{"title":"Connections between physics, mathematics, and deep learning.","authors":"Jean Thierry-Mieg","doi":"10.31526/lhep.3.2019.110","DOIUrl":"https://doi.org/10.31526/lhep.3.2019.110","url":null,"abstract":"<p><p>Starting from Fermat's principle of least action, which governs classical and quantum mechanics and from the theory of exterior differential forms, which governs the geometry of curved manifolds, we show how to derive the equations governing neural networks in an intrinsic, coordinate-invariant way, where the loss function plays the role of the Hamiltonian. To be covariant, these equations imply a layer metric which is instrumental in pretraining and explains the role of conjugation when using complex numbers. The differential formalism clarifies the relation of the gradient descent optimizer with Aristotelian and Newtonian mechanics. The Bayesian paradigm is then analyzed as a renormalizable theory yielding a new derivation of the Bayesian information criterion. We hope that this formal presentation of the differential geometry of neural networks will encourage some physicists to dive into deep learning and, reciprocally, that the specialists of deep learning will better appreciate the close interconnection of their subject with the foundations of classical and quantum field theory.</p>","PeriodicalId":36085,"journal":{"name":"Letters in High Energy Physics","volume":"2 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8462849/pdf/nihms-1732645.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39453131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Polarizability of the nucleon","authors":"M. Schumacher","doi":"10.31526/LHEP.4.2019.136","DOIUrl":"https://doi.org/10.31526/LHEP.4.2019.136","url":null,"abstract":"The status of the experimental and theoretical investigations on the polarizabilities of the nucleon is presented. This includes a confirmation of the validity of the previously introduced recommended values of the polarizabilities [1,2]. It is shown that the only meaningful approach to a prediction of the polarizabilities is obtained from the nonsubtracted dispersion theory, where the appropriate degrees of freedom taken from other precise experimental data are taken in account. The present values of the recommended polarizabilities are $alpha_p= 12.0 pm 0.5$, $beta_p= 1.9 mp 0.5$, $alpha_n= 12.6 pm 1.2$, $beta_n= 2.6 mp 1.2$ in units of $10^{-4}$fm$^3$ and $gamma^{(p)}_pi= -36.4 pm 1.5$, $gamma^{(n)}_pi =+58.6 pm 4.0$, $gamma^{(p)}_0=-0.58 pm 0.20$, $gamma^{(n)}_0= +0.38pm 0.22$ in units of $10^{-4}$fm$^4$.","PeriodicalId":36085,"journal":{"name":"Letters in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48197221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Asymmetric nonsingular bounce from a dynamic scalar field","authors":"F. Klinkhamer, Z. L. Wang","doi":"10.31526/lhep.3.2019.132","DOIUrl":"https://doi.org/10.31526/lhep.3.2019.132","url":null,"abstract":"We present a dynamical model for a time-asymmetric nonsingular bouncewith a post-bounce change of the effective equation-of-state parameter.Specifically, we consider a scalar-field model with atime-reversal-noninvariant effective potential.","PeriodicalId":36085,"journal":{"name":"Letters in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47556668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Thermodynamics of Relativistic Multi-Fluid Systems","authors":"B. Osano","doi":"10.31526/lhep.1.2020.141","DOIUrl":"https://doi.org/10.31526/lhep.1.2020.141","url":null,"abstract":"This article extends the single-fluid relativistic irreversible thermodynamics theory of {it M{u}ller}, {it Israel} and {it Stewart} (hereafter the {MIS} theory) to a multi-fluid system with inherent species interactions. This is illustrated in a two-fluid toy-model where an effective complex 4-velocity plays the role of a primary dynamical parameter. We find that an observer who resides in the {it real}-part of this universe will notice that their knowledge of the universe parametrized using {it real}, rather than {it imaginary}, quantities are insufficient to fully determine properties such as the total energy density, pressure or entropy, In fact, such an observer will deduce the existence of some negative energy that affects the expansion of their perceived {it real} universe.","PeriodicalId":36085,"journal":{"name":"Letters in High Energy Physics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41379164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A new perspective on the Ermakov-Pinney and scalar wave equations","authors":"G. Esposito, M. Minucci","doi":"10.31526/LHEP.3.2019.134","DOIUrl":"https://doi.org/10.31526/LHEP.3.2019.134","url":null,"abstract":"The first part of the paper proves that a subset of the general set of Ermakov-Pinney equations can be obtained by differentiation of a first-order non-linear differential equation. The second part of the paper proves that, similarly, the equation for the amplitude function for the parametrix of the scalar wave equation can be obtained by covariant differentiation of a first-order non-linear equation. The construction of such a first-order non-linear equation relies upon a pair of auxiliary 1-forms (psi,rho). The 1-form psi satisfies the divergenceless condition div(psi)=0, whereas the 1-form rho fulfills the non-linear equation div(rho)+rho**2=0. The auxiliary 1-forms (psi,rho) are evaluated explicitly in Kasner space-time, and hence also amplitude and phase function in the parametrix are obtained. Thus, the novel method developed in this paper can be used with profit in physical applications.","PeriodicalId":36085,"journal":{"name":"Letters in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46089026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Recipe for Conformal Blocks","authors":"J. Fortin, W. Skiba","doi":"10.31526/lhep.2022.293","DOIUrl":"https://doi.org/10.31526/lhep.2022.293","url":null,"abstract":"We describe a prescription for constructing conformal blocks in conformal field theories in any space-time dimension with arbitrary quantum numbers. Our procedure reduces the calculation of conformal blocks to constructing certain group theoretic structures that depend on the quantum numbers of primary operators. These structures project into irreducible Lorentz representations. Once the Lorentz quantum numbers are accounted for there are no further calculations left to do. We compute a multivariable generalization of the Exton function. This generalized Exton function, together with the group theoretic structures, can be used to construct conformal blocks for four-point as well as higher-point correlation functions.","PeriodicalId":36085,"journal":{"name":"Letters in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47232498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The role of residual symmetries in dark matter stability and the neutrino nature","authors":"C. Bonilla, E. Peinado, R. Srivastava","doi":"10.31526/lhep.1.2019","DOIUrl":"https://doi.org/10.31526/lhep.1.2019","url":null,"abstract":"We consider the class of models where Dirac neutrino masses at one loop and the dark matter stability can be obtained using only the global $U(1)_{B-L}$ symmetry already present in Standard Model. We discuss how the residual $mathcal{Z}_n$ subgroup, left unbroken after the breaking of $U(1)_{B-L}$, dictates the neutrino nature, namely if they are Dirac or Majorana particles, as well as determines the stability of the dark matter candidate in such models. In particular, we show that without the correct breaking of $U(1)_{B-L}$ to an appropriate residual $mathcal{Z}_n$ symmetry, the Dirac nature of neutrinos and/or dark matter stability might be lost. For completeness we also provide some examples where the dark matter stability is accidental or lost completely. Finally, we discuss one example model where the Dirac neutrinos with naturally small one loop masses as well as dark matter stability, are both protected by the same residual $mathcal{Z}_6$ subgroup, without need for adding any new explicit or accidental symmetries beyond the Standard Model symmetries.","PeriodicalId":36085,"journal":{"name":"Letters in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44588401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Group–Theoretical Origin of CP Violation","authors":"Mu-Chun Chen, M. Ratz","doi":"10.31526/LHEP.1.2019.125","DOIUrl":"https://doi.org/10.31526/LHEP.1.2019.125","url":null,"abstract":"This is a short review of the proposal that CP violation may be due to the fact that certain finite groups do not admit a physical CP transformation. This origin of CP violation is realized in explicit string compactifications exhibiting the Standard Model spectrum.","PeriodicalId":36085,"journal":{"name":"Letters in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41463047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quest for new physics in flavor mixing and Dirac neutrino masses","authors":"Gui-Jun Ding","doi":"10.31526/LHEP.1.2019.120","DOIUrl":"https://doi.org/10.31526/LHEP.1.2019.120","url":null,"abstract":"We show that a unified description of the observed patterns of quark and lepton mixing can be achieved if the flavor group $D_n$ and CP symmetry are broken to $Z_2times CP$ in the neutrino, charged lepton, up quark as well as down quark sectors, and the smallest group is $D_{14}$. We also perform a systematic study of how a dimension six operator $overline{L}widetilde{H}nu_{R}left(H^{dagger}Hright)$ for Dirac neutrino masses may occur at tree level and in one loop.","PeriodicalId":36085,"journal":{"name":"Letters in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47803425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Scalar Models of Formally Interacting Non-Standard Quantum Fields in Minkowski Space-Time","authors":"Andreas Walter Aste","doi":"10.31526/LHEP.2.2019.121","DOIUrl":"https://doi.org/10.31526/LHEP.2.2019.121","url":null,"abstract":"For decades, a lot of work has been devoted to the problem of constructing a non-trivial quantum field theory in four-dimensional space-time. This letter addresses the attempts to construct an algebraic quantum field theory in the framework of non-standard theories like hyperfunction or ultra-hyperfunction quantum field theory. Model theories of formally self-coupled interacting neutral scalar fields are solved and discussed from a non-perturbative point of view.","PeriodicalId":36085,"journal":{"name":"Letters in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48200258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
