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Anirudh Goyal

Alumni

Publications

AI-Assisted Generation of Difficult Math Questions
Dingli Yu
Kaifeng Lyu
Simon Park
Nan Rosemary Ke
Michael Curtis Mozer
Sanjeev Arora
Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet dem… (see more)and for diverse and challenging math questions. Relying solely on human experts is both time-consuming and costly, while LLM-generated questions often lack the requisite diversity and difficulty. We present a design framework that combines the strengths of LLMs with a human-in-the-loop approach to generate a diverse array of challenging math questions. We leverage LLM metacognition skills [Didolkar et al., 2024] of a strong LLM to extract core"skills"from existing math datasets. These skills serve as the basis for generating novel and difficult questions by prompting the LLM with random pairs of core skills. The use of two different skills within each question makes finding such questions an"out of distribution"task for both LLMs and humans. Our pipeline employs LLMs to iteratively generate and refine questions and solutions through multiturn prompting. Human annotators then verify and further refine the questions, with their efficiency enhanced via further LLM interactions. Applying this pipeline on skills extracted from the MATH dataset [Hendrycks et al., 2021] resulted in MATH
AI-Assisted Generation of Difficult Math Questions
Dingli Yu
Kaifeng Lyu
Simon Park
Nan Rosemary Ke
Michael Curtis Mozer
Sanjeev Arora
Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet dem… (see more)and for diverse and challenging math questions. Relying solely on human experts is both time-consuming and costly, while LLM-generated questions often lack the requisite diversity and difficulty. We present a design framework that combines the strengths of LLMs with a human-in-the-loop approach to generate a diverse array of challenging math questions. We leverage LLM metacognition skills [Didolkar et al., 2024] of a strong LLM to extract core"skills"from existing math datasets. These skills serve as the basis for generating novel and difficult questions by prompting the LLM with random pairs of core skills. The use of two different skills within each question makes finding such questions an"out of distribution"task for both LLMs and humans. Our pipeline employs LLMs to iteratively generate and refine questions and solutions through multiturn prompting. Human annotators then verify and further refine the questions, with their efficiency enhanced via further LLM interactions. Applying this pipeline on skills extracted from the MATH dataset [Hendrycks et al., 2021] resulted in MATH
AI-Assisted Generation of Difficult Math Questions
Dingli Yu
Kaifeng Lyu
Simon Park
Nan Rosemary Ke
Michael Curtis Mozer
Sanjeev Arora
Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet dem… (see more)and for diverse and challenging math questions. Relying solely on human experts is both time-consuming and costly, while LLM-generated questions often lack the requisite diversity and difficulty. We present a design framework that combines the strengths of LLMs with a human-in-the-loop approach to generate a diverse array of challenging math questions. We leverage LLM metacognition skills [Didolkar et al., 2024] of a strong LLM to extract core"skills"from existing math datasets. These skills serve as the basis for generating novel and difficult questions by prompting the LLM with random pairs of core skills. The use of two different skills within each question makes finding such questions an"out of distribution"task for both LLMs and humans. Our pipeline employs LLMs to iteratively generate and refine questions and solutions through multiturn prompting. Human annotators then verify and further refine the questions, with their efficiency enhanced via further LLM interactions. Applying this pipeline on skills extracted from the MATH dataset [Hendrycks et al., 2021] resulted in MATH
Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving
Aniket Rajiv Didolkar
Nan Rosemary Ke
Siyuan Guo
Michal Valko
Timothy P Lillicrap
Danilo Jimenez Rezende
Michael Curtis Mozer
Sanjeev Arora
Metacognitive knowledge refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly posse… (see more)ss some reasoning processes. The paper gives evidence that they also have metacognitive knowledge, including ability to name skills and procedures to apply given a task. We explore this primarily in context of math reasoning, developing a prompt-guided interaction procedure to get a powerful LLM to assign sensible skill labels to math questions, followed by having it perform semantic clustering to obtain coarser families of skill labels. These coarse skill labels look interpretable to humans. To validate that these skill labels are meaningful and relevant to the LLM's reasoning processes we perform the following experiments. (a) We ask GPT-4 to assign skill labels to training questions in math datasets GSM8K and MATH. (b) When using an LLM to solve the test questions, we present it with the full list of skill labels and ask it to identify the skill needed. Then it is presented with randomly selected exemplar solved questions associated with that skill label. This improves accuracy on GSM8k and MATH for several strong LLMs, including code-assisted models. The methodology presented is domain-agnostic, even though this article applies it to math problems.
Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving
Aniket Rajiv Didolkar
Nan Rosemary Ke
Siyuan Guo
Michal Valko
Timothy P Lillicrap
Danilo Jimenez Rezende
Michael Curtis Mozer
Sanjeev Arora
Metacognitive knowledge refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly posse… (see more)ss some reasoning processes. The paper gives evidence that they also have metacognitive knowledge, including ability to name skills and procedures to apply given a task. We explore this primarily in context of math reasoning, developing a prompt-guided interaction procedure to get a powerful LLM to assign sensible skill labels to math questions, followed by having it perform semantic clustering to obtain coarser families of skill labels. These coarse skill labels look interpretable to humans. To validate that these skill labels are meaningful and relevant to the LLM's reasoning processes we perform the following experiments. (a) We ask GPT-4 to assign skill labels to training questions in math datasets GSM8K and MATH. (b) When using an LLM to solve the test questions, we present it with the full list of skill labels and ask it to identify the skill needed. Then it is presented with randomly selected exemplar solved questions associated with that skill label. This improves accuracy on GSM8k and MATH for several strong LLMs, including code-assisted models. The methodology presented is domain-agnostic, even though this article applies it to math problems.
Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving
Aniket Rajiv Didolkar
Nan Rosemary Ke
Siyuan Guo
Michal Valko
Timothy P Lillicrap
Danilo Jimenez Rezende
Michael Curtis Mozer
Sanjeev Arora
Metacognitive knowledge refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly posse… (see more)ss some reasoning processes. The paper gives evidence that they also have metacognitive knowledge, including ability to name skills and procedures to apply given a task. We explore this primarily in context of math reasoning, developing a prompt-guided interaction procedure to get a powerful LLM to assign sensible skill labels to math questions, followed by having it perform semantic clustering to obtain coarser families of skill labels. These coarse skill labels look interpretable to humans. To validate that these skill labels are meaningful and relevant to the LLM's reasoning processes we perform the following experiments. (a) We ask GPT-4 to assign skill labels to training questions in math datasets GSM8K and MATH. (b) When using an LLM to solve the test questions, we present it with the full list of skill labels and ask it to identify the skill needed. Then it is presented with randomly selected exemplar solved questions associated with that skill label. This improves accuracy on GSM8k and MATH for several strong LLMs, including code-assisted models. The methodology presented is domain-agnostic, even though this article applies it to math problems.
Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving
Aniket Rajiv Didolkar
Nan Rosemary Ke
Siyuan Guo
Michal Valko
Timothy P Lillicrap
Danilo Jimenez Rezende
Michael Curtis Mozer
Sanjeev Arora
Metacognitive knowledge refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly posse… (see more)ss some reasoning processes. The paper gives evidence that they also have metacognitive knowledge, including ability to name skills and procedures to apply given a task. We explore this primarily in context of math reasoning, developing a prompt-guided interaction procedure to get a powerful LLM to assign sensible skill labels to math questions, followed by having it perform semantic clustering to obtain coarser families of skill labels. These coarse skill labels look interpretable to humans. To validate that these skill labels are meaningful and relevant to the LLM's reasoning processes we perform the following experiments. (a) We ask GPT-4 to assign skill labels to training questions in math datasets GSM8K and MATH. (b) When using an LLM to solve the test questions, we present it with the full list of skill labels and ask it to identify the skill needed. Then it is presented with randomly selected exemplar solved questions associated with that skill label. This improves accuracy on GSM8k and MATH for several strong LLMs, including code-assisted models. The methodology presented is domain-agnostic, even though this article applies it to math problems.
Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving
Aniket Rajiv Didolkar
Nan Rosemary Ke
Siyuan Guo
Michal Valko
Timothy P Lillicrap
Danilo Jimenez Rezende
Michael Curtis Mozer
Sanjeev Arora
Metacognitive knowledge refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly posse… (see more)ss some reasoning processes. The paper gives evidence that they also have metacognitive knowledge, including ability to name skills and procedures to apply given a task. We explore this primarily in context of math reasoning, developing a prompt-guided interaction procedure to get a powerful LLM to assign sensible skill labels to math questions, followed by having it perform semantic clustering to obtain coarser families of skill labels. These coarse skill labels look interpretable to humans. To validate that these skill labels are meaningful and relevant to the LLM's reasoning processes we perform the following experiments. (a) We ask GPT-4 to assign skill labels to training questions in math datasets GSM8K and MATH. (b) When using an LLM to solve the test questions, we present it with the full list of skill labels and ask it to identify the skill needed. Then it is presented with randomly selected exemplar solved questions associated with that skill label. This improves accuracy on GSM8k and MATH for several strong LLMs, including code-assisted models. The methodology presented is domain-agnostic, even though this article applies it to math problems.
Cycle Consistency Driven Object Discovery
Aniket Rajiv Didolkar
Developing deep learning models that effectively learn object-centric representations, akin to human cognition, remains a challenging task. … (see more)Existing approaches facilitate object discovery by representing objects as fixed-size vectors, called ``slots'' or ``object files''. While these approaches have shown promise in certain scenarios, they still exhibit certain limitations. First, they rely on architectural priors which can be unreliable and usually require meticulous engineering to identify the correct objects. Second, there has been a notable gap in investigating the practical utility of these representations in downstream tasks. To address the first limitation, we introduce a method that explicitly optimizes the constraint that each object in a scene should be associated with a distinct slot. We formalize this constraint by introducing consistency objectives which are cyclic in nature. By integrating these consistency objectives into various existing slot-based object-centric methods, we showcase substantial improvements in object-discovery performance. These enhancements consistently hold true across both synthetic and real-world scenes, underscoring the effectiveness and adaptability of the proposed approach. To tackle the second limitation, we apply the learned object-centric representations from the proposed method to two downstream reinforcement learning tasks, demonstrating considerable performance enhancements compared to conventional slot-based and monolithic representation learning methods. Our results suggest that the proposed approach not only improves object discovery, but also provides richer features for downstream tasks.
Gemini: A Family of Highly Capable Multimodal Models
Gemini Team Google Rohan Anil
Sebastian Borgeaud
Yonghui Wu
Jean-Baptiste Alayrac
Jiahui Yu
Radu Soricut
J. Schalkwyk
Andrew M. Dai
Anja Hauth
Katie Millican
David Silver
Slav Petrov
Melvin Johnson
Ioannis Antonoglou
Julian Schrittwieser
Amelia Glaese
Jilin Chen
Emily Pitler
Timothy P. Lillicrap
Angeliki Lazaridou … (see 480 more)
James L. Molloy
Michael Acheson Isard
Paul R. Barham
Tom Hennigan
Benjamin Lee
Malcolm Reynolds
Yuanzhong Xu
Ryan Doherty
Eli Collins
Clemens Meyer
Eliza Rutherford
Erica Moreira
Kareem W. Ayoub
Megha Goel
George Tucker
Enrique Piqueras
M. Krikun
Iain Barr
Nikolay Savinov
Ivo Danihelka
Becca Roelofs
Anais White
Anders Johan Andreassen
Tamara von Glehn
Laksh-man Yagati
Mehran Kazemi
Lucas Gonzalez
Misha Khalman
Alexandre Fréchette
Charlotte Smith
Laura Culp
Lev Proleev
Yi Luan
X. T. Chen
James Lottes
Federico Lebron
Alban Rrustemi
Natalie Clay
Phil Crone
Tomas Kocisky
Jeffrey Zhao
Bartek Perz
Dian Yu
Heidi Howard
Adam E. Bloniarz
Jack W. Rae
Han Lu
Laurent Sifre
Marcello Maggioni
Fred Alcober
Dan Garrette
Megan Barnes
Shantanu Thakoor
Jacob Austin
Gabriel Barth-Maron
William Wong
Rishabh Joshi
Rahma Chaabouni
Deeni Fatiha
Arun Ahuja
Ruibo Liu
Yunxuan Li
Sarah Cogan
Jeremy Chen
Chao Jia
Chenjie Gu
Qiao Zhang
Jordan Grimstad
Ale Jakse Hartman
Martin J. Chadwick
Gaurav Singh Tomar
Xavier Garcia
Evan Senter
Emanuel Taropa
Thanumalayan Sankaranarayana Pillai
Jacob Devlin
Michael Laskin
Diego de Las Casas
Dasha Valter
Connie Tao
Lorenzo Blanco
Adrià Puigdomènech Badia
David Reitter
Mianna Chen
Jenny Brennan
Clara E. Rivera
Sergey Brin
Shariq Iqbal
Gabriela Surita
Jane Labanowski
Abhishek Rao
Stephanie Winkler
Emilio Parisotto
Yiming Gu
Kate Olszewska
Yujing Zhang
Ravichandra Addanki
Antoine Miech
Annie Louis
Laurent El Shafey
Denis Teplyashin
Geoff Brown
Elliot Catt
Nithya Attaluri
Jan Balaguer
Jackie Xiang
Pidong Wang
Zoe Ashwood
Anton Briukhov
Alex Webson
Sanjay Ganapathy
Smit Sanghavi
Ajay Kannan
Ming-Wei Chang
Axel Stjerngren
Josip Djolonga
Yuting Sun
Ankur Bapna
Matthew Aitchison
Pedram Pejman
Henryk Michalewski
Tianhe Yu
Cindy Wang
J Christopher Love
Junwhan Ahn
Dawn Bloxwich
Kehang Han
Peter Conway Humphreys
Thibault Sellam
James Bradbury
Varun Godbole
Sina Samangooei
Bogdan Damoc
Alex Kaskasoli
S'ebastien M. R. Arnold
Vijay Vasudevan
Shubham Agrawal
Jason Riesa
Dmitry Lepikhin
Richard Tanburn
Srivatsan Srinivasan
Hyeontaek Lim
Sarah Hodkinson
Pranav Shyam
Johan Ferret
Steven Hand
Ankush Garg
T. Paine
Jian Li
Yujia Li
Minh Giang
Zaheer Abbas
Sarah York
Machel Reid
Elizabeth Cole
Aakanksha Chowdhery
Dipanjan Das
Dominika Rogozi'nska
Vitaly Nikolaev
Pablo G. Sprechmann
Zachary Nado
Lukáš Žilka
Flavien Prost
Luheng He
Marianne Monteiro
Gaurav Mishra
Christoper A. Welty
Joshua Newlan
Dawei Jia
Miltiadis Allamanis
Clara Huiyi Hu
Raoul de Liedekerke
Justin Gilmer
Carl Saroufim
Shruti Rijhwani
Shaobo Hou
Disha Shrivastava
Anirudh Baddepudi
Alex Goldin
Adnan Ozturel
Albin Cassirer
Yunhan Xu
Daniel Sohn
Devendra Singh Sachan
Reinald Kim Amplayo
Craig Swanson
Dessie Petrova
Shashi Narayan
Arthur Guez
Siddhartha Brahma
Jessica Landon
Miteyan Patel
Ruizhe Zhao
Kevin Villela
Luyu Wang
Wenhao Jia
Matthew Rahtz
Mai Gim'enez
Legg Yeung
Hanzhao Lin
James Keeling
Petko Georgiev
Diana Mincu
Boxi Wu
Salem Haykal
Rachel Saputro
Kiran N. Vodrahalli
James Qin
Zeynep Cankara
Abhanshu Sharma
Nicholas Fernando
Will Hawkins
Behnam Neyshabur
Solomon Kim
Adrian Hutter
Priyanka Agrawal
Alex Castro-Ros
George van den Driessche
Tao Wang
Fan Yang
Shuo-yiin Chang
Paul Komarek
Ross McIlroy
Mario Luvci'c
Guodong Zhang
Wael Farhan
Michael Sharman
Paul Natsev
Paul Michel
Yong Cheng
Yamini Bansal
Siyuan Qiao
Kris Cao
Siamak Shakeri
Christina Butterfield
Justin Chung
Paul Kishan Rubenstein
Shivani Agrawal
Arthur Mensch
Kedar Soparkar
Karel Lenc
Timothy Chung
Aedan Pope
Lorenzo Maggiore
Jackie Kay
Priya Jhakra
Shibo Wang
Joshua Maynez
Mary Phuong
Taylor Tobin
Andrea Tacchetti
Maja Trebacz
Kevin Robinson
Yash Katariya
Sebastian Riedel
Paige Bailey
Kefan Xiao
Nimesh Ghelani
Lora Aroyo
Ambrose Slone
Neil Houlsby
Xuehan Xiong
Zhen Yang
Elena Gribovskaya
Jonas Adler
Mateo Wirth
Lisa Lee
Music Li
Thais Kagohara
Jay Pavagadhi
Sophie Bridgers
Anna Bortsova
Sanjay Ghemawat
Tianqi Liu
Richard Powell
Vijay Bolina
Mariko Iinuma
Polina Zablotskaia
James Besley
Da-Woon Chung
Timothy Dozat
Ramona Comanescu
Xiance Si
Jeremy Greer
Guolong Su
M. Polacek
Raphael Lopez Kaufman
Simon Tokumine
Hexiang Hu
Elena Buchatskaya
Yingjie Miao
Mohamed Elhawaty
Aditya Siddhant
Nenad Tomasev
Jinwei Xing
Christina Greer
Helen Miller
Shereen Ashraf
Aurko Roy
Zizhao Zhang
Ada Ma
Angelos Filos
Milos Besta
Rory Blevins
Ted Klimenko
Chih-Kuan Yeh
Soravit Changpinyo
Jiaqi Mu
Oscar Chang
Mantas Pajarskas
Carrie Muir
Vered Cohen
Krishna S Haridasan
Amit Marathe
Steven Hansen
Sholto Douglas
Rajkumar Samuel
Mingqiu Wang
Sophia Austin
Chang Lan
Jiepu Jiang
Justin Chiu
Jaime Alonso Lorenzo
Lars Lowe Sjosund
S'ebastien Cevey
Zach Gleicher
Thi Avrahami
Anudhyan Boral
Hansa Srinivasan
Vittorio Selo
Rhys May
Konstantinos Aisopos
L'eonard Hussenot
Livio Baldini Soares
Kate Baumli
Michael B. Chang
Adria Recasens
Benjamin Caine
Alexander Pritzel
Filip Pavetic
Fabio Pardo
Anita Gergely
Justin Frye
Vinay Venkatesh Ramasesh
Dan Horgan
Nora Kassner
Subhrajit Roy
Ethan Dyer
V'ictor Campos
Alex Tomala
Yunhao Tang
Dalia El Badawy
Elspeth White
Basil Mustafa
Oran Lang
Abhishek Jindal
Sharad Mandyam Vikram
Zhitao Gong
Sergi Caelles
Ross Hemsley
Gregory Thornton
Fangxiaoyu Feng
Wojciech Stokowiec
Ce Zheng
Phoebe Thacker
cCauglar Unlu
Zhishuai Zhang
Mohammad Saleh
James Svensson
Maxwell L. Bileschi
Piyush Patil
Roman Ring
Katerina Tsihlas
Arpi Vezer
Marco Selvi
Toby Shevlane
Mikel Rodriguez
Tom Kwiatkowski
Samira Daruki
Keran Rong
Allan Dafoe
Nicholas Fitzgerald
Keren Gu-Lemberg
Mina Khan
Lisa Anne Hendricks
Marie Pellat
Vladimir Feinberg
James Cobon-Kerr
Tara N. Sainath
Maribeth Rauh
Sayed Hadi Hashemi
Richard Ives
Yana Hasson
YaGuang Li
Eric Noland
Yuan Cao
Nathan Byrd
Le Hou
Qingze Wang
Thibault Sottiaux
Michela Paganini
Jean-Baptiste Lespiau
Alexandre Moufarek
Samer Hassan
Kaushik Shivakumar
Joost Van Amersfoort
Amol Mandhane
Pratik M. Joshi
Matthew Tung
Andy Brock
Hannah Rachel Sheahan
Vedant Misra
Cheng Li
Nemanja Raki'cevi'c
Mostafa Dehghani
Fangyu Liu
Sid Mittal
Junhyuk Oh
Seb Noury
Eren Sezener
Fantine Huot
Matthew Lamm
Nicola De Cao
Charlie Chen
Gamaleldin Elsayed
Ed Huai-hsin Chi
Mahdis Mahdieh
Ian F. Tenney
Nan Hua
Ivan Petrychenko
Patrick Kane
Dylan Scandinaro
Rishub Jain
Jonathan Uesato
Romina Datta
Adam Sadovsky
Oskar Bunyan
Dominik Rabiej
Shimu Wu
John Zhang
Gautam Vasudevan
Edouard Leurent
Mahmoud Alnahlawi
Ionut-Razvan Georgescu
Nan Wei
Ivy Zheng
Betty Chan
Pam G Rabinovitch
Piotr Stańczyk
Ye Zhang
David Steiner
Subhajit Naskar
Michael Azzam
Matthew Johnson
Adam Paszke
Chung-Cheng Chiu
Jaume Sanchez Elias
Afroz Mohiuddin
Faizan Muhammad
Jin Miao
Andrew Lee
Nino Vieillard
Sahitya Potluri
Jane Park
Elnaz Davoodi
Jiageng Zhang
Jeff Stanway
Drew Garmon
Abhijit Karmarkar
Zhe Dong
Unlearning via Sparse Representations
Ashish Malik
Michael Curtis Mozer
Sanjeev Arora
Unlearning via Sparse Representations
Ashish Malik
Michael Curtis Mozer
Sanjeev Arora
Machine \emph{unlearning}, which involves erasing knowledge about a \emph{forget set} from a trained model, can prove to be costly and infea… (see more)sible by existing techniques. We propose a nearly compute-free zero-shot unlearning technique based on a discrete representational bottleneck. We show that the proposed technique efficiently unlearns the forget set and incurs negligible damage to the model's performance on the rest of the data set. We evaluate the proposed technique on the problem of \textit{class unlearning} using three datasets: CIFAR-10, CIFAR-100, and LACUNA-100. We compare the proposed technique to SCRUB, a state-of-the-art approach which uses knowledge distillation for unlearning. Across all three datasets, the proposed technique performs as well as, if not better than SCRUB while incurring almost no computational cost.