LT2, William Gates Building
\[\text{data} + \text{model} \stackrel{\text{compute}}{\rightarrow} \text{prediction}\]
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\[\text{data} + \text{model} \stackrel{\text{compute}}{\rightarrow} \text{prediction}\] |
\[ \text{data} + \text{model} \stackrel{\text{compute}}{\rightarrow} \text{prediction}\]
\[\text{data} + \text{model} \stackrel{\text{compute}}{\rightarrow} \text{prediction}\]
\[ \text{odds} = \frac{p(\text{bought})}{p(\text{not bought})} \]
\[ \log \text{odds} = w_0 + w_1 \text{age} + w_2 \text{latitude}.\]
\[ p(\text{bought}) = \sigma\left(w_0 + w_1 \text{age} + w_2 \text{latitude}\right).\]
\[ p(\text{bought}) = \sigma\left(\mathbf{ w}^\top \mathbf{ x}\right).\]
\[ y= f\left(\mathbf{ x}, \mathbf{ w}\right).\]
We call \(f(\cdot)\) the prediction function.
\[E(\mathbf{ w}, \mathbf{Y}, \mathbf{X})\]
\[ p(\text{bought}) = \sigma\left(w_0 + w_1 \text{age} + w_2 \text{latitude}\right).\]
\[ p(\text{bought}) = \sigma\left(\beta_0 + \beta_1 \text{age} + \beta_2 \text{latitude}\right).\]
These are interpretable models: vital for disease modeling etc.
Modern machine learning methods are less interpretable
Example: face recognition
Outline of the DeepFace architecture. A front-end of a single convolution-pooling-convolution filtering on the rectified input, followed by three locally-connected layers and two fully-connected layers. Color illustrates feature maps produced at each layer. The net includes more than 120 million parameters, where more than 95% come from the local and fully connected.
There is a lot of evidence that probabilities aren’t interpretable.
See e.g. Thompson (1989)
Later in the 1940’s, when I was doing my Ph.D. work, there was much talk of the brain as a computer and of the early digital computers that were just making the headlines as “electronic brains.” As an analogue computer man I felt strongly convinced that the brain, whatever it was, was not a digital computer. I didn’t think it was an analogue computer either in the conventional sense.
A human-analogue machine is a machine that has created a feature space that is analagous to the “feature space” our brain uses to reason.
The latest generation of LLMs are exhibiting this charateristic, giving them ability to converse.
But if correctly done, the machine can be appropriately “psychologically represented”
This might allow us to deal with the challenge of intellectual debt where we create machines we cannot explain.
LLMs are already being used for robot planning Huang et al. (2023)
Ambiguities are reduced when the machine has had large scale access to human cultural understanding.
twitter: @lawrennd
podcast: The Talking Machines
newspaper: Guardian Profile Page
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