Autoencoder Implementations in the predictive coding framework

Abstract. We study the implementation and functionality of autoencoders based on the predictive coding model and the free energy framework, which have seen relatively little experimentation. This framework offers an alternative approach to constructing artificial neural networks in place of traditional backpropagation networks. The limited number of studies published on the subject indicate that the framework could provide better solutions to applications employing artificial intelligence. This work is meant to accessible to any university student wishing to gain a preliminary understanding for the concepts involved. To this end we provide a detailed walkthrough of the core mathematical ideas behind the implementation using Bogacz’s great tutorial as a guide. We document the implementation process of two autoencoders that learn to recreate handwritten digits from the MNIST dataset in an unsupervised learning scenario. Both of these implementations utilize fully connected layers and are tasked with encoding and decoding of handwritten digits from the MNIST dataset. We analyze graphs of the different variable values and compare the final images produced by the autoencoder to the original ones. The first implementation is an attempt at constructing an original network and serves as an example of how error sensitive the construction of these networks from the ground up can be. We study the applicability of the theory of predictive coding in practice and diagnose the issues that we encounter. In particular, we showcase problems relating to the update of variances within the network and general difficulties in achieving convergence for all nodes in the network. The second implementation is built on top of a predictive coding library built by B. Millidge and A. Tschantz and showcases the potential of predictive coding model as a basis for a functional autoencoder. We partially replicate the results obtained by Millidge to establish a baseline for the network’s performance. Furthermore, we study the effects of tuning different aspects of these networks to better understand the function of these types of networks. These aspects include the network depth, number of nodes per layer and activation functions. Subjective evaluation on the effects of these modifications is conducted. Our findings regarding the second implementation indicate that the most important factor in determining final image quality and classification capability is the width of the code layer of the autoencoder. Our experiments using different activation functions do not reveal significant performance gains for any of the functions used. Lastly, we look at the effects of deepening the network but find equal or worse performance when compared to shallow networks

High resolution pixel detectors for e+e- linear colliders

The physics goals at the future e+e- linear collider require high performance vertexing and impact parameter resolution. Two possible technologies for the vertex detector of an experimental apparatus are outlined in the paper: an evolution of the Hybrid Pixel Sensors already used in high energy physics experiments and a new detector concept based on the monolithic CMOS sensors.Comment: 8 pages, to appear on the Proceedings of the International Workshop on Linear Colliders LCWS99, Sitges (Spain), April 28 - May 5, 199

Measurement of the WW and WZ production cross section using final states with a charged lepton and heavy-flavor jets in the full CDF Run II data set

We present a measurement of the total WW and WZ production cross sections in p (p) over bar collision at root s = 1.96 TeV, in a final state consistent with leptonic W boson decay and jets originating from heavy-flavor quarks from either a W or a Z boson decay. This analysis uses the full data set collected with the CDF II detector during Run II of the Tevatron collider, corresponding to an integrated luminosity of 9.4 fb(-1). An analysis of the dijet mass spectrum provides 3.7 sigma evidence of the summed production processes of either WW or WZ bosons with a measured total cross section of sigma(WW+WZ) = 13.7 +/- 3.9 pb. Independent measurements of the WW and WZ production cross sections are allowed by the different heavy- flavor decay patterns of the W and Z bosons and by the analysis of secondary- decay vertices reconstructed within heavy- flavor jets. The productions of WW and of WZ dibosons are independently seen with significances of 2.9s and 2.1s, respectively, with total cross sections of sigma(WW) = 9.4 +/- 4.2 pb and sigma(WZ) = 3.7(-2.2)(+2.5) pb. The measurements are consistent with standard- model predictions.Peer reviewe

Measurement of the differential cross sections for W-boson production in association with jets in p(p)over-bar collisions at root s=1.96 TeV

This paper presents a study of the production of a single W boson in association with one or more jets in proton-antiproton collisions at is root s = 1.96 TeV, using the entire data set collected in 2001-2011 by the Collider Detector at Fermilab at the Tevatron, which corresponds to an integrated luminosity of 9.0 fb(-1). The W boson is identified through its leptonic decays into electron and muon. The production cross sections are measured for each leptonic decay mode and combined after testing that the ratio of the W(-> mu v) + jets cross section to the W(-> ev) + jets cross section agrees with the hypothesis of e-mu lepton universality. The combination of measured cross sections, differential in the inclusive jet multiplicity (W + >= N jets with N = 1, 2, 3, or 4) and in the transverse energy of the leading jet, are compared with theoretical predictions.Peer reviewe

Measurement of sin(2) theta(lept)(eff) using e(+)e(-) pairs from gamma*/Z bosons produced in p(p)over-bar collisions at a center- of- momentum energy of 1.96 TeV

At the Fermilab Tevatron proton-antiproton (p (p) over bar) collider, Drell-Yan lepton pairs are produced in the process p (p) over bar -> e(+)e(-) + X through an intermediate gamma*/Z boson. The forward-backward asymmetry in the polar-angle distribution of the e(-) as a function of the e(+)e(-)-pair mass is used to obtain sin(2) theta(lept)(eff), the effective leptonic determination of the electroweak-mixing parameter sin(2) theta(W). The measurement sample, recorded by the Collider Detector at Fermilab (CDF), corresponds to 9.4 fb(-1) of integrated luminosity from p (p) over bar collisions at a center-of-momentum energy of 1.96 TeV, and is the full CDF Run II data set. The value of sin(2) theta(lept)(eff) is found to be 0.23248 +/- 0.00053. The combination with the previous CDF measurement based on mu(+)mu(-) pairs yields sin(2) theta(lept)(eff) = 0.23221 +/- 0.00046. This result, when interpreted within the specified context of the standard model assuming sin(2) theta(W) = 1 - M-W(2)/M-Z(2) and that the W- and Z-boson masses are on-shell, yields sin(2) theta(W) = 0.22400 +/- 0.00045, or equivalently a W-boson mass of 80.328 +/- 0.024 GeV/c(2).Peer reviewe

Measurement of the D+-meson production cross section at low transverse momentum in p(p)over-bar collisions at root s=1.96 TeV

We report on a measurement of the D+ -meson production cross section as a function of transverse momentum (p(T)) in proton-antiproton (p (p) over bar) collisions at 1.96 TeV center-of-mass energy, using the full data set collected by the Collider Detector at Fermilab in Tevatron Run II and corresponding to 10 fb(-1) of integrated luminosity. We use D-broken vertical bar -> K- pi(broken vertical bar) pi(broken vertical bar) decays fully reconstructed in the central rapidity region broken vertical bar y broken vertical bar <1 with transverse momentum down to 1.5 GeV/c, a range previously unexplored in p collisions. Inelastic p (p) over bar -scattering events are selected online using minimally biasing requirements followed by an optimized offline selection. The K- pi(+) pi(+) mass distribution is used to identify the D+ signal, and the D+ transverse impact-parameter distribution is used to separate prompt production, occurring directly in the hard-scattering process, from secondary production from b-hadron decays. We obtain a prompt D+ signal of 2950 candidates corresponding to a total cross section sigma(D+), 1.5 <P-T <14.5 GeV/c, vertical bar y vertical bar <1) = 71.9 +/- 6.8 (stat) +/- 9.3 (syst) mu b.While the measured cross sections are consistent with theoretical estimates in each p(T) bin, the shape of the observed p(T) spectrum is softer than the expectation from quantum chromodynamics. The results are unique in p collisions and can improve the shape and uncertainties of future predictions.Peer reviewe

Measurement of the charge asymmetry of electrons from the decays of W bosons produced in p p ¯ collisions at s =1.96 TeV

Publisher Copyright: © 2021 authors. Published by the American Physical Society.At the Fermilab Tevatron proton-antiproton (pp¯) collider, high-mass electron-neutrino (eν) pairs are produced predominantly in the process pp¯→W(→eν)+X. The asymmetry of the electron and positron yield as a function of their pseudorapidity constrain the slope of the ratio of the u- to d-quark parton distributions versus the fraction of the proton momentum carried by the quarks. This paper reports on the measurement of the electron-charge asymmetry using the full data set recorded by the Collider Detector at Fermilab in 2001-2011 and corresponding to 9.1 fb-1 of integrated luminosity. The measurement significantly improves the precision of the Tevatron constraints on the parton-distribution functions of the proton. Numerical tables of the measurement are provided.Peer reviewe

Dual-Regge Approach to High-Energy, Low-Mass Diffraction Dissociation

A dual-Regge model with a nonlinear proton Regge trajectory in the missing mass channel, describing the experimental data on low-mass single diffraction dissociation, is constructed. Predictions for the LHC energies are given.Comment: 14 pages, 12 figure

High-precision measurement of the W boson mass with the CDF II detector

The mass of the W boson, a mediator of the weak force between elementary particles, is tightly constrained by the symmetries of the standard model of particle physics. The Higgs boson was the last missing component of the model. After observation of the Higgs boson, a measurement of the W boson mass provides a stringent test of the model. We measure the W boson mass, M-W, using data corresponding to 8.8 inverse femtobarns of integrated luminosity collected in proton-antiproton collisions at a 1.96 tera-electron volt center-of-mass energy with the CDF II detector at the Fermilab Tevatron collider. A sample of approximately 4 million W boson candidates is used to obtain M-W = 80,433.5 +/- 6.4(stat) +/- 6.9(syst) = 80,433.5 +/- 9.4MeV/c(2), the precision of which exceeds that of all previous measurements combined (stat, statistical uncertainty; syst, systematic uncertainty; MeV, mega-electron volts; c, speed of light in a vacuum). This measurement is in significant tension with the standard model expectation.Peer reviewe

Production of pi(0) and eta mesons up to high transverse momentum in pp collisions at 2.76 TeV

Correction: DOI:10.1140/epjc/s10052-017-5144-7The invariant differential cross sections for inclusive pi(0) and eta mesons at midrapidity were measured in pp collisions at root s = 2.76 TeV for transverse momenta 0.4 <pT <40 GeV/c and 0.6 <pT <20 GeV/c, respectively, using the ALICE detector. This large range in pT was achieved by combining various analysis techniques and different triggers involving the electromagnetic calorimeter (EMCal). In particular, a newsingle-cluster, shower-shape based method was developed for the identification of high-pT neutral pions, which exploits that the showers originating from their decay photons overlap in the EMCal. Above 4 GeV/c, the measured cross sections are found to exhibit a similar power-law behavior with an exponent of about 6.3. Next-to-leading-order perturbative QCD calculations differ from the measured cross sections by about 30% for the pi(0), and between 30-50% for the. meson, while generator-level simulations with PYTHIA 8.2 describe the data to better than 10-30%, except at pT <1 GeV/c. The new data can therefore be used to further improve the theoretical description of pi(0) and eta meson production.Peer reviewe