Timezone: »
Poster
Depth-Width Tradeoffs in Approximating Natural Functions With Neural Networks
Itay Safran · Ohad Shamir
We provide several new depth-based separation results for feed-forward neural networks, proving that various types of simple and natural functions can be better approximated using deeper networks than shallower ones, even if the shallower networks are much larger. This includes indicators of balls and ellipses; non-linear functions which are radial with respect to the $L_1$ norm; and smooth non-linear functions. We also show that these gaps can be observed experimentally: Increasing the depth indeed allows better learning than increasing width, when training neural networks to learn an indicator of a unit ball.
[ PDF]
[
Summary/Notes]
Summary/Notes]
Author Information
Itay Safran (Weizmann Institute of Science)
Ohad Shamir (Weizmann Institute of Science)
Related Events (a corresponding poster, oral, or spotlight)
-
2017 Talk: Depth-Width Tradeoffs in Approximating Natural Functions With Neural Networks »
Mon Aug 7th 06:24 -- 06:42 AM Room C4.8
More from the Same Authors
-
2020 Poster: The Complexity of Finding Stationary Points with Stochastic Gradient Descent »
Yoel Drori · Ohad Shamir -
2020 Poster: Proving the Lottery Ticket Hypothesis: Pruning is All You Need »
Eran Malach · Gilad Yehudai · Shai Shalev-Schwartz · Ohad Shamir -
2020 Poster: Is Local SGD Better than Minibatch SGD? »
Blake Woodworth · Kumar Kshitij Patel · Sebastian Stich · Zhen Dai · Brian Bullins · Brendan McMahan · Ohad Shamir · Nati Srebro -
2018 Poster: Spurious Local Minima are Common in Two-Layer ReLU Neural Networks »
Itay Safran · Ohad Shamir -
2018 Oral: Spurious Local Minima are Common in Two-Layer ReLU Neural Networks »
Itay Safran · Ohad Shamir -
2017 Poster: Oracle Complexity of Second-Order Methods for Finite-Sum Problems »
Yossi Arjevani · Ohad Shamir -
2017 Poster: Online Learning with Local Permutations and Delayed Feedback »
Liran Szlak · Ohad Shamir -
2017 Poster: Communication-efficient Algorithms for Distributed Stochastic Principal Component Analysis »
Dan Garber · Ohad Shamir · Nati Srebro -
2017 Poster: Failures of Gradient-Based Deep Learning »
Shaked Shammah · Shai Shalev-Shwartz · Ohad Shamir -
2017 Talk: Failures of Gradient-Based Deep Learning »
Shaked Shammah · Shai Shalev-Shwartz · Ohad Shamir -
2017 Talk: Oracle Complexity of Second-Order Methods for Finite-Sum Problems »
Yossi Arjevani · Ohad Shamir -
2017 Talk: Online Learning with Local Permutations and Delayed Feedback »
Liran Szlak · Ohad Shamir -
2017 Talk: Communication-efficient Algorithms for Distributed Stochastic Principal Component Analysis »
Dan Garber · Ohad Shamir · Nati Srebro