Thus, if we perform L1-regularized learning as defined in 1 of Definition 4.1, Ng's theorem implies that Equations (6) and (7) hold, satisfying f 1 (m) = 0 and f 2 (m) = 0.
the above theorem implies that if we add the conditions defined in Equation (4)) to Ng's theorem, it is possible to obtain a succinct representation (Equation (5)) whose predictive performance is nearly as good as that of Ng's theorem, albeit with a probabilistic penalty f 1 (m) and an error penalty f 2 (m).