Autoregressive Extrapolation

Two ReLU-MLP approaches for predicting beyond the training region (shaded blue). Method 1 learns f : x → y — a piecewise-linear function that has no reason to continue the signal outside training. Method 2 learns to map a sliding context window of n recent y values to the next y. Given a context of n true values, it then rolls out autoregressively — feeding its own predictions back as context — and can continue the pattern far past the training boundary.

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prediction
ground truth
training region
Method 1  ·  f : x → y
Method 2  ·  [xt−n, yt−n, …, xt] → yt
press Train M1 loss — M2 loss —