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Great question! Yes, theoretically you can use a learned parametric curve (such as a DL model) to extrapolate outside of the training zone. But will this be meaningful, i.e. will it lead to generalization? Well, there are two possible settings.https://twitter.com/Gavin_Cawley/status/1450726111957209093 …
The ideal case: if your model structure is shaped by a sufficiently strong prior, you'll be able to extrapolate. In this case it's your prior knowledge that "transports you" from your known areas to novel areas. You need to know what the data manifold is supposed to look like!pic.twitter.com/TBi5h8SUYq
However, if you don't have such a prior, you are limited to local, interpolative generalization. You don't have sufficient information about the structure of the latent manifold to meaningfully walk out of the known area.pic.twitter.com/MNIM1D0VRG
In practice, we encode priors in deep learning models in two ways: 1. Architecture patterns (e.g. convolution, recurrence, attention...) 2. Data augmentation (random-yet-valid input variations) They represent assumptions about the structure of your latent manifold.
Unfortunately, the kind of prior knowledge we inject in this way is very weak compared to the complexity and unpredictability of most real-world datasets. As a result, deep learning models cannot meaningfully extrapolate except on very simple problems (special cases).
Your DL-only domestic robot won't be able to make sense of a new kitchen layout. Your DL-only self driving car won't be able to train itself in Berlin then drive in London, etc.
Your model priors can't make that jump -- not even close. They can barely move you from "here's this scene" to "here's the same scene but a bit cloudy".
(Note: you could achieve this type of local, mini-extrapolation either via a brightness normalization step or via data augmentation, both of which encode prior knowledge about the characteristics of the visual world.)
Meanwhile, a trivial example of meaningful extrapolation would be the case of a linear dataset. If your data fits on a line, *and* you make the strong (and correct) assumption that it fits on a line, then you can use your learned model to extrapolate outside of the training zone.
But in most practical settings, the answer is no, you can't extrapolate. If you want models that can extrapolate in the real world, you should move away from differentiable curves and use… discrete search over graphs of logical operators (programs). This is for another thread...
Also, if these topics sound interesting to you, remember -- there's this book you can grab.https://www.manning.com/books/deep-learning-with-python-second-edition?a_aid=keras&a_bid=76564dff …
We use engineering physics to define the pattern, especially in non-linear problems encountered in the industrial applications…
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