Qiaochu Yuan

Qiaochu Yuan, Ming Gu, Bo Li

The low rank approximation of matrices is a crucial component in many data mining applications today. A competitive algorithm for this class of problems is the randomized block Lanczos algorithm - an amalgamation of the traditional block Lanczos algorithm with a randomized starting matrix. While empirically this algorithm performs quite well, there has been scant new theoretical results on its convergence behavior and approximation accuracy, and past results have been restricted to certain parameter settings. In this paper, we present a unified singular value convergence analysis for this algorithm, for all valid choices of the block size parameter. We present novel results on the rate of singular value convergence and show that under certain spectrum regimes, the convergence is superlinear. Additionally, we provide results from numerical experiments that validate our analysis.

Long Phan, Alice Gatti, Ziwen Han et al. · amazon-science, apple-ml

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 2,500 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai.

Peter H. Jin, Qiaochu Yuan, Forrest Iandola et al.

Training time on large datasets for deep neural networks is the principal workflow bottleneck in a number of important applications of deep learning, such as object classification and detection in automatic driver assistance systems (ADAS). To minimize training time, the training of a deep neural network must be scaled beyond a single machine to as many machines as possible by distributing the optimization method used for training. While a number of approaches have been proposed for distributed stochastic gradient descent (SGD), at the current time synchronous approaches to distributed SGD appear to be showing the greatest performance at large scale. Synchronous scaling of SGD suffers from the need to synchronize all processors on each gradient step and is not resilient in the face of failing or lagging processors. In asynchronous approaches using parameter servers, training is slowed by contention to the parameter server. In this paper we compare the convergence of synchronous and asynchronous SGD for training a modern ResNet network architecture on the ImageNet classification problem. We also propose an asynchronous method, gossiping SGD, that aims to retain the positive features of both systems by replacing the all-reduce collective operation of synchronous training with a gossip aggregation algorithm. We find, perhaps counterintuitively, that asynchronous SGD, including both elastic averaging and gossiping, converges faster at fewer nodes (up to about 32 nodes), whereas synchronous SGD scales better to more nodes (up to about 100 nodes).