{"componentChunkName":"component---src-templates-course-unit-page-tsx","path":"/en/courseunit/802679s/","result":{"data":{"translations":{"edges":[{"node":{"context":{"locale":"fi","code":"802679S","title":"Mathematical Principles of Deep Learning"},"path":"/fi/opintojakso/802679s/"}},{"node":{"context":{"locale":"en","code":"802679S","title":"Mathematical Principles of Deep Learning"},"path":"/en/courseunit/802679s/"}}]},"SISU":{"courseUnit":[{"id":"otm-c100300c-ebe0-3931-92e5-e4786c2c1b49","code":"802679S","name":{"en":"Mathematical Principles of Deep Learning","fi":"Mathematical Principles of Deep Learning","sv":"Mathematical Principles of Deep Learning"},"credits":{"max":5,"min":5},"studyLevel":null,"possibleAttainmentLanguages":[{"name":{"en":"English","fi":"englanti","sv":"engelska"}}],"responsibleOrganisations":[],"coordinatingOrganisations":[],"curriculumPeriods":[],"cooperationNetworkDirection":"INBOUND","cooperationNetworks":[{"targetGroups":[{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["jy-DP-21321","jy-DP-13215","otm-157daa3c-6f87-4d1d-86e2-5f2ed9872b58","jy-DP-13221","jy-DP-21280"],"phase2OptionGroupIds":null,"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":null,"phase2OptionGroupIds":["jy-DP-15471","jy-DP-13215"],"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["otm-af81f116-e2c7-4ddd-a995-b5a3f769efd0"],"phase2OptionGroupIds":null,"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":["otm-7115fcfa-a836-4071-87dd-12907142ff6e"],"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["otm-d4ca8e88-2100-4732-9b27-613c74807e98"],"phase2OptionGroupIds":null,"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":["otm-56907236-443b-46cc-82cd-4f5f900be109"],"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["otm-141caed2-2906-4382-8115-8a32f8aea2d9"],"phase2OptionGroupIds":null,"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":["otm-a1152c89-5848-4824-b84c-d9b9366c8de3"],"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":null,"phase2OptionGroupIds":["otm-141caed2-2906-4382-8115-8a32f8aea2d9"],"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":["otm-a1152c89-5848-4824-b84c-d9b9366c8de3"],"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null}],"description":{"en":"<p>This course is offered through the Network for Advanced Studies in Mathematics. 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Verkoston opinnot ovat tarjolla seuraaville opiskelijoille:</p><ul><li>Matematiikan kandidaattiohjelma</li><li>Matematiikan maisteriohjelma</li><li>Matematiikan aineenopettajien kandidaattiohjelma</li><li>Matematiikan aineenopettajien maisteriohjelma</li><li>Matematiikan, kemian tai fysiikan aineenopettajan ja luokanopettajan kandidaattiohjelma (matematiikan opintosuunta)</li><li>Matematiikan, kemian tai fysiikan aineenopettajan ja luokanopettajan maisteriiohjelma (matematiikan opintosuunta)</li><li>Matematiikan ja tilastotieteen tohtoriohjelma</li><li>Matemaattisten tieteiden ja luonnontieteiden tohtoriohjelma (matematiikan opintosuunta)</li><br></ul>"},"cooperationNetwork":{"abbreviation":"matematiikansyventavat","name":{"en":"Cross-institutional studies in advanced courses in mathematics and statistics","fi":"Matematiikan ja tilastotieteen syventävien kurssien ristiinopiskelu","sv":"Korsstudier i fördjupade kurser i matematik och statistik"}}},{"targetGroups":[{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["jy-DP-15471","jy-DP-21321","jy-DP-13215","otm-157daa3c-6f87-4d1d-86e2-5f2ed9872b58","jy-DP-13221","jy-DP-21280","jy-DP-30241"],"phase2OptionGroupIds":null,"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":null,"phase2OptionGroupIds":["jy-DP-15471","jy-DP-13215","jy-DP-30241"],"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null}],"description":{"en":"<p>This course is offered through the Network for Inverse Problems. These studies are available for the following degree students:<br><br></p><ul><li>Bachelor's Degree Programme in Mathematics</li><li>Bachelor's Degree Programme in Mathematics (Subject Teacher)</li><li>Master’s Degree Programme in Mathematics</li><li>Master's degree Programme in Mathematics (Subject Teacher)</li><li>Doctoral Degree Programme in Mathematics and Statistics</li></ul>","fi":"<p>Tämä opintojakso on tarjolla Inversio-ongelmien verkostossa. Verkoston opinnot ovat tarjolla seuraavien tutkinto-ohjelmien opiskelijoille:<br><br></p><ul><li>Matematiikan kandidaattiohjelma</li><li>Matematiikan aineenopettajan kandidaattiohjelma</li><li>Matematiikan maisteriohjelma</li><li>Matematiikan aineenopettajan&nbsp;maisteriohjelma</li><li>Matematiikan\nja tilastotieteen tohtoriohjelma</li></ul>"},"cooperationNetwork":{"abbreviation":"inversio","name":{"en":"Education network on Inverse Problems","fi":"Inversio-ongelmien koulutusverkosto"}}}],"gradeScaleId":"sis-0-5","outcomes":{"en":"Students will get familiar with mathematical concepts of neural networks and deep learning. We will introduce neural networks in a mathematical framework of function approximation and show that neural networks are universal approximator and how deep neural networks achieve efficient representations. We will discuss the concept of infinite width neural networks and Barron spaces.\r\nFurthermore, optimization methods, backpropagation and generalization properties of neural networks will be discussed. After the course, the student will understand neural networks from a fundamental mathematical perspective. The course is NOT aimed to discuss applications of neural networks beyond classification.","fi":"Students will get familiar with mathematical concepts of neural networks and deep learning. We will introduce neural networks in a mathematical framework of function approximation and show that neural networks are universal approximator and how deep neural networks achieve efficient representations. We will discuss the concept of infinite width neural networks and Barron spaces.\r\nFurthermore, optimization methods and generalization of neural networks will be discussed. After the course, the student will understand neural networks from a fundamental mathematical perspective. The course is NOT aimed to discuss applications of neural networks beyond classification."},"tweetText":null,"content":{"en":"Universal approximation theorem, benefit of depth in neural networks (deep learning), infinite width networks, Barron spaces, Neural Tangent Kernel, Optimization and stochastic gradient descent, backpropagation, non differentiability, Nesterov acceleration, Generalisation properties, margin maximization, implicit Bias, Rademacher complexity.","fi":"Universal approximation theorem, benefit of depth in neural networks (deep learning), infinite width networks, Barron spaces, Neural Tangent Kernel, Optimization and stochastic gradient descent, backpropagation, non differentiability, Nesterov acceleration, Generalisation properties, margin maximization, implicit Bias, Rademacher complexity."},"additional":{"en":"Timing\r\n3rd/last year during B.Sc., M.Sc. studies or PhD studies.\r\n\r\nTarget group\r\nStudents having mathematics, applied mathematics, or statistics as the major or a minor subject. Theoretical Computer Science. Background in mathematics is necessary.","fi":"Timing\r\n3rd/last year during B.Sc., M.Sc. studies or PhD studies.\r\n\r\nTarget group\r\nStudents having mathematics, applied mathematics, or statistics as the major or a minor subject. Theoretical Computer Science. Background in mathematics is necessary."},"prerequisites":{"en":"Core courses in the B.Sc curriculum of mathematical sciences, especially Analysis 1 NM00BD54, Analysis 2 NM00BD55,802651S Measure and Integral.\r\n\r\nAdditionally as recommended: optimization (recommended), Mathematics of Imaging and Vision (beneficial, but not necessary).","fi":"Core courses in the B.Sc curriculum of mathematical sciences, especially Analysis 1 NM00BD54, Analysis 2 NM00BD55,802651S Measure and Integral.\r\n\r\nAdditionally as recommended: optimization (recommended), Mathematics of Imaging and Vision (beneficial, but not necessary)."},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Mathematical Principles of Deep Learning","id":"otm-c100300c-ebe0-3931-92e5-e4786c2c1b49","code":"802679S","prerequisiteCourseUnitIds":[],"prerequisiteModuleIds":[],"parentModuleIds":[],"curriculumPeriodStartDate":"2026-08-01","curriculumPeriodEndDate":"2027-08-01","coordinatingOrgIds":[],"searchable":false,"searchTags":null,"organisationIds":["otm-71fd8cc0-9fb4-38e1-bbb0-d1d63f911ddf"],"organisations":[],"attainmentLanguages":["en"],"hasSummerStudies":false,"teachingPeriods":[],"cooperationNetworkDirection":"INBOUND","hasCooperationNetworkSettings":true,"hasAvoinTeaching":false}}}