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09/11/2023
Textbooks Are All You Need II: phi-1.5 technical report
We continue the investigation into the power of smaller Transformer-base...
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05/12/2023
TinyStories: How Small Can Language Models Be and Still Speak Coherent English?
Language models (LMs) are powerful tools for natural language processing...
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03/22/2023
Sparks of Artificial General Intelligence: Early experiments with GPT-4
Artificial intelligence (AI) researchers have been developing and refini...
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12/01/2022
Hit-and-run mixing via localization schemes
We analyze the hit-and-run algorithm for sampling uniformly from an isot...
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08/12/2022
Noise stability on the Boolean hypercube via a renormalized Brownian motion
We consider a variant of the classical notion of noise on the Boolean hy...
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08/06/2022
An Optimal "It Ain't Over Till It's Over" Theorem
We study the probability of Boolean functions with small max influence t...
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06/09/2022
Unveiling Transformers with LEGO: a synthetic reasoning task
We propose a synthetic task, LEGO (Learning Equality and Group Operation...
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04/14/2022
Isoperimetric Inequalities Made Simpler
We give an alternative, simple method to prove isoperimetric inequalitie...
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03/08/2022
Localization Schemes: A Framework for Proving Mixing Bounds for Markov Chains
Two recent and seemingly-unrelated techniques for proving mixing bounds ...
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02/17/2021
Non-asymptotic approximations of neural networks by Gaussian processes
We study the extent to which wide neural networks may be approximated by...
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06/28/2020
Community detection and percolation of information in a geometric setting
We make the first steps towards generalizing the theory of stochastic bl...
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06/23/2020
Reduction From Non-Unique Games To Boolean Unique Games
We reduce the problem of proving a "Boolean Unique Games Conjecture" (wi...
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06/04/2020
Network size and weights size for memorization with two-layers neural networks
In 1988, Eric B. Baum showed that two-layers neural networks with thresh...
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09/26/2019
Concentration on the Boolean hypercube via pathwise stochastic analysis
We develop a new technique for proving concentration inequalities which ...
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09/26/2019
Stability of Talagrand's influence inequality
We strengthen several classical inequalities concerning the influences o...
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06/25/2019
Krivine diffusions attain the Goemans--Williamson approximation ratio
Answering a question of Abbasi-Zadeh, Bansal, Guruganesh, Nikolov, Schwa...
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04/15/2019
Depth Separations in Neural Networks: What is Actually Being Separated?
Existing depth separation results for constant-depth networks essentiall...
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03/17/2019
Stability of the Shannon-Stam inequality via the Föllmer process
We prove stability estimates for the Shannon-Stam inequality (also known...
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06/24/2018
The CLT in high dimensions: quantitative bounds via martingale embedding
We introduce a new method for obtaining quantitative convergence rates f...
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07/11/2016
Kernel-based methods for bandit convex optimization
We consider the adversarial convex bandit problem and we build the first...
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12/12/2015