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Large language models (LLMs) have played a pivotal role in revolutionizing various facets of our daily existence.
Rapid multiplication of rectangular matrices
Don Coppersmith · 1982
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Extensions of lipschitz mappings into a hilbert space
William B Johnson and Joram Lindenstrauss · 1984
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Algebraic complexity theory
Peter Bürgisser, Michael Clausen, and Mohammad A Shokrollahi · 1997
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Training v-support vector classifiers: theory and algorithms
Chih-Chung Chang and Chih-Jen Lin · 2001
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Approximate nearest neighbors and the fast johnson-lindenstrauss transform
Nir Ailon and Bernard Chazelle · 2006
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Training linear svms in linear time
Thorsten Joachims · 2006
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Improved approximation algorithms for large matrices via random projections
Tamas Sarlos · 2006
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Multiplying matrices faster than coppersmith-winograd
Virginia Vassilevska Williams · 2012
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Low-rank approximation and regression in input sparsity time
Kenneth L Clarkson and David P Woodruff · 2013
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Faster ridge regression via the subsampled randomized hadamard transform
Yichao Lu, Paramveer Dhillon, Dean P Foster, and Lyle Ungar · 2013
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Low-distortion subspace embeddings in input-sparsity time and applications to robust linear regression
Xiangrui Meng and Michael W Mahoney · 2013
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Osnap: Faster numerical linear algebra algorithms via sparser subspace embeddings
Jelani Nelson and Huy L Nguyên · 2013
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Compressed matrix multiplication
Rasmus Pagh · 2013
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Neural machine translation by jointly learning to align and translate
Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio · 2014
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Optimal cur matrix decompositions
Christos Boutsidis and David P Woodruff · 2014
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Powers of tensors and fast matrix multiplication
François Le Gall · 2014
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Effective approaches to attention-based neural machine translation
Minh-Thang Luong, Hieu Pham, and Christopher D Manning · 2015
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A faster cutting plane method and its implications for combinatorial and convex optimization
Yin Tat Lee, Aaron Sidford, and Sam Chiu-wai Wong · 2015
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Show, attend and tell: Neural image caption generation with visual attention
Kelvin Xu, Jimmy Ba, Ryan Kiros, Kyunghyun Cho, Aaron Courville, Ruslan Salakhudinov, Rich Zemel, and Yoshua Bengio · 2015
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Optimal principal component analysis in distributed and streaming models
Christos Boutsidis, David P Woodruff, and Peilin Zhong · 2016
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Nearly tight oblivious subspace embeddings by trace inequalities
Michael B Cohen · 2016
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Weighted low rank approximations with provable guarantees
Ilya Razenshteyn, Zhao Song, and David P Woodruff · 2016
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Distributed low rank approximation of implicit functions of a matrix
David P Woodruff and Peilin Zhong · 2016
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Low rank approximation with entrywise l1-norm error
Zhao Song, David P Woodruff, and Peilin Zhong · 2017
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Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio · 2017
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Attention is all you need
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin · 2017
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Subspace embedding and linear regression with orlicz norm
Alexandr Andoni, Chengyu Lin, Ying Sheng, Peilin Zhong, and Ruiqi Zhong · 2018
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Bert: Pre-training of deep bidirectional transformers for language understanding
Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova · 2018
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Sketching for kronecker product regression and p-splines
Huaian Diao, Zhao Song, Wen Sun, and David Woodruff · 2018
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Gradient descent provably optimizes over-parameterized neural networks
Simon S Du, Xiyu Zhai, Barnabas Poczos, and Aarti Singh · 2018
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Characterizing implicit bias in terms of optimization geometry
Suriya Gunasekar, Jason Lee, Daniel Soudry, and Nathan Srebro · 2018
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Improved rectangular matrix multiplication using powers of the coppersmith-winograd tensor
François Le Gall and Florent Urrutia · 2018
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Risk and parameter convergence of logistic regression
Ziwei Ji and Matus Telgarsky · 2018
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Learning overparameterized neural networks via stochastic gradient descent on structured data
Yuanzhi Li and Yingyu Liang · 2018
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Improving language understanding by generative pre-training
Alec Radford, Karthik Narasimhan, Tim Salimans, Ilya Sutskever, et al · 2018
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The implicit bias of gradient descent on separable data
Daniel Soudry, Elad Hoffer, Mor Shpigel Nacson, Suriya Gunasekar, and Nathan Srebro · 2018
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Bourgan: Generative networks with metric embeddings
Chang Xiao, Peilin Zhong, and Changxi Zheng · 2018
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Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks
Sanjeev Arora, Simon Du, Wei Hu, Zhiyuan Li, and Ruosong Wang · 2019
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On exact computation with an infinitely wide neural net
Sanjeev Arora, Simon S Du, Wei Hu, Zhiyuan Li, Russ R Salakhutdinov, and Ruosong Wang · 2019
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A convergence theory for deep learning via over-parameterization
Zeyuan Allen-Zhu, Yuanzhi Li, and Zhao Song · 2019
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On the convergence rate of training recurrent neural networks
Zeyuan Allen-Zhu, Yuanzhi Li, and Zhao Song · 2019
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Gram-gauss-newton method: Learning overparameterized neural networks for regression problems
Tianle Cai, Ruiqi Gao, Jikai Hou, Siyu Chen, Dong Wang, Di He, Zhihua Zhang, and Liwei Wang · 2019
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Solving linear programs in the current matrix multiplication time
Michael B Cohen, Yin Tat Lee, and Zhao Song · 2019
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Optimal sketching for kronecker product regression and low rank approximation
Huaian Diao, Rajesh Jayaram, Zhao Song, Wen Sun, and David Woodruff · 2019
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A structural probe for finding syntax in word representations
John Hewitt and Christopher D Manning · 2019
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The implicit bias of gradient descent on nonseparable data
Ziwei Ji and Matus Telgarsky · 2019
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Ziwei Ji and Matus Telgarsky · 2019
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Solving empirical risk minimization in the current matrix multiplication time
Yin Tat Lee, Zhao Song, and Qiuyi Zhang · 2019
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Towards explaining the regularization effect of initial large learning rate in training neural networks
Yuanzhi Li, Colin Wei, and Tengyu Ma · 2019
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Convergence of gradient descent on separable data
Mor Shpigel Nacson, Jason Lee, Suriya Gunasekar, Pedro Henrique Pamplona Savarese, Nathan Srebro, and Daniel Soudry · 2019
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The implicit bias of adagrad on separable data
Qian Qian and Xiaoyuan Qian · 2019
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Language models are unsupervised multitask learners
Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, Ilya Sutskever, et al · 2019
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Visualizing and measuring the geometry of bert
Emily Reif, Ann Yuan, Martin Wattenberg, Fernanda B Viegas, Andy Coenen, Adam Pearce, and Been Kim · 2019
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Relative error tensor low rank approximation
Zhao Song, David P Woodruff, and Peilin Zhong · 2019
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Implicit regularization for optimal sparse recovery
Tomas Vaskevicius, Varun Kanade, and Patrick Rebeschini · 2019
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An improved analysis of training over-parameterized deep neural networks
Difan Zou and Quanquan Gu · 2019
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Oblivious sketching of high-degree polynomial kernels
Thomas D Ahle, Michael Kapralov, Jakob BT Knudsen, Rasmus Pagh, Ameya Velingker, David P Woodruff, and Amir Zandieh · 2020
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Winnowing with gradient descent
Ehsan Amid and Manfred K Warmuth · 2020
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Reparameterizing mirror descent as gradient descent
Ehsan Amid and Manfred KK Warmuth · 2020
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Implicit regularization for deep neural networks driven by an ornstein-uhlenbeck like process
Guy Blanc, Neha Gupta, Gregory Valiant, and Paul Valiant · 2020
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Language models are few-shot learners
Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al · 2020
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Training (overparametrized) neural networks in near-linear time
Jan van den Brand, Binghui Peng, Zhao Song, and Omri Weinstein · 2020
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A deterministic linear program solver in current matrix multiplication time
Jan van den Brand · 2020
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Barriers for rectangular matrix multiplication
Matthias Christandl, François Le Gall, Vladimir Lysikov, and Jeroen Zuiddam · 2020
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Gradient descent follows the regularization path for general losses
Ziwei Ji, Miroslav Dudik, Robert E Schapire, and Matus Telgarsky · 2020
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A faster interior point method for semidefinite programming
Haotian Jiang, Tarun Kathuria, Yin Tat Lee, Swati Padmanabhan, and Zhao Song · 2020
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An improved cutting plane method for convex optimization, convex-concave games, and its applications
Haotian Jiang, Yin Tat Lee, Zhao Song, and Sam Chiu-wai Wong · 2020
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Directional convergence and alignment in deep learning
Ziwei Ji and Matus Telgarsky · 2020
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Reformer: The efficient transformer
Nikita Kitaev, Łukasz Kaiser, and Anselm Levskaya · 2020
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Scaling laws for neural language models
Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario Amodei · 2020
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Just interpolate: Kernel “ridgeless” regression can generalize
Tengyuan Liang and Alexander Rakhlin · 2020
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Generalized leverage score sampling for neural networks
Jason D Lee, Ruoqi Shen, Zhao Song, Mengdi Wang, et al · 2020
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Improved guarantees for k-means++ and k-means++ parallel
Konstantin Makarychev, Aravind Reddy, and Liren Shan · 2020
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Implicit bias in deep linear classification: Initialization scale vs training accuracy
Edward Moroshko, Blake E Woodworth, Suriya Gunasekar, Jason D Lee, Nati Srebro, and Daniel Soudry · 2020
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Toward moderate overparameterization: Global convergence guarantees for training shallow neural networks
Samet Oymak and Mahdi Soltanolkotabi · 2020
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Meet google meena, 2020
Kovid Rathee · 2020
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Kernel and rich regimes in overparametrized models
Blake Woodworth, Suriya Gunasekar, Jason D Lee, Edward Moroshko, Pedro Savarese, Itay Golan, Daniel Soudry, and Nathan Srebro · 2020
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Assessing cross-cultural alignment between chatgpt and human societies: An empirical study
Yong Cao, Li Zhou, Seolhwa Lee, Laura Cabello, Min Chen, and Daniel Hershcovich · 2023
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How ready are pre-trained abstractive models and llms for legal case judgement summarization?
Aniket Deroy, Kripabandhu Ghosh, and Saptarshi Ghosh · 2023
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Planning with general objective functions: Going beyond total rewards
Ruosong Wang, Peilin Zhong, Simon S Du, Russ R Salakhutdinov, and Lin Yang · 2020
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A unifying view on implicit bias in training linear neural networks
Chulhee Yun, Shankar Krishnan, and Hossein Mobahi · 2020
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Why are adaptive methods good for attention models?
Jingzhao Zhang, Sai Praneeth Karimireddy, Andreas Veit, Seungyeon Kim, Sashank Reddi, Sanjiv Kumar, and Suvrit Sra · 2020
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Over-parameterized adversarial training: An analysis overcoming the curse of dimensionality
Yi Zhang, Orestis Plevrakis, Simon S Du, Xingguo Li, Zhao Song, and Sanjeev Arora · 2020
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Stochastic mirror descent on overparameterized nonlinear models
Navid Azizan, Sahin Lale, and Babak Hassibi · 2021
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A refined laser method and faster matrix multiplication
Josh Alman and Virginia Vassilevska Williams · 2021
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Zero-th order algorithm for softmax attention optimization
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Faster robust tensor power method for arbitrary order
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Efficient algorithm for solving hyperbolic programs
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Should chatgpt be biased? challenges and risks of bias in large language models
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Baby steps in evaluating the capacities of large language models
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Fast quantum algorithm for attention computation
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Low rank matrix completion via robust alternating minimization in nearly linear time
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