S. Natarajan
Publications
Geometry-Aware Probabilistic Circuits via Voronoi Tessellations
Probabilistic circuits (PCs) enable exact and tractable inference but employ data independent mixture weights that limit their ability to capture local geometry of the data manifold. We propose Voronoi tessellations (VT) as a natural way to incorporate geometric structure directly into the sum nodes of a PC. However, naïvely introducing such structure breaks tractability. We formalize this incompatibility and develop two complementary solutions: (1) an approximate inference framework that provides guaranteed lower and upper bounds for inference, and (2) a structural condition for VT under which exact tractable inference is recovered. Finally, we introduce a differentiable relaxation for VT that enables gradient-based learning and empirically validate the resulting approach on standard density estimation tasks.
Recursive Inference Machines for Neural Reasoning
Neural reasoners such as Tiny Recursive Models (TRMs) solve complex problems by combining neural backbones with specialized inference schemes. Such inference schemes have been a central component of stochastic reasoning systems, where inference rules are applied to a stochastic model to derive answers to complex queries. In this work, we bridge these two paradigms by introducing Recursive Inference Machines (RIMs), a neural reasoning framework that explicitly incorporates recursive inference mechanisms inspired by classical inference engines. We show that TRMs can be expressed as an instance of RIMs, allowing us to extend them through a reweighting component, yielding better performance on challenging reasoning benchmarks, including ARC-AGI-1, ARC-AGI-2, and Sudoku Extreme. Furthermore, we show that RIMs can be used to improve reasoning on other tasks, such as the classification of tabular data, outperforming TabPFNs.