Fetching the paper…
Reading the bibliography…
A soft-max function has two main efficiency measures: (1) approximation - which corresponds to how well it approximates the maximum function, (2) smoothness - which shows how sensitive it is to changes of its input.
Elementary Principles in Statistical Mechanics: Developed with Especial Reference to the Rational Foundations of Thermodynamics
J.W. Gibbs · 1902
Earlier work this paper cites.
A further generalization of the kakutani fixed point theorem, with application to nash equilibrium points
Irving L Glicksberg · 1952
Earlier work this paper cites.
Individual Choice Behavior: A Theoretical Analysis
R. Duncan Luce · 1959
Earlier work this paper cites.
Optimal auction design
Roger B Myerson · 1981
Earlier work this paper cites.
The theory of the Riemann zeta-function
Edward Charles Titchmarsh and David Rodney Heath-Brown · 1986
Earlier work this paper cites.
Probabilistic interpretation of feedforward classification network outputs, with relationships to statistical pattern recognition
John S. Bridle · 1990
Earlier work this paper cites.
Training stochastic model recognition algorithms as networks can lead to maximum mutual information estimation of parameters
John S. Bridle · 1990
Earlier work this paper cites.
Hierarchical mixtures of experts and the em algorithm
Michael I. Jordan and Robert A. Jacobs · 1994
Earlier work this paper cites.
Computing the norm (oo,1) is np-hard
Jiří Rohn · 2000
Earlier work this paper cites.
Mechanism design via machine learning
M-F Balcan, Avrim Blum, Jason D Hartline, and Yishay Mansour · 2005
Earlier work this paper cites.
Hierarchical probabilistic neural network language model
Frederic Morin and Yoshua Bengio · 2005
Earlier work this paper cites.
Mechanism design via differential privacy
Frank McSherry and Kunal Talwar · 2007
Cited alongside, same era.
On the calculation of the l2→ l1 induced matrix norm
Konstantinos Drakakis and BA Pearlmutter · 2009
Cited alongside, same era.
Boosting and differential privacy
Cynthia Dwork, Guy N Rothblum, and Salil Vadhan · 2010
Cited alongside, same era.
Matrix p-norms are np-hard to approximate if p ≠ 1 , 2 , ∞ p\neq 1,2,\infty
Julien M Hendrickx and Alex Olshevsky · 2010
Cited alongside, same era.
The exponential mechanism for social welfare: Private, truthful, and nearly optimal
Zhiyi Huang and Sampath Kannan · 2012
Cited alongside, same era.
Supply-limiting mechanisms
Tim Roughgarden, Inbal Talgam-Cohen, and Qiqi Yan · 2012
Cited alongside, same era.
On the pseudo-dimension of nearly optimal auctions
Jamie H Morgenstern and Tim Roughgarden · 2015
Later among the works it cites.
Efficient exact gradient update for training deep networks with very large sparse targets
Pascal Vincent, Alexandre De Brébisson, and Xavier Bouthillier · 2015
Later among the works it cites.
The sample complexity of auctions with side information
Nikhil R Devanur, Zhiyi Huang, and Christos-Alexandros Psomas · 2016
Later among the works it cites.
Deep Learning
Ian Goodfellow, Yoshua Bengio, and Aaron Courville · 2016
Later among the works it cites.
From softmax to sparsemax: A sparse model of attention and multi-label classification
Andre Martins and Ramon Astudillo · 2016
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Distributed representations of words and phrases and their compositionality
Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean · 2013
Cited alongside, same era.
The sample complexity of revenue maximization
Richard Cole and Tim Roughgarden · 2014
Cited alongside, same era.
The algorithmic foundations of differential privacy
Cynthia Dwork and Aaron Roth · 2014
Cited alongside, same era.
An exploration of softmax alternatives belonging to the spherical loss family
Alexandre de Brébisson and Pascal Vincent · 2015
Cited alongside, same era.
Revenue maximization with a single sample
Peerapong Dhangwatnotai, Tim Roughgarden, and Qiqi Yan · 2015
Cited alongside, same era.
Studien uber das gleichgewicht der lebenden kraft
Ludwig Boltzmann
Cited in the paper.
Yang Cai and Constantinos Daskalakis · 2017
Later among the works it cites.
Bicriteria distributed submodular maximization in a few rounds
Alessandro Epasto, Vahab Mirrokni, and Morteza Zadimoghaddam · 2017
Later among the works it cites.
Differentially private submodular maximization: Data summarization in disguise
Marko Mitrovic, Mark Bun, Andreas Krause, and Amin Karbasi · 2017
Later among the works it cites.
On controllable sparse alternatives to softmax
Anirban Laha, Saneem Ahmed Chemmengath, Priyanka Agrawal, Mitesh Khapra, Karthik Sankaranarayanan, and Harish G Ramaswamy · 2018
Later among the works it cites.
Reinforcement Learning: An Introduction
Richard S. Sutton and Andrew G. Barto · 2018
Later among the works it cites.