Organizations: University of Pennsylvania · The George Washington University · Brown University
Abstract
In this work, we study TabPFN as a training-free, modular summary network for simulation-based Bayesian inference (SBI). Tabular foundation models such as TabPFN are pretrained on broad families of synthetic tabular data-generating processes and adapt at test time through in-context learning, making them natural candidates for SBI, where posterior estimation often depends on learning informative summaries of simulated observations. We propose PFN-NPE: a general recipe that uses a pretrained TabPFN encoder as a fixed summary network for simulator outputs, then pairs the resulting summaries with a downstream inference head chosen for the problem. With normalizing flows as the default inference head, PFN-NPE matches established posterior approximation methods and sometimes outperforms them. More importantly, diagnostic probes show that the TabPFN-derived summaries often preserve useful posterior location and marginal information. These analyses also reveal a limitation in that TabPFN-derived summaries may struggle to represent the joint posterior structure even when the marginals are well recovered. Still, our experiments show that TabPFN can serve as an effective summary network across a diverse set of SBI settings, with the inference network left modular and task-dependent.
The cost of simulator evaluations is a key practical bottleneck for Simulation Based Inference (SBI). In hierarchical settings with shared global parameters and exchangeable site-level parameters and observations, this structure can be exploited to improve simulation efficiency. Existing hierarchical SBI approaches factorise the posterior yet still simulate across multiple sites per training sample; We instead explore likelihood factorisation (LF) to train from single-site simulations. In LF sampling we learn a per-site neural surrogate of the simulator and then assemble synthetic multi-site observations to amortise inference for the full hierarchical posterior. Building on this, we propose Tokenised Flow Matching for Posterior Estimation (TFMPE), a tokenised flow matching approach that supports function-valued observations through likelihood factorisation. To enable systematic evaluation, we introduce a benchmark for hierarchical SBI. We validate TFMPE on this benchmark and on realistic infectious disease and computational fluid dynamics models, finding well-calibrated posteriors while reducing computational cost.
We introduce TabPFN-3.5, our new flagship Tabular Foundation Model. It significantly outperforms its predecessor, TabPFN-3, and all existing baselines across a broad range of tabular problems. TabPFN-3.5 sets a new state of the art on standard tabular prediction in TabArena, and extends it to the data practitioners encounter in practice: non-i.i.d. data with temporal or grouped splits, tables with strings, text and images, high-cardinality categorical features, and wide tables with many features. These gains carry over to our task-specific harnesses: state of the art on relational data and stronger time-series forecasting. For faster inference, our variant TabPFN-3.5-Fast runs up to 3x faster than TabPFN-3 while keeping most of the accuracy gains. In addition, we upgrade TabPFN-3.5-Plus, expanding our multimodal capabilities with advanced text and date handling alongside proprietary inference optimizations. Finally, we release a new version of our Thinking mode, TabPFN-3.5-Thinking, which scales inference-time computation to push the state of the art further. It benefits from our stronger base model and from inference-time improvements that make it up to 12x faster than TabPFN-3-Thinking.
Prior-fitted networks (PFNs) are a promising class of tabular foundation models that perform in-context learning, whereby the entire labelled training set is supplied as context, and predictions for test queries are produced in a single forward pass. However, the quadratically scaling self-attention mechanism in many PFN architectures makes inference prohibitive for very large training datasets. We propose CRUMB (Clustered Retrieval Using Minimised-MMD Batching), a three-stage inference wrapper that (i) clusters the test queries, (ii) selects a small, distributionally matched training subset for each cluster by greedily minimising the maximum mean discrepancy (MMD), and (iii) runs exact PFN inference on each reduced-context batch. CRUMB is architecture-agnostic and requires no retraining. On the 51-dataset TabArena benchmark, evaluated across three PFN architectures (TabPFNv2, TabICLv1, TabICLv2), we show that CRUMB outperforms similar state-of-the-art context selection strategies. We also show that CRUMB is resilient to covariate drift, as the MMD-minimisation step naturally helps align the training context distribution to match the current test batch distributions.
Jamie Heredge, Mattia J. Villani, Pranav Deshpande +2