Madaline Rule I (1962) could adapt only the first layer of Widrow's networks — the second layer stayed fixed, making it the ceiling of pre-backpropagation multilayer training

Madaline Rule I (MRI), devised by Bernard Widrow's Stanford group around 1961–62, is described in Widrow's own retrospective (Widrow & Lehr 1990) as "the earliest popular learning rule" for networks of multiple adaptive elements. Its limit was structural: the Madalines of the 1960s had an adaptive first layer of Adaline units feeding a fixed second (logic) layer. Only one layer actually learned — so MRI was not multilayer training in the modern sense, but a single trainable layer wired into a hand-set downstream combiner.

The obstacle to going further was the non-differentiable element. Widrow & Lehr state that "the adaptive elements in the original Madaline structure used hard-limiting quantizers (signums), while the elements in the backpropagation network use only differentiable nonlinearities, or 'sigmoid' functions." A hard-limiting quantizer has no usable gradient, so the error at the output cannot be propagated back to adjust a hidden layer — the credit-assignment barrier that Minsky and Papert only conjectured to be fatal (claim-perceptrons-multilayer-sterile-was-conjecture), Widrow's group hit empirically. Their later attempts to adapt multiple layers while keeping the simpler quantizers produced Madaline Rule II (1987) and III (1988), not a 1960s solution.

This makes MRI the concrete high-water mark behind the stall the field is mapped around (backpropagation-gap): the method to train hidden layers did not exist until the differentiable-nonlinearity route (claim-rhw-1986-demonstration-not-invention) reopened it. Widrow himself did not return to neural nets until backpropagation reached him in the mid-1980s (claim-widrow-abandoned-multilayer-training-until-1985-backprop). See moc-backpropagation-origins.