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Incorporating Piecewise Linear Funct...

Dogan, Adnan Harun,

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Incorporating Piecewise Linear Functions with Constant Regions in Backpropagation = = Sabit Bolgeli Parcali Dogrusal Fonsi̇yonlarin Geri Yayilim Algoritmasina Dahil Edilmesi /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Incorporating Piecewise Linear Functions with Constant Regions in Backpropagation =/ Adnan Harun Dogan.
Reminder of title:	Sabit Bolgeli Parcali Dogrusal Fonsi̇yonlarin Geri Yayilim Algoritmasina Dahil Edilmesi /
Author:	Dogan, Adnan Harun,
Description:	1 electronic resource (106 pages)
Notes:	Source: Masters Abstracts International, Volume: 86-10.
Contained By:	Masters Abstracts International86-10.
Subject:	Integer programming. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31929028
ISBN:	9798311929455

Incorporating Piecewise Linear Functions with Constant Regions in Backpropagation = = Sabit Bolgeli Parcali Dogrusal Fonsi̇yonlarin Geri Yayilim Algoritmasina Dahil Edilmesi /
Dogan, Adnan Harun,

Incorporating Piecewise Linear Functions with Constant Regions in Backpropagation =Sabit Bolgeli Parcali Dogrusal Fonsi̇yonlarin Geri Yayilim Algoritmasina Dahil Edilmesi /Adnan Harun Dogan. - 1 electronic resource (106 pages)

Source: Masters Abstracts International, Volume: 86-10.

Solving many fundamental problems, such as travelling salesman (TS), shortest path (SP), and graph matching (GM), requires the use of piecewise linear functions with constant regions (PFC). Although using such functions in deep neural networks (DNN) is promising, integrating a PFC into a DNN poses a significant challenge for gradient-based iterative optimizations. That is, traditional backpropagation methods struggle when encountering PFCs in DNN pipelines, leading to zero or undefined gradients that stall training. Although various heuristics-based gradient approximations exist, these approaches often remain task-specific and theoretically ungrounded.This thesis addresses the need for a unified and theoretically sound methodology for gradient approximation through PFC layers. First, it provides a comprehensive review and comparative analysis of existing techniques, highlighting that, despite their diversity, most methods share a common underlying principle. Building on these insights, the thesis introduces the Generalized Update (GU) as a unifying framework capable of representing known approximations as special cases and inspiring the development of new variants. The thesis also integrates Optimal Transport (OT) theory to replace non-differentiable label assignment in models like DEtection TRansformer (DETR), demonstrating how OT-based solutions can enhance tasks involving discrete decision-making.Overall, the thesis empirically validates the Generalized Update method's effectiveness across multiple domains, including object detection, combinatorial optimization, and quantization. By closing the theoretical gap, offering a unified perspective, and validating the proposed approach in practice, this work provides a robust foundation for incorporating PFCs into DNN pipelines, ultimately broadening the scope and applicability of gradient-based optimization methods.

English

ISBN: 9798311929455Subjects--Topical Terms:

648270
Integer programming.

Incorporating Piecewise Linear Functions with Constant Regions in Backpropagation = = Sabit Bolgeli Parcali Dogrusal Fonsi̇yonlarin Geri Yayilim Algoritmasina Dahil Edilmesi /
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500 $a Advisors: Kalkan, Sinan; Akbas, Emre.
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520 $a Solving many fundamental problems, such as travelling salesman (TS), shortest path (SP), and graph matching (GM), requires the use of piecewise linear functions with constant regions (PFC). Although using such functions in deep neural networks (DNN) is promising, integrating a PFC into a DNN poses a significant challenge for gradient-based iterative optimizations. That is, traditional backpropagation methods struggle when encountering PFCs in DNN pipelines, leading to zero or undefined gradients that stall training. Although various heuristics-based gradient approximations exist, these approaches often remain task-specific and theoretically ungrounded.This thesis addresses the need for a unified and theoretically sound methodology for gradient approximation through PFC layers. First, it provides a comprehensive review and comparative analysis of existing techniques, highlighting that, despite their diversity, most methods share a common underlying principle. Building on these insights, the thesis introduces the Generalized Update (GU) as a unifying framework capable of representing known approximations as special cases and inspiring the development of new variants. The thesis also integrates Optimal Transport (OT) theory to replace non-differentiable label assignment in models like DEtection TRansformer (DETR), demonstrating how OT-based solutions can enhance tasks involving discrete decision-making.Overall, the thesis empirically validates the Generalized Update method's effectiveness across multiple domains, including object detection, combinatorial optimization, and quantization. By closing the theoretical gap, offering a unified perspective, and validating the proposed approach in practice, this work provides a robust foundation for incorporating PFCs into DNN pipelines, ultimately broadening the scope and applicability of gradient-based optimization methods.
520 $a Bircok temel problemi cozmek ---ornegin Gezgin Satici (TS), En Kisa Yol (SP) ve Cizge Izleme (GM)--- icin parcali dogrusal sabit aralikli fonksiyonlarin (PFC) kullanilmasi gerekir. Bu fonksiyonlari derin sinir aglarinda (DNN) kullanmak umut vaat etse de, bu entegrasyon gradyan tabanli yinelemeli optimizasyon icin onemli bir zorluk olusturur. Oyle ki, derin sinir aglarinda de kullanilan geleneksel geri yayilim yontemleri, bu fonksiyonlarla karsilastiklarinda, sifir veya tanimsiz turevin egitimi durdurmasindan dolayi, calismaz ve sorun yasarlar. Cesitli sezgisel gradyan benzetimleri gelistirilmis olsa da, bu yaklasimlar genellikle probleme ozgu ve/veya kuramsal temelden yoksun kalmaktadir.Bu tez, PFC katmanlari uzerinden gradyan benzetimi icin birlesik ve kuramsal acidan saglam bir metodoloji ihtiyacini ele almaktadir. Ilk olarak, mevcut tekniklerin kapsamli bir incelemesi ve karsilastirmali analizi sunularak, yontemlerin cesitliligine ragmen ortak bir temel ilkeye dayandigi vurgulanmistir. Bu analizden hareketle, bilinen benzetimleri ozel durumlar olarak temsil edebilen ve yeni varyantlarin gelistirilmesine ilham veren Genellestirilmis Guncelleme (Generalized Update - GU) yontemi tanitilmistir. Ayrica, DEtection TRansformer (DETR) gibi modellerde turevi alinamayan etiket atamasini degistirmek amaciyla Optimal Tasima (OT) kurami entegre edilerek, OT tabanli cozumlerin ayrik karar sureclerini iyilestirebilecegi gosterilmistir.Genel olarak, tez, Genellestirilmis Guncelleme yonteminin nesne tespiti, kombinatoryel optimizasyon ve kuantizasyon gibi alanlarda etkinligini deneysel olarak dogrulamaktadir. Bu yaklasim, bu fonksiyonlarin derin sinir aglarina entegrasyonu icin saglam bir temel sunarak, gradyan tabanli optimizasyon yontemlerinin kapsamini ve uygulanabilirligini genisletmektedir.
546 $a English
590 $a School code: 2013
650 4 $a Integer programming. $3 648270
650 4 $a Deep learning. $3 3554982
650 4 $a Back propagation. $3 3681810
650 4 $a Success. $3 518195
650 4 $a Decision making. $3 517204
650 4 $a Neural networks. $3 677449
650 4 $a Linear programming. $3 560448
650 4 $a Natural language processing. $3 1073412
650 4 $a Semantics. $3 520060
650 4 $a Robotics. $3 519753
690 $a 0771
690 $a 0800
710 2 $a Middle East Technical University (Turkey). $b Department of Computer Engineering. $e degree granting institution. $3 3821962
720 1 $a Kalkan, Sinan $e degree supervisor.
720 1 $a Akbas, Emre $e degree supervisor.
773 0 $t Masters Abstracts International $g 86-10.
790 $a 2013
791 $a M.S.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31929028