A General Theory for Softmax Gating Multinomial Logistic Mixture of Experts Article Swipe

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Huy Hung Nguyen , Pedram Akbarian , TrungTin Nguyen , Nhat Ho ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2310.14188

Mixture-of-experts (MoE) model incorporates the power of multiple submodels via gating functions to achieve greater performance in numerous regression and classification applications. From a theoretical perspective, while there have been previous attempts to comprehend the behavior of that model under the regression settings through the convergence analysis of maximum likelihood estimation in the Gaussian MoE model, such analysis under the setting of a classification problem has remained missing in the literature. We close this gap by establishing the convergence rates of density estimation and parameter estimation in the softmax gating multinomial logistic MoE model. Notably, when part of the expert parameters vanish, these rates are shown to be slower than polynomial rates owing to an inherent interaction between the softmax gating and expert functions via partial differential equations. To address this issue, we propose using a novel class of modified softmax gating functions which transform the input before delivering them to the gating functions. As a result, the previous interaction disappears and the parameter estimation rates are significantly improved.

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Artificial Intelligence

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Softmax function Gating Multinomial logistic regression Multinomial distribution Sketch Mixture model Logistic regression Mathematics Computer science Applied mathematics Convergence (economics) Artificial intelligence Econometrics Statistics Pattern recognition (psychology) Algorithm Artificial neural network Biology Economics Economic growth Physiology

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2310.14188
PDF: https://arxiv.org/pdf/2310.14188
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Cited By: 2
Related Works: 10
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DOI: https://doi.org/10.48550/arxiv.2310.14188

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Title: A General Theory for Softmax Gating Multinomial Logistic Mixture of Experts

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Language: en

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Publication year: 2023

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Publication date: 2023-10-22

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Authors: Huy Hung Nguyen, Pedram Akbarian, TrungTin Nguyen, Nhat Ho

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Landing page: https://arxiv.org/abs/2310.14188

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Concepts: Softmax function, Gating, Multinomial logistic regression, Multinomial distribution, Sketch, Mixture model, Logistic regression, Mathematics, Computer science, Applied mathematics, Convergence (economics), Artificial intelligence, Econometrics, Statistics, Pattern recognition (psychology), Algorithm, Artificial neural network, Biology, Economics, Economic growth, Physiology

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Cited by: 2

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abstract_inverted_index.(MoE)	1
abstract_inverted_index.class	137
abstract_inverted_index.close	72
abstract_inverted_index.input	146
abstract_inverted_index.model	2, 38
abstract_inverted_index.novel	136
abstract_inverted_index.owing	112
abstract_inverted_index.power	5
abstract_inverted_index.rates	79, 103, 111, 165
abstract_inverted_index.shown	105
abstract_inverted_index.there	27
abstract_inverted_index.these	102
abstract_inverted_index.under	39, 58
abstract_inverted_index.using	134
abstract_inverted_index.which	143
abstract_inverted_index.while	26
abstract_inverted_index.before	147
abstract_inverted_index.expert	99, 122
abstract_inverted_index.gating	10, 89, 120, 141, 152
abstract_inverted_index.issue,	131
abstract_inverted_index.model,	55
abstract_inverted_index.model.	93
abstract_inverted_index.slower	108
abstract_inverted_index.achieve	13
abstract_inverted_index.address	129
abstract_inverted_index.between	117
abstract_inverted_index.density	81
abstract_inverted_index.greater	14
abstract_inverted_index.maximum	48
abstract_inverted_index.missing	67
abstract_inverted_index.partial	125
abstract_inverted_index.problem	64
abstract_inverted_index.propose	133
abstract_inverted_index.result,	156
abstract_inverted_index.setting	60
abstract_inverted_index.softmax	88, 119, 140
abstract_inverted_index.through	43
abstract_inverted_index.vanish,	101
abstract_inverted_index.Gaussian	53
abstract_inverted_index.Notably,	94
abstract_inverted_index.analysis	46, 57
abstract_inverted_index.attempts	31
abstract_inverted_index.behavior	35
abstract_inverted_index.inherent	115
abstract_inverted_index.logistic	91
abstract_inverted_index.modified	139
abstract_inverted_index.multiple	7
abstract_inverted_index.numerous	17
abstract_inverted_index.previous	30, 158
abstract_inverted_index.remained	66
abstract_inverted_index.settings	42
abstract_inverted_index.functions	11, 123, 142
abstract_inverted_index.improved.	168
abstract_inverted_index.parameter	84, 163
abstract_inverted_index.submodels	8
abstract_inverted_index.transform	144
abstract_inverted_index.comprehend	33
abstract_inverted_index.delivering	148
abstract_inverted_index.disappears	160
abstract_inverted_index.equations.	127
abstract_inverted_index.estimation	50, 82, 85, 164
abstract_inverted_index.functions.	153
abstract_inverted_index.likelihood	49
abstract_inverted_index.parameters	100
abstract_inverted_index.polynomial	110
abstract_inverted_index.regression	18, 41
abstract_inverted_index.convergence	45, 78
abstract_inverted_index.interaction	116, 159
abstract_inverted_index.literature.	70
abstract_inverted_index.multinomial	90
abstract_inverted_index.performance	15
abstract_inverted_index.theoretical	24
abstract_inverted_index.differential	126
abstract_inverted_index.establishing	76
abstract_inverted_index.incorporates	3
abstract_inverted_index.perspective,	25
abstract_inverted_index.applications.	21
abstract_inverted_index.significantly	167
abstract_inverted_index.classification	20, 63
abstract_inverted_index.Mixture-of-experts	0
cited_by_percentile_year
countries_distinct_count	1
institutions_distinct_count	4
citation_normalized_percentile