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We argue that, in a theory of quantum gravity in a four dimensional asymptotically flat spacetime, all information about massless excitations can be obtained from an infinitesimal neighbourhood of the past boundary of future null infinity and does not require observations over all of future null infinity. Moreover, all information about the state that can be obtained through observations near a cut of future null infinity can also be obtained from observations near any earlier cut although the converse is not true. We provide independent arguments for these two assertions. Similar statements hold for past null infinity. These statements have immediate implications for the information paradox since they suggest that the fine-grained von Neumann entropy of the state defined on a segment $(-\infty,u)$ of future null infinity is independent of u. This is very different from the oft-discussed Page curve that this entropy is sometimes expected to obey. We contrast our results with recent discussions of the Page curve in the context of black hole evaporation, and also discuss the relation of our results to other proposals for holography in flat space., Comment: 44 pages (v2) refs added. typos fixed

In [1], two of the present authors along with P. Raman attempted to extend the Amplituhedron program for scalar field theories [2] to quartic scalar interactions. In this paper we develop various aspects of this proposal. Using recent seminal results in Representation theory [3,4], we show that projectivity of scattering forms and existence of kinematic space associahedron completely capture planar amplitudes of quartic interaction. We generalise the results of [1] and show that for any $n$-particle amplitude, the positive geometry associated to the projective scattering form is a convex realisation of Stokes polytope which can be naturally embedded inside one of the ABHY associahedra defined in [2,5]. For a special class of Stokes polytopes with hyper-cubic topology, we show that they have a canonical convex realisation in kinematic space as boundaries of kinematic space associahedra. We then use these kinematic space geometric constructions to write worldsheet forms for $\phi^{4}$ theory which are forms of lower rank on the CHY moduli space. We argue that just as in the case of bi-adjoint $\phi^3$ scalar amplitudes, scattering equations can be used as diffeomorphisms between certain $\frac{n-4}{2}$ forms on the worldsheet and $\frac{n-4}{2}$ forms on ABHY associahedron that generate quartic amplitudes., Comment: 58 pages, 7 figures, Section 6 revised and a new Appendix (Appendix G) added

Motivated by the Dikin walk, we develop aspects of an interior-point theory for sampling in high dimension. Specifically, we introduce a symmetric parameter and the notion of strong self-concordance. These properties imply that the corresponding Dikin walk mixes in $\tilde{O}(n\bar{\nu})$ steps from a warm start in a convex body in $\mathbb{R}^{n}$ using a strongly self-concordant barrier with symmetric self-concordance parameter $\bar{\nu}$. For many natural barriers, $\bar{\nu}$ is roughly bounded by $\nu$, the standard self-concordance parameter. We show that this property and strong self-concordance hold for the Lee-Sidford barrier. As a consequence, we obtain the first walk to mix in $\tilde{O}(n^{2})$ steps for an arbitrary polytope in $\mathbb{R}^{n}$. Strong self-concordance for other barriers leads to an interesting (and unexpected) connection -- for the universal and entropic barriers, it is implied by the KLS conjecture.

Classical soft graviton theorem gives an expression for the spectrum of low frequency gravitational radiation, emitted during a classical scattering process, in terms of the trajectories and spin angular momenta of ingoing and outgoing objects, including hard radiation. This has been proved to subleading order in the expansion in powers of frequency by taking the classical limit of the quantum soft graviton theorem. In this paper we give a direct proof of this result by analyzing the classical equations of motion of a generic theory of gravity coupled to interacting matter in space-time dimensions larger than four., Comment: LaTeX; 32 pages

In this paper, we present an extension to LaserNet, an efficient and state-of-the-art LiDAR based 3D object detector. We propose a method for fusing image data with the LiDAR data and show that this sensor fusion method improves the detection performance of the model especially at long ranges. The addition of image data is straightforward and does not require image labels. Furthermore, we expand the capabilities of the model to perform 3D semantic segmentation in addition to 3D object detection. On a large benchmark dataset, we demonstrate our approach achieves state-of-the-art performance on both object detection and semantic segmentation while maintaining a low runtime., Comment: Accepted for publication at CVPR Workshop on Autonomous Driving 2019

Recently Sahoo and Sen obtained a series of remarkable results concerning sub-leading soft photon and graviton theorems in four dimensions. Even though the S- matrix is infrared divergent, they have shown that the sub-leading soft theorems are well defined and exact statements in QED and perturbative Quantum Gravity. However unlike the well studied Cachazo-Strominger soft theorems in tree-level amplitudes, the new sub-leading soft expansion is at the order ln {\omega} (where {\omega} is the soft frequency) and the corresponding soft factors structurally show completely different properties then their tree-level counterparts. Whence it is natural to ask if these theorems are associated to asymptotic symmetries of the S-matrix. We consider this question in the context of sub-leading soft photon theorem in scalar QED and show that there are indeed an infinity of conservation laws whose Ward identities are equivalent to the loop-corrected soft photon theorem. This shows that in the case of four dimensional QED, the leading and sub-leading soft photon theorems are equivalent to Ward identities of (asymptotic) charges., Comment: 33 pages, no figures

In this paper, we present LaserNet, a computationally efficient method for 3D object detection from LiDAR data for autonomous driving. The efficiency results from processing LiDAR data in the native range view of the sensor, where the input data is naturally compact. Operating in the range view involves well known challenges for learning, including occlusion and scale variation, but it also provides contextual information based on how the sensor data was captured. Our approach uses a fully convolutional network to predict a multimodal distribution over 3D boxes for each point and then it efficiently fuses these distributions to generate a prediction for each object. Experiments show that modeling each detection as a distribution rather than a single deterministic box leads to better overall detection performance. Benchmark results show that this approach has significantly lower runtime than other recent detectors and that it achieves state-of-the-art performance when compared on a large dataset that has enough data to overcome the challenges of training on the range view., Comment: Accepted for publication at CVPR 2019

Opinion phrase extraction is one of the key tasks in fine-grained sentiment analysis. While opinion expressions could be generic subjective expressions, aspect specific opinion expressions contain both the aspect as well as the opinion expression within the original sentence context. In this work, we formulate the task as an instance of token-level sequence labeling. When multiple aspects are present in a sentence, detection of opinion phrase boundary becomes difficult and label of each word depend not only upon the surrounding words but also with the concerned aspect. We propose a neural network architecture with bidirectional LSTM (Bi-LSTM) and a novel attention mechanism. Bi-LSTM layer learns the various sequential pattern among the words without requiring any hand-crafted features. The attention mechanism captures the importance of context words on a particular aspect opinion expression when multiple aspects are present in a sentence via location and content based memory. A Conditional Random Field (CRF) model is incorporated in the final layer to explicitly model the dependencies among the output labels. Experimental results on Hotel dataset from Tripadvisor.com showed that our approach outperformed several state-of-the-art baselines., Comment: 12 pages, Accepted paper in CICLing 2018

Stickers are popularly used in messaging apps such as Hike to visually express a nuanced range of thoughts and utterances to convey exaggerated emotions. However, discovering the right sticker from a large and ever expanding pool of stickers while chatting can be cumbersome. In this paper, we describe a system for recommending stickers in real time as the user is typing based on the context of the conversation. We decompose the sticker recommendation (SR) problem into two steps. First, we predict the message that the user is likely to send in the chat. Second, we substitute the predicted message with an appropriate sticker. Majority of Hike's messages are in the form of text which is transliterated from users' native language to the Roman script. This leads to numerous orthographic variations of the same message and makes accurate message prediction challenging. To address this issue, we learn dense representations of chat messages employing character level convolution network in an unsupervised manner. We use them to cluster the messages that have the same meaning. In the subsequent steps, we predict the message cluster instead of the message. Our approach does not depend on human labelled data (except for validation), leading to fully automatic updation and tuning pipeline for the underlying models. We also propose a novel hybrid message prediction model, which can run with low latency on low-end phones that have severe computational limitations. Our described system has been deployed for more than $6$ months and is being used by millions of users along with hundreds of thousands of expressive stickers.