Abstmct-In this correspondence, we show how to recover the motion of an observer relative to a planar surface from image brightness derivatives. We do not compute the optical flow as an intermediate step, only the spatial and temporal brightness gradients (at a minimum of eight points). We first present two iterative schemes for solving nine nonlinear equations in terms of the motion and surface parameters that are derived from a least-squares fomulation. An initial pass over the relevant image region is wed to accumulate a number of moments of the image brightness derivatives. All of the quantities used in the iteration are efficiently computed from these totals without the need to refer back to the image. We then show that either of two possible solutions can be obtained in closed form. We first solve a linear matrix equation for the elements of a 3 x 3 matrix. The eigenvalue decomposition of the symmetric part of the matrix is then used to compute the motion parameters and the plane orientation. A new compact notation allows us to show easily that there are at most two planar solutions.

IEEE Transactions on Pattern Analysis and Machine Intelligence

Learning from data has led to paradigm shifts in a multitude of disciplines, including web, text and image search, speech recognition, as well as bioinformatics. Can machine learning enable similar breakthroughs in understanding quantum many-body systems? Here we develop an efficient deep learning approach that enables spatially and chemically resolved insights into quantum-mechanical observables of molecular systems. We unify concepts from many-body Hamiltonians with purpose-designed deep tensor neural networks, which leads to size-extensive and uniformly accurate (1 kcal mol−1) predictions in compositional and configurational chemical space for molecules of intermediate size. As an example of chemical relevance, the model reveals a classification of aromatic rings with respect to their stability. Further applications of our model for predicting atomic energies and local chemical potentials in molecules, reliable isomer energies, and molecules with peculiar electronic structure demonstrate the potential of machine learning for revealing insights into complex quantum-chemical systems.

/pdf/quantum-chemical-insights-from-deep-tensor-neural-networks-266u885pa4.pdf

Quantum-Chemical Insights from Deep Tensor Neural Networks

We introduce a potentially powerful new method of searching for new physics at the LHC, using autoencoders and unsupervised deep learning The key idea of the autoencoder is that it learns to map ``normal'' events back to themselves, but fails to reconstruct ``anomalous'' events that it has never encountered before The reconstruction error can then be used as an anomaly threshold We demonstrate the effectiveness of this idea using QCD jets as background and boosted top jets and R-parity violating (RPV) gluino jets as signal We show that a deep autoencoder can significantly improve signal over background when trained on backgrounds only, or even directly on data which contain a small admixture of signal Finally, we examine the correlation of the autoencoders with jet mass and show how the jet mass distribution can be stable against cuts in reconstruction loss This may be important for estimating QCD backgrounds from data As a test case, we show how one could plausibly discover 400 GeV RPV gluinos using an autoencoder combined with a bump hunt in jet mass This opens up the exciting possibility of training directly on actual data to discover new physics with no prior expectations or theory prejudice

Searching for New Physics with Deep Autoencoders

Autoencoder networks, trained only on QCD jets, can be used to search foranomalies in jet-substructure. We show how, based either on images or on4-vectors, they identify jets from decays of arbitrary heavy resonances. Tocontrol the backgrounds and the underlying systematics we can de-correlate thejet mass using an adversarial network. Such an adversarial autoencoder allowsfor a general and at the same time easily controllable search for new physics.Ideally, it can be trained and applied to data in the same phase space region,allowing us to efficiently search for new physics using un-supervised learning.

QCD or What

Particle physics is a branch of science aiming at discovering the fundamental laws of matter and forces. Graph neural networks are trainable functions which operate on graphs---sets of elements and their pairwise relations---and are a central method within the broader field of geometric deep learning. They are very expressive and have demonstrated superior performance to other classical deep learning approaches in a variety of domains. The data in particle physics are often represented by sets and graphs and as such, graph neural networks offer key advantages. Here we review various applications of graph neural networks in particle physics, including different graph constructions, model architectures and learning objectives, as well as key open problems in particle physics for which graph neural networks are promising.

Graph neural networks in particle physics

Top-squarks (stops) play a crucial role for the naturalness of supersymmetry (SUSY). However, searching for the stops is a tough task at the LHC. To dig the stops out of the huge LHC data, various expert-constructed kinematic variables or cutting-edge analysis techniques have been invented. In this paper, we propose to represent collision events as event graphs and use the message passing neutral network (MPNN) to analyze the events. As a proof-of-concept, we use our method in the search of the stop pair production at the LHC, and find that our MPNN can efficiently discriminate the signal and back-ground events. In comparison with other machine learning methods (e.g. DNN), MPNN can enhance the mass reach of stop mass by several tens of GeV to over a hundred GeV.

/pdf/probing-stop-pair-production-at-the-lhc-with-graph-neural-1lut13jlhm.pdf

Probing stop pair production at the LHC with graph neural networks

We consider a supersymmetric type-I seesaw framework with non-universal scalar masses at the GUT scale to explain the long-standing discrepancy of the anomalous magnetic moment of the muon. We find that it is difficult to accommodate the muon g-2 while keeping charged-lepton flavor violating processes under control for the conventional SO(10)-based relation between the up sector and neutrino sector. However, such tension can be relaxed by adding a Georgi-Jarlskog factor for the Yukawa matrices, which requires a non-trivial GUT-based model. In this model, we find that both observables are compatible for small mixings, CKM-like, in the neutrino Dirac Yukawa matrix.

/pdf/lfv-and-g-2-in-non-universal-susy-models-with-light-21kqyrvz3l.pdf

LFV and (g-2) in non-universal SUSY models with light higgsinos

Top-squarks (stops) play a crucial role for the naturalness of supersymmetry (SUSY). However, searching for the stops at the LHC is a tough task especially for some corners of parameter space. To dig the stops out of the huge LHC data, various expert-constructed kinematic variables or cutting-edge analysis techniques have been invented. In this paper, we propose to represent events as graphs and use the message passing neutral network to search for the stops through the process $pp \to \tilde{t}_1\tilde{t}^*_1 \to t\bar{t}\chi^0_1 \chi^0_1$ at the LHC. We find that the signal and background events can be efficiently discriminated by the patterns of event graphs. Such an approach can thus greatly improve the current LHC sensitivity for the stops.

Probing stop with graph neural network at the LHC

The natural supersymmetry usually predicts an under-abundance of thermally-produced higgsino LSP (lightest supersymmetric particle). Allowing for a sizable bino mixture into the LSP can readily achieve the observed dark matter relic density without worsening the naturalness. In this work, we examine such mixed bino-higgsino dark matter in natural supersymmetry by considering various constraints from the LEP, the dark matter direct detections and the LHC experiments. We find that the relative sign between the mass parameters $\mu$ and $M_1$ plays an important role in the phenomenology of this scenario. For $sign(\mu/M_1)=+1$, the most stringent constraints are from the very recent spin-independent (SI) scattering cross section limits given by the Xenon1T (2017) experiment, which can almost exclude the whole parameter space allowed by the relic density and collider bounds. But for $sign(\mu/M_1)=-1$, the SI limits can be evaded due to the cancelation effects in the $h\tilde{\chi}^0_1\tilde{\chi}^0_1$ coupling, while rather stringent constraints come from the PandaX-II (2016) spin-dependent (SD) scattering cross section limits, which can exclude the higgsino mass $|\mu|$ up to about 230 GeV. The projected XENON1T experiment will be able to fully cover such mixed bino-higgsino dark matter scenario in the future. Besides, we also estimate the HL-LHC potential to probe this scenario through searching for the trilepton events.

The mixed bino-higgsino dark matter in natural SUSY confronted with XENON1T/PandaX and LHC data

Top-squarks (stops) play a crucial role for the naturalness of supersymmetry (SUSY). However, searching for the stops is a tough task at the LHC. To dig the stops out of the huge LHC data, various expert-constructed kinematic variables or cutting-edge analysis techniques have been invented. In this paper, we propose to represent collision events as event graphs and use the message passing neutral network (MPNN) to analyze the events. As a proof-of-concept, we use our method in the search of the stop pair production at the LHC, and find that our MPNN can efficiently discriminate the signal and background events. In comparison with other machine learning methods (e.g. DNN), MPNN can enhance the mass reach of stop mass by several tens of GeV to over a hundred GeV.

/pdf/probing-stop-pair-production-at-the-lhc-with-graph-neural-3nxx700x2o.pdf

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Probing stop pair production at the LHC with graph neural networks

LFV and (g-2) in non-universal SUSY models with light higgsinos

Probing stop with graph neural network at the LHC

The mixed bino-higgsino dark matter in natural SUSY confronted with XENON1T/PandaX and LHC data

Probing stop pair production at the LHC with graph neural networks