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Product of experts (PoE) are layered networks in which the value at each node is an AND (or product) of the values (possibly negated) at its inputs. These were introduced as a neural network architecture that can efficiently learn to generate high-dimensional data which satisfy many low-dimensional constraints---thereby allowing each individual expert to perform a simple task. PoEs have found a variety of applications in learning. We study the problem of identifiability of a product of experts model having a layer of binary latent variables, and a layer of binary observables that are iid conditional on the latents. The previous best upper bound on the number of observables needed to identify the model was exponential in the number of parameters. We show: (a) When the latents are uniformly distributed, the model is identifiable with a number of observables equal to the number of parameters (and hence best possible). (b) In the more general case of arbitrarily distributed latents, the model is identifiable for a number of observables that is still linear in the number of parameters (and within a factor of two of best-possible). The proofs rely on root interlacing phenomena for some special three-term recurrences. 

The ALICE Collaboration reports measurements of the semi-inclusive distribution of charged-particle jets recoiling from a high transverse momentum (high$p_{\mathrm{T}}$) charged hadron, in$pp$and central Pb-Pb collisions at center-of-mass energy per nucleon–nucleon collision$\sqrt{s_{\mathrm{NN}}}=5.02$TeV. The large uncorrelated background in central Pb-Pb collisions is corrected using a data-driven statistical approach which enables precise measurement of recoil jet distributions over a broad range in$p_{\mathrm{T},\mathrm{ch}\mathrm{jet}}$and jet resolution parameter$R$. Recoil jet yields are reported for$R=0.2$, 0.4, and 0.5 in the range$7<p_{\mathrm{T},\mathrm{ch}\mathrm{jet}}<140 \mathrm{GeV}/c$and$\pi /2<\mathrm{\Delta }\phi <\pi$, where$\mathrm{\Delta }\phi$is the azimuthal angular separation between hadron trigger and recoil jet. The low-$p_{\mathrm{T},\mathrm{ch}\mathrm{jet}}$reach of the measurement explores unique phase space for studying jet quenching, the interaction of jets with the quark–gluon plasma generated in high-energy nuclear collisions. Comparison of$p_{\mathrm{T},\mathrm{ch}\mathrm{jet}}$distributions from$pp$and central Pb-Pb collisions probes medium-induced jet energy loss and intra-jet broadening, while comparison of their acoplanarity distributions explores in-medium jet scattering and medium response. The measurements are compared to theoretical calculations incorporating jet quenching.

Measurements of inclusive charged-particle jet production in pp and p-Pb collisions at center-of-mass energy per nucleon-nucleon collision$$ \sqrt{s_{\textrm{NN}}} $$$\sqrt{s_{\mathrm{NN}}}$= 5.02 TeV and the corresponding nuclear modification factor$$ {R}_{\textrm{pPb}}^{\textrm{ch}\ \textrm{jet}} $$$R_{\mathrm{pPb}}^{\mathrm{ch}\mathrm{jet}}$are presented, using data collected with the ALICE detector at the LHC. Jets are reconstructed in the central rapidity region |η_jet|<0.5 from charged particles using the anti-k_Talgorithm with resolution parametersR= 0.2, 0.3, and 0.4. Thep_T-differential inclusive production cross section of charged-particle jets, as well as the corresponding cross section ratios, are reported for pp and p-Pb collisions in the transverse momentum range 10<$$ {p}_{\textrm{T},\textrm{jet}}^{\textrm{ch}} $$$p_{T,\mathrm{jet}}^{\mathrm{ch}}$<140 GeV/cand 10<$$ {p}_{\textrm{T},\textrm{jet}}^{\textrm{ch}} $$$p_{T,\mathrm{jet}}^{\mathrm{ch}}$<160 GeV/c, respectively, together with the nuclear modification factor$$ {R}_{\textrm{pPb}}^{\textrm{ch}\ \textrm{jet}} $$$R_{\mathrm{pPb}}^{\mathrm{ch}\mathrm{jet}}$in the range 10<$$ {p}_{\textrm{T},\textrm{jet}}^{\textrm{ch}} $$$p_{T,\mathrm{jet}}^{\mathrm{ch}}$<140 GeV/c. The analysis extends thep_Trange of the previously-reported charged-particle jet measurements by the ALICE Collaboration. The nuclear modification factor is found to be consistent with one and independent of the jet resolution parameter with the improved precision of this study, indicating that the possible influence of cold nuclear matter effects on the production cross section of charged-particle jets in p-Pb collisions at$$ \sqrt{s_{\textrm{NN}}} $$$\sqrt{s_{\mathrm{NN}}}$= 5.02 TeV is smaller than the current precision. The obtained results are in agreement with other minimum bias jet measurements available for RHIC and LHC energies, and are well reproduced by the NLO perturbative QCD Powhegcalculations with parton shower provided by Pythia8 as well as by Jetscapesimulations.

 

The ALICE Collaboration reports a search for jet quenching effects in high-multiplicity (HM) proton-proton collisions at$$ \sqrt{s} $$$\sqrt{s}$= 13 TeV, using the semi-inclusive azimuthal-difference distribution ∆φof charged-particle jets recoiling from a high transverse momentum (high-p_T,trig) trigger hadron. Jet quenching may broaden the ∆φdistribution measured in HM events compared to that in minimum bias (MB) events. The measurement employs ap_T,trig-differential observable for data-driven suppression of the contribution of multiple partonic interactions, which is the dominant background. While azimuthal broadening is indeed observed in HM compared to MB events, similar broadening for HM events is observed for simulations based on the PYTHIA 8 Monte Carlo generator, which does not incorporate jet quenching. Detailed analysis of these data and simulations show that the azimuthal broadening is due to bias of the HM selection towards events with multiple jets in the final state. The identification of this bias has implications for all jet quenching searches where selection is made on the event activity.