arXiv subjects

Nikhil Singh

Publications and source records attributed to Nikhil Singh.

46 records · Page 3Linked to original sources

arXiv2022

niksss at HinglishEval: Language-agnostic BERT-based Contextual Embeddings with Catboost for Quality Evaluation of the Low-Resource Synthetically Generated Code-Mixed Hinglish Text

This paper describes the system description for the HinglishEval challenge at INLG 2022. The goal of this task was to investigate the factors influencing the quality of the code-mixed text generation system. The task was divided into two subtasks, quality rating prediction and annotators disagreement prediction of the synthetic Hinglish dataset. We attempted to solve these tasks using sentence-level embeddings, which are obtained from mean pooling the contextualized word embeddings for all input tokens in our text. We experimented with various classifiers on top of the embeddings produced for respective tasks. Our best-performing system ranked 1st on subtask B and 3rd on subtask A.

cs.CL↗

arXiv2022

A Neural Network Solves, Explains, and Generates University Math Problems by Program Synthesis and Few-Shot Learning at Human Level

We demonstrate that a neural network pre-trained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates new questions at a human level. We automatically synthesize programs using few-shot learning and OpenAI's Codex transformer and execute them to solve course problems at 81% automatic accuracy. We curate a new dataset of questions from MIT's largest mathematics courses (Single Variable and Multivariable Calculus, Differential Equations, Introduction to Probability and Statistics, Linear Algebra, and Mathematics for Computer Science) and Columbia University's Computational Linear Algebra. We solve questions from a MATH dataset (on Prealgebra, Algebra, Counting and Probability, Intermediate Algebra, Number Theory, and Precalculus), the latest benchmark of advanced mathematics problems designed to assess mathematical reasoning. We randomly sample questions and generate solutions with multiple modalities, including numbers, equations, and plots. The latest GPT-3 language model pre-trained on text automatically solves only 18.8% of these university questions using zero-shot learning and 30.8% using few-shot learning and the most recent chain of thought prompting. In contrast, program synthesis with few-shot learning using Codex fine-tuned on code generates programs that automatically solve 81% of these questions. Our approach improves the previous state-of-the-art automatic solution accuracy on the benchmark topics from 8.8% to 81.1%. We perform a survey to evaluate the quality and difficulty of generated questions. This work is the first to automatically solve university-level mathematics course questions at a human level and the first work to explain and generate university-level mathematics course questions at scale, a milestone for higher education.

cs.LG↗

arXiv2022

Topology Optimization with Tetra-kai-decahedra and Spheroidal Masks

A novel meshing scheme, based on regular tetra-kai-decahedron, also referred to as truncated octahedron, cells is presented for use in spatial topology optimization. A tetra-kai-decahedron mesh ensures face connectivity between elements thereby eliminating singular solutions from the solution space. Various other benefits of implementing the said mesh are also highlighted, and the corresponding finite element is introduced. Material mask overlay strategy or MMOS, a feature based method for topology optimization is extended for use in 3-dimensions (MMOS-3D) via the aforementioned finite element and spheroidal negative masks. Formulation for density computation and sensitivity analysis for gradient based optimization is developed. Examples on traditional structural topology optimization problems are presented with detailed discussion on efficacy of the proposed approach.

cs.CE↗

arXiv2021

Solving Probability and Statistics Problems by Program Synthesis

We solve university level probability and statistics questions by program synthesis using OpenAI's Codex, a Transformer trained on text and fine-tuned on code. We transform course problems from MIT's 18.05 Introduction to Probability and Statistics and Harvard's STAT110 Probability into programming tasks. We then execute the generated code to get a solution. Since these course questions are grounded in probability, we often aim to have Codex generate probabilistic programs that simulate a large number of probabilistic dependencies to compute its solution. Our approach requires prompt engineering to transform the question from its original form to an explicit, tractable form that results in a correct program and solution. To estimate the amount of work needed to translate an original question into its tractable form, we measure the similarity between original and transformed questions. Our work is the first to introduce a new dataset of university-level probability and statistics problems and solve these problems in a scalable fashion using the program synthesis capabilities of large language models.

cs.LG↗

arXiv2021

Image2Lego: Customized LEGO Set Generation from Images

Although LEGO sets have entertained generations of children and adults, the challenge of designing customized builds matching the complexity of real-world or imagined scenes remains too great for the average enthusiast. In order to make this feat possible, we implement a system that generates a LEGO brick model from 2D images. We design a novel solution to this problem that uses an octree-structured autoencoder trained on 3D voxelized models to obtain a feasible latent representation for model reconstruction, and a separate network trained to predict this latent representation from 2D images. LEGO models are obtained by algorithmic conversion of the 3D voxelized model to bricks. We demonstrate first-of-its-kind conversion of photographs to 3D LEGO models. An octree architecture enables the flexibility to produce multiple resolutions to best fit a user's creative vision or design needs. In order to demonstrate the broad applicability of our system, we generate step-by-step building instructions and animations for LEGO models of objects and human faces. Finally, we test these automatically generated LEGO sets by constructing physical builds using real LEGO bricks.

cs.CV↗

arXiv2021

Image2Reverb: Cross-Modal Reverb Impulse Response Synthesis

Measuring the acoustic characteristics of a space is often done by capturing its impulse response (IR), a representation of how a full-range stimulus sound excites it. This work generates an IR from a single image, which can then be applied to other signals using convolution, simulating the reverberant characteristics of the space shown in the image. Recording these IRs is both time-intensive and expensive, and often infeasible for inaccessible locations. We use an end-to-end neural network architecture to generate plausible audio impulse responses from single images of acoustic environments. We evaluate our method both by comparisons to ground truth data and by human expert evaluation. We demonstrate our approach by generating plausible impulse responses from diverse settings and formats including well known places, musical halls, rooms in paintings, images from animations and computer games, synthetic environments generated from text, panoramic images, and video conference backgrounds.

cs.SD↗

arXiv2021

Solving Machine Learning Problems

Can a machine learn Machine Learning? This work trains a machine learning model to solve machine learning problems from a University undergraduate level course. We generate a new training set of questions and answers consisting of course exercises, homework, and quiz questions from MIT's 6.036 Introduction to Machine Learning course and train a machine learning model to answer these questions. Our system demonstrates an overall accuracy of 96% for open-response questions and 97% for multiple-choice questions, compared with MIT students' average of 93%, achieving grade A performance in the course, all in real-time. Questions cover all 12 topics taught in the course, excluding coding questions or questions with images. Topics include: (i) basic machine learning principles; (ii) perceptrons; (iii) feature extraction and selection; (iv) logistic regression; (v) regression; (vi) neural networks; (vii) advanced neural networks; (viii) convolutional neural networks; (ix) recurrent neural networks; (x) state machines and MDPs; (xi) reinforcement learning; and (xii) decision trees. Our system uses Transformer models within an encoder-decoder architecture with graph and tree representations. An important aspect of our approach is a data-augmentation scheme for generating new example problems. We also train a machine learning model to generate problem hints. Thus, our system automatically generates new questions across topics, answers both open-response questions and multiple-choice questions, classifies problems, and generates problem hints, pushing the envelope of AI for STEM education.

cs.LG↗

arXiv2021

Privileged Zero-Shot AutoML

This work improves the quality of automated machine learning (AutoML) systems by using dataset and function descriptions while significantly decreasing computation time from minutes to milliseconds by using a zero-shot approach. Given a new dataset and a well-defined machine learning task, humans begin by reading a description of the dataset and documentation for the algorithms to be used. This work is the first to use these textual descriptions, which we call privileged information, for AutoML. We use a pre-trained Transformer model to process the privileged text and demonstrate that using this information improves AutoML performance. Thus, our approach leverages the progress of unsupervised representation learning in natural language processing to provide a significant boost to AutoML. We demonstrate that using only textual descriptions of the data and functions achieves reasonable classification performance, and adding textual descriptions to data meta-features improves classification across tabular datasets. To achieve zero-shot AutoML we train a graph neural network with these description embeddings and the data meta-features. Each node represents a training dataset, which we use to predict the best machine learning pipeline for a new test dataset in a zero-shot fashion. Our zero-shot approach rapidly predicts a high-quality pipeline for a supervised learning task and dataset. In contrast, most AutoML systems require tens or hundreds of pipeline evaluations. We show that zero-shot AutoML reduces running and prediction times from minutes to milliseconds, consistently across datasets. By speeding up AutoML by orders of magnitude this work demonstrates real-time AutoML.

cs.LG↗

arXiv2020

On Topology optimization with elliptical masks and honeycomb tessellation with explicit length scale constraints

Topology optimization using gradient search with negative and positive elliptical masks and honeycomb tessellation is presented. Through a novel skeletonization algorithm for topologies defined using filled and void hexagonal cells/elements, explicit minimum and maximum length scales are imposed on solid states in the solutions. An analytical example is presented which suggests that for a skeletonized topology, optimal solutions may not always exist for any specified volume fraction, minimum and maximum length scales, and that there may exist implicit interdependence between them. A Sequence for Length Scale (SLS) methodology is proposed wherein solutions are sought by specifying only the minimum and maximum length scales with volume fraction getting determined systematically. Through four benchmark problems in small deformation topology optimization, it is demonstrated that solutions by-and-large satisfy the length scale constraints though the latter may get violated at certain local sites. The proposed approach seems promising, noting especially that solutions, if rendered perfectly {\it black and white} with minimum length scale explicitly imposed and boundaries smoothened, are quite close in performance compared to the parent topologies. Attaining {\it volume distributed} topologies, wherein members are more or less of the same thickness, may also be possible with the proposed approach.

cs.CE↗

arXiv2015

Parametric Regression on the Grassmannian

We address the problem of fitting parametric curves on the Grassmann manifold for the purpose of intrinsic parametric regression. As customary in the literature, we start from the energy minimization formulation of linear least-squares in Euclidean spaces and generalize this concept to general nonflat Riemannian manifolds, following an optimal-control point of view. We then specialize this idea to the Grassmann manifold and demonstrate that it yields a simple, extensible and easy-to-implement solution to the parametric regression problem. In fact, it allows us to extend the basic geodesic model to (1) a time-warped variant and (2) cubic splines. We demonstrate the utility of the proposed solution on different vision problems, such as shape regression as a function of age, traffic-speed estimation and crowd-counting from surveillance video clips. Most notably, these problems can be conveniently solved within the same framework without any specifically-tailored steps along the processing pipeline.

cs.CV↗