Communication Complexity of Universal Features
Motivated by the notion of features from machine learning, we study the complexity of representing data that allows for evaluation with a given family of functions. Concretely, we consider a deterministic encoder that observes $X\sim D$ and produces a finite encoding before a task $f\in\mathcal{F}\subseteq\{0,1\}^{\mathcal{X}}$ is specified. For each task, a decoder must predict $f(X)$ with error at most $\varepsilon$ under $D$. We construct an encoder that outputs a representation with $O(d^{*}\log(1/\varepsilon))$ bits, where $d^{*}$ is the dual VC dimension of $\mathcal{F}$. Our encoder greedily selects $O((d^{*}/\varepsilon)\log(1/\varepsilon))$ functions from the class and uses their...
| Authors | Lunjia Hu, Anish Jayant, Peter Li et al. |
|---|---|
| Primary category | stat.ML |
| Published | 19 October 2026 |
| Last updated at source | 19 October 2026 |
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