Just One Layer Norm Guarantees Stable Extrapolation
This addresses the critical issue of unreliable extrapolation in neural networks for applications like protein structure prediction and demographic fairness, though it is incremental as it builds on existing NTK theory.
The paper tackles the problem of neural networks producing unstable outputs when extrapolating far from training data, proving theoretically and showing empirically that adding just one Layer Norm layer ensures bounded outputs even on distant inputs, with experiments demonstrating effective mitigation of instability in finite-width networks.
In spite of their prevalence, the behaviour of Neural Networks when extrapolating far from the training distribution remains poorly understood, with existing results limited to specific cases. In this work, we prove general results -- the first of their kind -- by applying Neural Tangent Kernel (NTK) theory to analyse infinitely-wide neural networks trained until convergence and prove that the inclusion of just one Layer Norm (LN) fundamentally alters the induced NTK, transforming it into a bounded-variance kernel. As a result, the output of an infinitely wide network with at least one LN remains bounded, even on inputs far from the training data. In contrast, we show that a broad class of networks without LN can produce pathologically large outputs for certain inputs. We support these theoretical findings with empirical experiments on finite-width networks, demonstrating that while standard NNs often exhibit uncontrolled growth outside the training domain, a single LN layer effectively mitigates this instability. Finally, we explore real-world implications of this extrapolatory stability, including applications to predicting residue sizes in proteins larger than those seen during training and estimating age from facial images of underrepresented ethnicities absent from the training set.