arXiv subjects

Girish Varma

Publications and source records attributed to Girish Varma.

31 records · Page 2Linked to original sources

arXiv2018

City-Scale Road Audit System using Deep Learning

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.

cs.CV↗

arXiv2018

Improved Visual Relocalization by Discovering Anchor Points

We address the visual relocalization problem of predicting the location and camera orientation or pose (6DOF) of the given input scene. We propose a method based on how humans determine their location using the visible landmarks. We define anchor points uniformly across the route map and propose a deep learning architecture which predicts the most relevant anchor point present in the scene as well as the relative offsets with respect to it. The relevant anchor point need not be the nearest anchor point to the ground truth location, as it might not be visible due to the pose. Hence we propose a multi task loss function, which discovers the relevant anchor point, without needing the ground truth for it. We validate the effectiveness of our approach by experimenting on CambridgeLandmarks (large scale outdoor scenes) as well as 7 Scenes (indoor scenes) using variousCNN feature extractors. Our method improves the median error in indoor as well as outdoor localization datasets compared to the previous best deep learning model known as PoseNet (with geometric re-projection loss) using the same feature extractor. We improve the median error in localization in the specific case of Street scene, by over 8m.

cs.CV↗

arXiv2018

Class2Str: End to End Latent Hierarchy Learning

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.

cs.CV↗

arXiv2018

Deep Expander Networks: Efficient Deep Networks from Graph Theory

Efficient CNN designs like ResNets and DenseNet were proposed to improve accuracy vs efficiency trade-offs. They essentially increased the connectivity, allowing efficient information flow across layers. Inspired by these techniques, we propose to model connections between filters of a CNN using graphs which are simultaneously sparse and well connected. Sparsity results in efficiency while well connectedness can preserve the expressive power of the CNNs. We use a well-studied class of graphs from theoretical computer science that satisfies these properties known as Expander graphs. Expander graphs are used to model connections between filters in CNNs to design networks called X-Nets. We present two guarantees on the connectivity of X-Nets: Each node influences every node in a layer in logarithmic steps, and the number of paths between two sets of nodes is proportional to the product of their sizes. We also propose efficient training and inference algorithms, making it possible to train deeper and wider X-Nets effectively. Expander based models give a 4% improvement in accuracy on MobileNet over grouped convolutions, a popular technique, which has the same sparsity but worse connectivity. X-Nets give better performance trade-offs than the original ResNet and DenseNet-BC architectures. We achieve model sizes comparable to state-of-the-art pruning techniques using our simple architecture design, without any pruning. We hope that this work motivates other approaches to utilize results from graph theory to develop efficient network architectures.

cs.CV↗

arXiv2018

Efficient Semantic Segmentation using Gradual Grouping

Deep CNNs for semantic segmentation have high memory and run time requirements. Various approaches have been proposed to make CNNs efficient like grouped, shuffled, depth-wise separable convolutions. We study the effectiveness of these techniques on a real-time semantic segmentation architecture like ERFNet for improving run time by over 5X. We apply these techniques to CNN layers partially or fully and evaluate the testing accuracies on Cityscapes dataset. We obtain accuracy vs parameters/FLOPs trade offs, giving accuracy scores for models that can run under specified runtime budgets. We further propose a novel training procedure which starts out with a dense convolution but gradually evolves towards a grouped convolution. We show that our proposed training method and efficient architecture design can improve accuracies by over 8% with depth wise separable convolutions applied on the encoder of ERFNet and attaching a light weight decoder. This results in a model which has a 5X improvement in FLOPs while only suffering a 4% degradation in accuracy with respect to ERFNet.

cs.CV↗

arXiv2015

On Fortification of Projection Games

A recent result of Moshkovitz \cite{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 \cite{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 $\ell_1$ and $\ell_2$ 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 \cite{Moshkovitz15} of \cite{Moshkovitz14} with an alternate argument), is a good fortifier. We also show that using a fortifier (in particular $\ell_2$ guarantees) is necessary for obtaining the robustness required for fortification.

cs.CC↗

arXiv2015

Derandomized Graph Product Results using the Low Degree Long Code

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.

cs.CC↗

arXiv2014

Reducing uniformity in Khot-Saket hypergraph coloring hardness reductions

In a recent result, Khot and Saket [FOCS 2014] proved the quasi-NP-hardness of coloring a 2-colorable 12-uniform hypergraph with $2^{(\log n)^{Ω(1)}}$ colors. This result was proved using a novel outer PCP verifier which had a strong soundness guarantee. In this note, we show that we can reduce the arity of their result by modifying their 12-query inner verifier to an 8-query inner verifier based on the hypergraph coloring hardness reductions of Guruswami et. al. [STOC 2014]. More precisely, we prove quasi-NP-hardness of the following problems on n-vertex hypergraphs. - Coloring a 2-colorable 8-uniform hypergraph with $2^{(\log n)^{Ω(1)}}$ colors. - Coloring a 4-colorable 4-uniform hypergraph with $2^{(\log n)^{Ω(1)}}$ colors.

cs.CC↗

arXiv2014

Playing games in an uncertain world

Traditional game theory assumes that the players in the game are aware of the rules of the game. However, in practice, often the players are unaware or have only partial knowledge about the game they are playing. They may also have knowledge that other players have only partial knowledge of the game they are playing, which they can try to exploit. We present a novel mathematical formulation of such games. We make use of Kripke semantics, which are a way to keep track of what different players know and do not know about the world. We propose a notion of equilibrium for such games, and show that equilibrium always exists.

cs.GT↗

arXiv2013

Super-polylogarithmic hypergraph coloring hardness via low-degree long codes

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. In particular, we prove quasi-NP-hardness of the following problems on $n$-vertex hyper-graphs: * Coloring a 2-colorable 8-uniform hypergraph with $2^{2^{Ω(\sqrt{\log\log n})}}$ colors. * Coloring a 4-colorable 4-uniform hypergraph with $2^{2^{Ω(\sqrt{\log\log n})}}$ colors. * Coloring a 3-colorable 3-uniform hypergraph with $(\log n)^{Ω(1/\log\log\log n)}$ colors. In each of these cases, the hardness results obtained are (at least) exponentially stronger than what was previously known for the respective cases. In fact, prior to this result, polylog n colors was the strongest quantitative bound on the number of colors ruled out by inapproximability results for O(1)-colorable hypergraphs. The fundamental bottleneck in obtaining coloring inapproximability results using the low- degree long code was a multipartite structural restriction in the PCP construction of Dinur-Guruswami. We are able to get around this restriction by simulating the multipartite structure implicitly by querying just one partition (albeit requiring 8 queries), which yields our result for 2-colorable 8-uniform hypergraphs. The result for 4-colorable 4-uniform hypergraphs is obtained via a 'query doubling' method. For 3-colorable 3-uniform hypergraphs, we exploit the ternary domain to design a test with an additive (as opposed to multiplicative) noise function, and analyze its efficacy in killing high weight Fourier coefficients via the pseudorandom properties of an associated quadratic form.

cs.CC↗

arXiv2011

Physarum Can Compute Shortest Paths

Physarum Polycephalum is a slime mold that is apparently 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.

cs.DS↗

arXiv2011

Streaming algorithms for language recognition problems

We study the complexity of the following problems in the streaming model. Membership testing for \DLIN We show that every language in \DLIN\ can be recognised by a randomized one-pass $O(\log n)$ space algorithm with inverse polynomial one-sided error, and by a deterministic p-pass $O(n/p)$ space algorithm. We show that these algorithms are optimal. Membership testing for \LL$(k)$ For languages generated by \LL$(k)$ grammars with a bound of $r$ on the number of nonterminals at any stage in the left-most derivation, we show that membership can be tested by a randomized one-pass $O(r\log n)$ space algorithm with inverse polynomial (in $n$) one-sided error. Membership testing for \DCFL We show that randomized algorithms as efficient as the ones described above for \DLIN\ and $\LL(k)$ (which are subclasses of \DCFL) cannot exist for all of \DCFL: there is a language in \VPL\ (a subclass of \DCFL) for which any randomized p-pass algorithm with error bounded by $ε< 1/2$ must use $Ω(n/p)$ space. Degree sequence problem We study the problem of determining, given a sequence $d_1, d_2,..., d_n$ and a graph $G$, whether the degree sequence of $G$ is precisely $d_1, d_2,..., d_n$. We give a randomized one-pass $O(\log n)$ space algorithm with inverse polynomial one-sided error probability. We show that our algorithms are optimal. Our randomized algorithms are based on the recent work of Magniez et al. \cite{MMN09}; our lower bounds are obtained by considering related communication complexity problems.

cs.DS↗

arXiv2010

Conductance and Eigenvalue

We show the following. \begin{theorem} Let $M$ be an finite-state ergodic time-reversible Markov chain with transition matrix $P$ and conductance $ϕ$. Let $λ\in (0,1)$ be an eigenvalue of $P$. Then, $$ϕ^2 + λ^2 \leq 1$$ \end{theorem} This strengthens the well-known~\cite{HLW,Dod84, AM85, Alo86, JS89} inequality $λ\leq 1- ϕ^2/2$. We obtain our result by a slight variation in the proof method in \cite{JS89, HLW}; the same method was used earlier in \cite{RS06} to obtain the same inequality for random walks on regular undirected graphs.

cs.DM↗