tackling this problem is to design a pollution-aware traffic routing policy that balances multiple objectives of i) avoiding extreme pollution in any area ii) enabling short transit times, and iii) making effective use of the road capacities. We propose a novel sampling-based approach for this problem. We give the first construction of a Markov Chain that can sample integer max flow solutions of a planar graph, with theoretical guarantees that the probabilities depend on the aggregate transit length. We designed a traffic policy using diverse samples and simulated traffic on real-world road maps using the SUMO traffic simulator. We observe a considerable decrease in areas with severe pollution when experimented with maps of large cities across the world compared to other approaches.

Summary Sparse neural networks are shown to give accurate predictions competitive to denser versions, while also minimizing the number of arithmetic operations performed. However current GPU hardware can only exploit structured sparsity patterns for better efficiency. We propose a framework for generating structured multilevel block sparse neural networks by using the theory of graph products. Our Ramanujan bipartite graph product (RBGP) framework uses products of Ramanujan graphs to obtain the best connectivity for a given level of sparsity. This essentially ensures that the i.) the networks has the structured block sparsity for which runtime efficient algorithms exists, ii.) the model gives high prediction accuracy, due to the better expressive power derived from the connectivity of the graph, iii.) the graph data structure has a succinct representation that can be stored efficiently in memory. We use our framework to design a specific connectivity pattern called RBGP4 which makes efficient use of the memory hierarchy available on GPU. We benchmark our approach on image classification and machine translation tasks with an edge (Jetson Nano 2GB) as well as server (V100) GPUs. When compared with commonly used sparsity patterns like unstructured and block, we obtain significant speedups while achieving the same level of accuracy.

Parametric path problems arise independently in diverse domains, ranging from transportation to finance, where they are studied under various assumptions. We formulate a general path problem with relaxed assumptions, and describe how this formulation is applicable in these domains. We study the complexity of the general problem, and a variant of it where preprocessing is allowed. We show that when the parametric weights are linear functions, algorithms remain tractable even under our relaxed assumptions. Furthermore, we show that if the weights are allowed to be non-linear, the problem becomes NP-hard. We also study the multi-dimensional version of the problem where the weight functions are parameterized by multiple parameters. We show that even with two parameters, this problem is NP-hard.

In recent years, the need for semantic segmentation has arisen across several different applications and environments. However, the expense and redundancy of annotation often limits the quantity of labels available for training in any domain, while deployment is easier if a single model works well across domains. In this paper, we pose the novel problem of universal semi-supervised semantic segmentation and propose a solution framework, to meet the dual needs of lower annotation and deployment costs. In contrast to counterpoints such as fine tuning, joint training or unsupervised domain adaptation, universal semi-supervised segmentation ensures that across all domains: (i) a single model is deployed, (ii) unlabeled data is used, (iii) performance is improved, (iv) only a few labels are needed and (v) label spaces may differ. To address this, we minimize supervised as well as within and cross-domain unsupervised losses, introducing a novel feature alignment objective based on pixel-aware entropy regularization for the latter. We demonstrate quantitative advantages over other approaches on several combinations of segmentation datasets across different geographies (Germany, England, India) and environments (outdoors, indoors), as well as qualitative insights on the aligned representations.

While several datasets for autonomous navigation have become available in recent years, they have tended to focus on structured driving environments. This usually corresponds to well-delineated infrastructure such as lanes, a small number of well-defined categories for traffic participants, low variation in object or background appearance and strong adherence to traffic rules. We propose DS, a novel dataset for road scene understanding in unstructured environments where the above assumptions are largely not satisfied. It consists of 10,004 images, finely annotated with 34 classes collected from 182 drive sequences on Indian roads. The label set is expanded in comparison to popular benchmarks such as Cityscapes, to account for new classes. It also reflects label distributions of road scenes significantly different from existing datasets, with most classes displaying greater within-class diversity. Consistent with real driving behaviors, it also identifies new classes such as drivable areas besides the road. We propose a new four-level label hierarchy, which allows varying degrees of complexity and opens up possibilities for new training methods. Our empirical study provides an in-depth analysis of the label characteristics. State-of-the-art methods for semantic segmentation achieve much lower accuracies on our dataset, demonstrating its distinction compared to Cityscapes. Finally, we propose that our dataset is an ideal opportunity for new problems such as domain adaptation, few-shot learning and behavior prediction in road scenes.

Deep neural networks for image classification typically consists of a convolutional feature extractor followed by a fully connected classifier network. The predicted and the ground truth labels are represented as one hot vectors. Such a representation assumes that all classes are equally dissimilar. However, classes have visual similarities and often form a hierarchy. Learning this latent hierarchy explicitly in the architecture could provide invaluable insights. We propose an alternate architecture to the classifier network called the Latent Hierarchy (LH) Classifier and an end to end learned Class2Str mapping which discovers a latent hierarchy of the classes. We show that for some of the best performing architectures on CIFAR and Imagenet datasets, the proposed replacement and training by LH classifier recovers the accuracy, with a fraction of the number of parameters in the classifier part. Compared to the previous work of HDCNN, which also learns a 2 level hierarchy, we are able to learn a hierarchy at an arbitrary number of levels as well as obtain an accuracy improvement on the Imagenet classification task over them. We also verify that many visually similar classes are grouped together, under the learnt hierarchy.

Road networks in cities are massive and is a critical component of mobility. Fast response to defects, that can occur not only due to regular wear and tear but also because of extreme events like storms, is essential. Hence there is a need for an automated system that is quick, scalable and cost-effective for gathering information about defects. We propose a system for city-scale road audit, using some of the most recent developments in deep learning and semantic segmentation. For building and benchmarking the system, we curated a dataset which has annotations required for road defects. However, many of the labels required for road audit have high ambiguity which we overcome by proposing a label hierarchy. We also propose a multi-step deep learning model that segments the road, subdivide the road further into defects, tags the frame for each defect and finally localizes the defects on a map gathered using GPS. We analyze and evaluate the models on image tagging as well as segmentation at different levels of the label hierarchy.

We prove improved inapproximability results for hypergraph coloring using the low-degree polynomial code (aka the “short code” of Barak et al. [SIAM J. Comput., 44 (2015), pp. 1287--1324]) and the techniques proposed by Dinur and Guruswami [Israel J. Math., 209 (2015), pp. 611--649] to incorporate this code for inapproximability results. In particular, we prove quasi NP-hardness of the following problems on $n$-vertex hypergraphs: coloring a 2-colorable 8-uniform hypergraph with $2^{2^{\Omega(\sqrt{\log \log n})}}$ colors; coloring a 4-colorable 4-uniform hypergraph with $2^{2^{\Omega(\sqrt{\log \log n})}}$ colors; and coloring a 3-colorable 3-uniform hypergraph with $(\log n)^{\Omega(1/\log\log\log n)}$ colors. For the first two cases, the hardness results obtained are superpolynomial in what was previously known, and in the last case it is an exponential improvement. In fact, prior to this result, $(\log n)^{O(1)}$ colors was the strongest quantitative bound on the number of colors ruled out by inapproximability results for $O(1)$-colorable hypergraphs, and $(\log\log n)^{O(1)}$ for $O(1)$-colorable, 3-uniform hypergraphs.

A recent result of Moshkovitz [Moshkovitz14] presented an ingenious method to provide a completely elementary proof of the Parallel Repetition Theorem for certain projection games via a construction called fortification. However, the construction used in [Moshkovitz14] to fortify arbitrary label cover instances using an arbitrary extractor is insufficient to prove parallel repetition. In this paper, we provide a fix by using a stronger graph that we call fortifiers. Fortifiers are graphs that have both l_1 and l_2 guarantees on induced distributions from large subsets. We then show that an expander with sufficient spectral gap, or a bi-regular extractor with stronger parameters (the latter is also the construction used in an independent update [Moshkovitz15] of [Moshkovitz14] with an alternate argument), is a good fortifier. We also show that using a fortifier (in particular l_2 guarantees) is necessary for obtaining the robustness required for fortification.

In this paper, we address the question of whether the recent derandomization results obtained by the use of the low-degree long code can be extended to other product settings. We consider two settings: (1) the graph product results of Alon, Dinur, Friedgut and Sudakov [GAFA, 2004] and (2) the "majority is stablest" type of result obtained by Dinur, Mossel and Regev [SICOMP, 2009] and Dinur and Shinkar [In Proc. APPROX, 2010] while studying the hardness of approximate graph coloring. In our first result, we show that there exists a considerably smaller subgraph of $K_3^{\otimes R}$ which exhibits the following property (shown for $K_3^{\otimes R}$ by Alon et al.): independent sets close in size to the maximum independent set are well approximated by dictators. The "majority is stablest" type of result of Dinur et al. and Dinur and Shinkar shows that if there exist two sets of vertices $A$ and $B$ in $K_3^{\otimes R}$ with very few edges with one endpoint in $A$ and another in $B$, then it must be the case that the two sets $A$ and $B$ share a single influential coordinate. In our second result, we show that a similar "majority is stablest" statement holds good for a considerably smaller subgraph of $K_3^{\otimes R}$. Furthermore using this result, we give a more efficient reduction from Unique Games to the graph coloring problem, leading to improved hardness of approximation results for coloring.

We prove improved inapproximability results for hypergraph coloring using the low-degree polynomial code (aka, the"short code" of Barak et. al. [FOCS 2012]) and the techniques proposed by Dinur and Guruswami [FOCS 2013] to incorporate this code for inapproximability results.

Physarum Polycephalum is a slime mold that apparently is able to solve shortest path problems. A mathematical model has been proposed by biologists to describe the feedback mechanism used by the slime mold to adapt its tubular channels while foraging two food sources s0 and s1. We prove that, under this model, the mass of the mold will eventually converge to the shortest s0-s1 path of the network that the mold lies on, independently of the structure of the network or of the initial mass distribution. This matches the experimental observations by the biologists and can be seen as an example of a “natural algorithm”, that is, an algorithm developed by evolution over millions of years.