TabK: Amortized Bayesian Estimation of the Number of Clusters in Tabular Data

Estimating the number of clusters, $k$, is a fundamental prerequisite for most clustering algorithms. Traditionally, this estimation has relied on computationally expensive grid searches over internal cluster validity indices (CVIs) or adaptive clustering algorithms, both constrained by specific statistical assumptions. We introduce TabK, a zero-shot, permutation-invariant transformer architecture that frames the estimation of $k$ as an amortized Bayesian inference problem for tabular data. TabK leverages a novel Quantile Feature Encoder (QFE) to extract position-free, content-derived representations from empirical marginal distributions. By learning a generalized structural bias over a diverse synthetic prior, TabK estimates the number of clusters in a single forward pass. Evaluated across 50 diverse real-world benchmarks, TabK outperforms its closest competitor, TabClustPFN, reducing the Mean Absolute Error (MAE) of the number of clusters estimation by 1.2 (from 2.24 to 1.04). Furthermore, TabK empirically achieves the best position on the Pareto frontier among 12 evaluated methods, providing predictions of $k$ in an average time of less than one second, which is $2\times$ faster than TabClustPFN and $30\times$ faster than traditional CVIs such as Silhouette and Calinski-Harabasz. *Code and data are available at:* https://anonymous.4open.science/r/TabK.