Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Geometric Approach to Sample Compression   The Sample Compression Conjecture of Littlestone & Warmuth has remained
unsolved for over two decades. This paper presents a systematic geometric
investigation of the compression of finite maximum concept classes. Simple
arrangements of hyperplanes in Hyperbolic space, and Piecewise-Linear
hyperplane arrangements, are shown to represent maximum classes, generalizing
the corresponding Euclidean result. A main result is that PL arrangements can
be swept by a moving hyperplane to unlabeled d-compress any finite maximum
class, forming a peeling scheme as conjectured by Kuzmin & Warmuth. A corollary
is that some d-maximal classes cannot be embedded into any maximum class of VC
dimension d+k, for any constant k. The construction of the PL sweeping involves
Pachner moves on the one-inclusion graph, corresponding to moves of a
hyperplane across the intersection of d other hyperplanes. This extends the
well known Pachner moves for triangulations to cubical complexes.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ