The search for the top quark at pjj colliders in the one-lepton-plus-jets channel is plagued by an irremovable background from W-boson-plus-multijet production. In this paper, we show how the top-quark signal can be distinguished from background in the distribution of neural network output. By making a cut on the network output, we maximize the ratio of signal to background in a final event sample, and compare our results with those obtained by making kinematical cuts on the data sample. We also demonstrate the robustness of the neural network method by training the neural network on signal events of one top mass and testing upon another. PACS number(s): 13.85.Qk, 14.80.DqThe top quark t is a necessary ingredient of the standard model (SM), as it is required to ensure the cancellation of triangle anomalies [I], to account for the e+e-+ b6 forward-backward jet asymmetry 121, and for the suppression of neutral current B decays [3]. Radiative corrections to SM parameters measured at the CERN e+e-collider LEP constrain the top-quark mass to be 89 GeV < mt < 191 GeV 141. The lack of a topquark signal at the Fermilab Tevatron to date furthermore restricts mt > 91 GeV 151. The search for top quarks of mass up to -120 -140 GeV at the Fermilab Tevatron is expected to resume in 1992, with the planned collection of 20 pb-l of data.The top quark at the Fermilab Tevatron collider is expected to be produced dominantly via the gg --+ tf and qq --+ tf pair production channels. Since mt > Mw + ma, a SM top quark decays via t + bW where the W is on shell; hence, a ti? event results in a b6W+Wd final state. The cleanest signal for tf occurs in the two-lepton channel; the two leptons arise from the leptonic decay of each W boson. The principal backgrounds from Wpair production and y, Z --, T+T-are expected to be controllable [6]. Event rates in the twelepton channel will be low because of the two leptonic branching ratios; moreover, this channel does not provide a direct determination of the topquark mass because the two neutrinos from W + lv carry off an unknown amount of pr. The best one can do is to either match the total event rate to QCD predictions (which depend on mt), or to measure the relative rates, Rllo and Rzll, of multijet production in events with two isolated leptons 161. Here, Rilj stands for the ratio of events with i jets to events with j jets.The single-lepton channel of tf decay, on the other hand, in which one W decays leptonically and the other hadronically, offers the possibility of a direct determination of the topquark mass, since the presence of only a single neutrino permits a kinematical reconstruction of the event. By computing the invariant mass of the three leading jets for each event, the first two of which are expected to come from the hadronic W and the third from one of two b quarks, one may be able to determine the top-quark mass. This channel will be sought by the experimentalists both for its confirmation of the existence of the top quark, as well as for its value in providing a direct reconstru...