Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eluder Dimension and Generalized Rank   We study the relationship between the eluder dimension for a function class
and a generalized notion of rank, defined for any monotone "activation" $\sigma
: \mathbb{R} \to \mathbb{R}$, which corresponds to the minimal dimension
required to represent the class as a generalized linear model. When $\sigma$
has derivatives bounded away from $0$, it is known that $\sigma$-rank gives
rise to an upper bound on eluder dimension for any function class; we show
however that eluder dimension can be exponentially smaller than $\sigma$-rank.
We also show that the condition on the derivative is necessary; namely, when
$\sigma$ is the $\mathrm{relu}$ activation, we show that eluder dimension can
be exponentially larger than $\sigma$-rank.

17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: physics