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# Energy-Based Model | ||
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Feed-forward networks use a finite number of steps to produce a single output. | ||
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However, what if.. | ||
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- The problem requires a complex computation to produce it's output? | ||
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- There are multiple possible outputs for a single input? | ||
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Energy function f(x, y) is a scalar-valued function, which takes low values when y is compatible with x, and higher values when y is less compatible with x. | ||
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Inference with Energy function finds values of y that make the f(x, y) small. You should note that the energy is only used for inference, not for learning. | ||
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 | ||
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In the example above, blue dots are data points. As you could see, the data are aligned at lower locations (spaces that have lower energy). | ||
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## Implicit Function | ||
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 | ||
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- A feed-forward model is an explicit function that calculates y from x. | ||
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- An EBM (Energy-Based Model) is an implicit function that captures the dependency between y and x. | ||
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- Multiple Y can be compatible with a single X. | ||
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 | ||
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- Energy function that captures the dependencies between x and y | ||
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1) Low energy near the data points | ||
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2) High energy everywhere else | ||
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3) If y is continuous, energy function f should be smoothe and differentiable, so we can use gradient-based inference algorithms | ||
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 | ||
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## When inference is hard | ||
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 | ||
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## When inference involves latent variables | ||
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 | ||
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## Latent Variable - EBM inference | ||
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 | ||
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- Allowing multiple predictions through a latent variable | ||
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- As latent variable z varies over a set, y varies over the manifold of possible predictions | ||
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 | ||
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- Useful then there are multiple correct (or plausible) outputs. | ||
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 | ||
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## References | ||
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[1] Yann LeCun [Lecture: Energy based models and self-supervised learning](https://www.youtube.com/watch?v=tVwV14YkbYs&list=PLLHTzKZzVU9eaEyErdV26ikyolxOsz6mq&index=12) |
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