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We seek to impose linear, equality constraints in feedforward neuralnetworks. As top layer predictors are usually nonlinear, this is a difficulttask if we seek to deploy standard convex optimization methods and strongduality. To overcome this, we introduce a new saddle-point Lagrangian withauxiliary predictor variables on which constraints are imposed. Elimination ofthe auxiliary variables leads to a dual minimization problem on the Lagrangemultipliers introduced to satisfy the linear constraints. This minimizationproblem is combined with the standard learning problem on the weight matrices.From this theoretical line of development, we obtain the surprisinginterpretation of Lagrange parameters as additional, penultimate layer hiddenunits with fixed weights stemming from the constraints. Consequently, standardminimization approaches can be used despite the inclusion of Lagrangeparameters -- a very satisfying, albeit unexpected, discovery. Examples rangingfrom multi-label classification to constrained autoencoders are envisaged inthe future. The code has been made available athttps://github.com/anandrajan0/smartalec

Expressing linear equality constraints in feedforward neural networks