Top-K

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Top-K#

Optimal Cutoff Timestep (OCT)#

g (X) = \arg min_{\hat{t}} {\forall {\hat{t}}_{1} > \hat{t} : 1 (f (X [{\hat{t}}_{1}]) = y)}

Top-K Gap for Cutoff Approximation#

The defination of $T o p_{k} (Y (t))$ as the top- $k$ output occurring in one neuron of the output layer,

Y_{g a p} = T o p_{1} (Y (t)) - T o p_{2} (Y (t)),

which denotes the gap of top-1 and top-2 values of output $Y (t)$ . Then, we let $D {\cdot}$ denote the inputs in subset of $D$ that satisfy a certain condition. Now, we can define the confidence rate as follows:

Confidence rate: C (\hat{t}, D {Y_{g a p} > β}) = \frac{1}{| D {Y_{g a p} > β} |} \sum_{X \in D {Y_{g a p} > β}} (g (X) \leq \hat{t}),

The algorithm searches for a minimum $β \in R^{+}$ at a specific $\hat{t}$ , as expressed in the following optimization objective:

\arg min_{β} C (\hat{t}, D {Y_{g a p} > β}) \geq 1 - ϵ,

where $ϵ$ is a pre-specified constant such that $1 - ϵ$ represents an acceptable level of confidence for activating cutoff, and a set of $β$ is extracted under different $\hat{t}$ using training samples.