Prior-Data Fitted Networks

Continual learning requires models to adapt to new domains and new classes while retaining prior knowledge. Many existing methods rely on continued optimization, using regularization, replay, or parameter expansion to prevent new updates from overwriting previously learned knowledge. Instead, we propose replacing continual training with continual inference: a PFN-based model that is meta-trained, and then frozen, adapting to new classes only by extending an in-context evidence set. Our model, Latent Concept PFN, performs in-context Bayesian inference over a latent concept space that captures semantic structure shared across domains and classes. As each new domain or class arrives, exemplars are added to the memory; adaptation reflects updated posterior beliefs over latent concepts rather than gradient updates. No parameters are changed, reducing forgetting. The same method handles both domain and class incremental continual learning without task identity. Concept annotations are only used during meta-training, acting as a soft anchor on the latent space rather than a fixed bottleneck. Unlike fixed-vocabulary concept methods, the model also handles noisy, ambiguous, or incomplete annotations by combining concept labels with raw input evidence to discover distinctions beyond the predefined concept set. Experiments on class and domain incremental learning datasets demonstrate competitive continual learning performance while learning interpretable latent concepts.

Standard causal identification methods often assume no unmeasured confounding and can fail when relevant confounders are unobserved. Proximal causal inference instead uses proxy variables to identify effects under hidden confounding. However, nonparametric proximal estimation can be challenging in practice: recovering causal estimands such as the conditional average treatment effect (CATE) requires solving an ill-posed integral equation that is data-hungry, hyperparameter-sensitive, and optimization-unstable. Bayesian inference for such models provides a desirable alternative, mitigating these difficulties by regularizing through the prior. However, computing a posterior is itself challenging, as a typical likelihood function will include latent variables. Following the recent success of tabular foundation models in backdoor, instrumental variable, and frontdoor settings, we propose that prior-data fitted networks (PFNs) are uniquely suited to resolve this bottleneck. Indeed, by training on synthetic data sampled from compliant structural causal models with access to oracle counterfactuals, we simplify the task substantially, amortizing the implied Bayesian operator inversion into a single transformer forward pass. Compared to prior literature that focuses primarily on point estimation, our model, ProximalFM, explicitly targets the Bayesian posterior distribution of the CATE. One unique aspect of this problem is that we need to provide Monte Carlo estimates of the oracle CATEs, leading to a novel variation of PFNs that accounts for the added stochastic error. Across a diverse suite of proximal regimes, ProximalFM achieves consistently strong CATE-estimation performance without dataset-specific tuning, with its largest advantage when latent confounding is substantial and the proxies are weakly informative; it also provides fast inference through a single amortized forward pass.

Prior Fitted Networks (PFNs) such as TabPFN now rival established statistical procedures across prediction and estimation tasks. A natural explanation is that PFNs have the property of statistical adaptivity, that is, they perform nearly as well as a method tailored to the true data-generating model for a heterogeneous set of models, while not being told which model the data comes from. We study how such adaptivity is learned in a controlled location-estimation problem. Each task is an unlabeled sample whose family is hidden: Gaussian data call for averaging, with error of order $n^{-1}$, whereas uniform data are best estimated from their extremes, at the faster rate $n^{-2}$. We also provide the example of a symmetric Gaussian mixture, for which a rate of $σ^2_n/n$ can be attained. On scalar inputs, softmax attention computes the derivative of the empirical cumulant-generating function. A single primitive therefore both supplies features that distinguish the families and forms estimators interpolating between the sample mean and the mid-range. We combine attention experts through either a softmax mixture of experts or a gated linear unit (GLU), and analyze stagewise gradient flow. With $\widetildeΩ(n^{1+ε})$ pretraining tasks, the learned estimator is asymptotically efficient on Gaussian tasks, within a factor $n^ε$ of the minimax rate on uniform tasks, and order-optimal on mixtures in a shrinking-variance regime. These guarantees extend to new locations and longer contexts. A risk decomposition separates expert error, routing error and normalization error, which clarifies the architectural contrast. Softmax gating enforces normalization and exact translation equivariance, whereas the GLU must learn it: its dynamics separate into fast bias removal followed by slow expert selection. End-to-end experiments recover the predicted specialization.

While deep features have transformed anomaly detection in images and video, their impact on tabular data has been less substantial, partly due to the limited availability of strong deep representations. Recently, prior-data fitted networks (PFNs) have emerged as a promising source of such representations for tabular data. In this work, we investigate how PFN representations can be adapted and leveraged for anomaly detection. The question is harder than it looks. No anomalies are available before deploy- ment, so model parameters cannot be tuned with supervision, and the reference set that defines normal behavior may itself contain the very anomalies it is supposed to reveal. We begin our study using frozen TabPFN features. Scoring each sam- ple by its distance to its nearest neighbors in feature space already gives strong results. We identify which layers to use and a feature-extraction procedure suited to the task. Next, to further improve performance, we use the reference set to fine- tune the model, so that the resulting features better separate normal samples from anomalies. On the ADBench benchmark, our fine-tuning free approach (ZEN) reaches a higher mean AUROC than every baseline, and our fine-tuned method (FOCUS) improves on it further. Our approach also generalizes across PFN models.

Spike-and-slab regression is a standard Bayesian formulation of variable selection: it returns a posterior distribution over which candidate effects are active rather than a single selected subset, so that every candidate effect carries an inclusion probability. Its cost grows exponentially with the number of candidate effects, so the posterior can be enumerated exactly only when the number of predictors is small. Beyond that reach, the posterior has to be approximated, typically by Markov chain Monte Carlo over the model space, which requires a fresh run for every dataset and, within a fixed budget of steps, may fail to converge. We present LinearPFN, a prior-data fitted transformer network that amortizes spike-and-slab inference for linear models with main effects and pairwise interactions. The network is pretrained once on synthetic datasets, drawn from an explicitly specified prior, and a single forward pass over a new dataset returns posterior inclusion probabilities, posterior-mean coefficients and posterior predictive distributions with no per-dataset fitting. The prior is conjugate by design, so that the posterior for each fixed set of active effects has a closed form, and wherever the exact posterior is still computable by enumeration we verify the network's outputs against it. On real predictor matrices from published social-science datasets, with outcomes drawn from the prior so that the true active set is known, LinearPFN attains a higher per-dataset selection AUC and a higher F1 under the median probability model rule than five classical baselines. The lead holds when the coefficients, the interactions or the noise depart from the prior. Code: https://github.com/schiekiera/LinearPFN. Trained model: https://huggingface.co/schiekiera/LinearPFN.

Bayesian Optimisation (BO) is a powerful framework for the optimisation of expensive black-box functions, but typically requires refitting a surrogate and maximising an acquisition function at every evaluation step. In-context approaches based on Prior-data Fitted Networks (PFNs) amortise part of this cost by pre-training transformers on functions drawn from synthetic priors. PFNs4BO amortises the surrogate but still relies on a numerically maximised acquisition function, while FIBO performs BO fully in-context by sampling optimiser locations from a learned density, which fixes the decision rule and admits no surrogate. Learned acquisition functions score a finite candidate set with a trained network, but, lacking a label for the query, learn the score by reinforcement learning on previously solved tasks. We propose IQS-BO, a PFN that learns the query decision by supervised learning on synthetic priors. In a single forward pass, IQS-BO predicts the probability that each candidate maximises the objective over the set, and we show that the minimiser of its objective is the posterior probability of this event. The model can be pre-trained without a surrogate for fully in-context BO, or take the predictions of a fixed probabilistic surrogate as additional input, amortising only the decision step. Our method proposes queries at a fraction of the cost of acquisition-based methods, while either matching or outperforming standard BO with Gaussian processes (GPs) and available in-context methods on synthetic and real-world benchmarks. Finally, we propose a mixture prior for pre-training PFNs which combines samples from GPs with functions exhibiting warped inputs, isolated narrow optima, or plateaus that are poorly modeled by stationary kernels common in GP surrogates. We show that pre-training on this prior can lead to improved optimisation performance.

Relational Prior-Data Fitted Networks (PFNs) such as RDB-PFN approximate Bayesian inference over multi-table relational databases by pretraining on millions of synthetic tasks. We investigate three intertwined questions about this paradigm. First, can a structurally different synthetic generator PluRel substitute for RDB-PFN's prior? Second, how much does the order in which synthetic data is presented to the PFN affect downstream performance? Third, how much relational reasoning can a PFN acquire from single-table synthetic pretraining alone, before any relational data is introduced? Using PluRel as the sole synthetic data source across all experiments, we find: (i) a progressive single-table curriculum that gradually widens schema complexity from 7 to 17 columns reaches 0.703 average ROC-AUC on the 23-task tabular benchmark using only approximately 13,300 synthetic tables (approximately 45x fewer single-table datasets than RDB-PFN's reported warm-up recipe), while the same data trained all-at-once collapses to 0.541 ROC-AUC; (ii) a relational curriculum trained from scratch on only approximately 5,500 PluRel databases reaches 0.638 average ROC-AUC on the 19-task RelBench/4DBInfer benchmark, recovering 88% of RDB-PFN's reported performance with approximately 220x less relational synthetic data; and (iii) the single-table curriculum model, evaluated directly on the relational benchmark without any relational adaptation, achieves 0.631, nearly matching the dedicated relational pipeline. Together, these findings suggest that curriculum design and synthetic data diversity may matter more for relational PFN pretraining than the specific relational generator or raw synthetic scale alone.

Predicting cellular responses to unseen chemical perturbations is challenging due to unknown targets and mechanisms, high-dimensional expression responses, and limited experimental coverage of the large small-molecule design space. We propose PerturbPFN, a PFN-style amortized model for unknown-target perturbation prediction under a hierarchical synthetic structural prior. Instead of directly regressing high-dimensional expression responses, PerturbPFN infers a latent system graph, sparse atomic intervention targets, and intervention strengths, then propagates their effects through an SCM decoder. The model is trained entirely on prior-predictive synthetic episodes generated from biologically motivated graph and expression simulators, enabling structured in-context learning without test-time gradient updates. We evaluate PerturbPFN on both real single-cell perturbation data and synthetic benchmarks, covering effect prediction, target identification, and regulatory structure discovery. Our results show that PerturbPFN offers a complementary trade-off to specialized baselines, achieving competitive perturbation prediction with low inference cost while exposing interpretable intermediate estimates of targets, strengths, and system structure.

Few-shot multimodal classification commonly attaches a lightweight head, such as $k$-nearest neighbors, logistic regression, or a linear SVM, to a frozen pretrained encoder. Although computationally efficient, these heads can produce poorly calibrated confidence scores, limiting their reliability in calibration-sensitive applications. We evaluate TabPFN as a plug-and-play, zero-gradient classification head for frozen image, text, and audio encoders. Across 22{,}820 evaluation episodes spanning 14 datasets, 11 encoders, and three modalities, TabPFN achieves the best mean rank among nine classification heads on both negative log-likelihood (NLL) and expected calibration error (ECE). At a representative setting, it reduces NLL by 48--62% and ECE by 2.1--5.3$\times$ relative to the average of the eight baselines while matching or exceeding their average accuracy. Its accuracy advantage is conditional, concentrating at moderate-to-high shot counts and low-to-moderate feature dimensions ($k \ge 50$, $d \le 32$), and diminishing when labeled data are scarce, feature dimensions are high, or competing methods approach ceiling accuracy. In targeted backbone-adaptation experiments, replacing the trained linear head with TabPFN substantially improves calibration while preserving competitive accuracy. These results provide empirical guidance for using TabPFN as a training-free head in calibration-sensitive multimodal classification. To support transparency and reproducibility, we publicly release the source code, experiment configurations, and evaluation scripts in our GitHub repository: https://github.com/Jingxiang-Zhang/tabpfn-multimodal-embeddings.

Due to the wide use of graph-structured data in different fields of industry and science, the development of Graph Foundation Models (GFMs) has recently attracted a lot of attention. While many different types of models are called GFMs, particular interest has been paid to GFMs designed for node property prediction tasks, which is one of the most popular settings in Graph ML with lots of real-world applications from fraud detection in financial and social networks to recommendation systems for e-commerce and user-generated content platforms. While a number of GFMs for this task have been recently proposed, the field has not converged to a unified evaluation setting, and different works evaluate their models in widely different ways, preventing reliable comparison of GFMs with each other and with other types of models. In this work, we conduct a fair and rigorous reevaluation of 9 recent GFMs for node property prediction, comparing them to strong Graph Neural Network (GNN) baselines. We find that, among these GFMs, only the most recent ones based on the Prior-data Fitted Networks paradigm outperform well-tuned GNNs in predictive performance, although at a higher inference cost.

A Prior-data fitted Network learns the posterior predictive induced by its training prior; bringing this paradigm to multivariate time-series classification therefore calls for a synthetic generator that produces complete labelled datasets with temporal structure. We introduce a causal prior that synthesizes each dataset from a randomly sampled DAG over typed nodes across two modalities (tabular attributes and time series), natively producing multivariate, multi-class TSC datasets with cross-modal causal structure across channels, timesteps and labels, a regime not addressed by existing synthetic priors. To validate the prior, we finetune TabPFN v2.5 with minimal adaptations and evaluate on 75 UCR/UEA datasets within TabPFN's operating regime. Finetuning on our generator significantly outperforms both the unmodified upstream model and a tabular-only ablation of the same prior (Wilcoxon signed-rank $p=3.0\times 10^{-8}$ on ROC-AUC), isolating the contribution of the cross-modal temporal structure.

Causal discovery is critical for understanding complex data-generating mechanisms, yet traditional algorithms often struggle with highly non-linear and noisy systems, or suffer from severe computational bottlenecks. Recent tabular foundation models based on Prior-Data Fitted Networks (PFNs) have demonstrated remarkable zero-shot inference capabilities, but their potential for explicit structural causal discovery remains underexplored. To bridge this gap, we propose DCD-PFN, a decoupling-aware foundation model for causal discovery. Instead of directly amortizing global graph reconstruction, DCD-PFN focuses on local causal discovery through a decoupling-based paradigm. Through pre-training on diverse synthetic Structural Causal Models (SCMs), the model learns sample-wise decoupling weights that enable Markov boundary (MB) identification. Furthermore, by leveraging parallelized local discovery, DCD-PFN efficiently reconstructs global causal graphs while remaining grounded in the theoretical foundations of decoupling-based causal discovery. Experiments demonstrate that our foundation model achieves robust zero-shot generalization.

Estimating causal effects in industrial time series requires handling temporal dynamics, time-varying treatments, and unobserved confounders. Existing causal foundation models (CausalPFN, CausalFM) operate only on static cross-sectional data; neural temporal methods (CRN, G-Net) require per-dataset training; and concurrent temporal-PFN proposals have not been demonstrated at industrial scale. None output explicit per-pair reliability signals alongside their CATE estimates. We introduce Temporal Causal Prior-Data Fitted Networks (TCPFN), a foundation model for zero-shot temporal causal discovery with learned reliability signals. TCPFN makes four contributions: (1) a Causal Judgment Head that jointly predicts null-effect probability, confounding strength, identifiability, mediation fraction, and causal regime; (2) a mixed training prior covering six causal regimes (independent, direct, confounded, mediated, time-varying confounded, feedback) plus CausalFM-style front-door and instrumental-variable priors; (3) a discrete-token panel-data architecture with cross-attention masking that prevents inter-horizon leakage; (4) zero-shot inference at industrial scale via FAISS-based context selection and one-step posterior correction. On 19 benchmark datasets across five domains, TCPFN achieves competitive zero-shot causal discovery: AUROC 0.96 on Tennessee Eastman, 0.93 on SWaT, 0.98 on Causal Rivers, 0.97 on CAUSRCA. The null detector reaches NullF1 0.94, AUROC 0.99. TCPFN scales to V=1,275 on a proprietary Kraft pulp-and-paper dataset in 6 hours on a single GPU; PCMCI, a CPU-only library, on a V=666 sub-panel of the same data took 81.5 hours, extrapolating by O(V^2) to ~12.5 days at V=1,275. TCPFN's top edges identify cross-subsystem causal relationships while PCMCI's surface within-instrument controller-measurement coupling -- a scalability case study.

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.

Information-theoretic acquisition functions such as Entropy Search (ES) offer a principled exploration-exploitation framework for Bayesian optimization (BO). However, their practical implementation relies on complicated and slow approximations, i.e., a Monte Carlo estimation of the information gain. This complexity can introduce numerical errors and requires specialized, hand-crafted implementations. We propose a two-stage amortization strategy that learns to approximate entropy search-based acquisition functions using Prior-data Fitted Networks (PFNs) in a single forward pass. A first PFN is trained to be conditioned on information about the optima; second, the $α$-PFN is trained to predict the expected information gain by training on information gains measured with the first PFN. The $α$-PFN offers a flexible learned approximation, which replaces the complex heuristic approximations with a single forward pass per candidate, enabling rapid and extensible acquisition evaluation. Empirically, our approach is competitive with state-of-the-art entropy search implementations on synthetic and real-world benchmarks, while accelerating the different entropy search variants across all our experiments, with speed ups over 50x. Source code: https://github.com/automl/AlphaPFN.

Longitudinal treatment decisions from multivariate time-series data require predicting potential outcomes under future treatment sequences in the presence of time-varying confounding, heterogeneous patient dynamics, and limited domain-specific data. Existing longitudinal causal estimators typically address this problem by training a new model for each cohort or simulator. We introduce Causal Longitudinal Prior-Fitted Networks (CausalLongPFN), a prior-fitted network for time-series causal inference in longitudinal treatment-response data and zero-shot in-context counterfactual outcome prediction. The model is pretrained entirely on synthetic episodes sampled from a broad prior over temporal structural causal models, exposing it to treatment-confounder feedback, latent heterogeneity, nonlinear state evolution, delayed effects, and cumulative treatment responses. At test time, CausalLongPFN remains frozen and is used zero-shot: it conditions on support trajectories, a query history, and a planned future treatment sequence, and returns a predictive distribution over future outcomes without gradient updates or propensity-model fitting. Multi-step predictions are obtained by recursively applying the one-step predictor under the specified treatment sequence. We evaluate the model on branchable cancer, HIV, and warfarin benchmarks with ground-truth counterfactual labels, and on factual-only rolling-origin prediction in MIMIC-III ICU trajectories. CausalLongPFN is competitive with domain-trained longitudinal baselines on counterfactual benchmarks and performs strongly on factual MIMIC-III prediction, suggesting that broad synthetic causal pretraining can provide a frozen, amortized alternative for zero-shot longitudinal treatment-response prediction when repeated domain-specific training is costly or impractical.

Tabular foundation models (TFMs) have made rapid progress in standard classification and regression, but time-to-event survival prediction tasks have remained largely untouched. Unlike in standard regression tasks, survival prediction models must account for censored data. Standard TFMs cannot handle natively censored data, leading to biased and inaccurate predictions, making them unsuitable for real-world applications. To overcome this fundamental limitation, we propose \texttt{SurvPFN}, a prior-data fitted network (PFN), for survival prediction tasks. We pretrain \texttt{SurvPFN} on millions of synthetic survival prediction tasks to learn survival via distributional regression that accounts for censored data. \texttt{SurvPFN} works by (1) generating data with Weibull event times and a non-informative censoring mechanism; (2) integrating a censored event indicator; and (3) minimizing a censored negative log-likelihood. On SurvSet, a collection of real-world survival tasks, \texttt{SurvPFN} is highly competitive with classical and deep survival baselines without per-dataset fitting, a survival-specific architecture, or feature engineering. We show that survival can be treated as a continuous-time distributional regression problem with censored loss, unlocking the power of PFNs for time-to-event predictions.

Foundation models (FMs) have achieved substantial success in generalizing across tasks without problemspecific training or fine-tuning. However, many critical applications in mechanics and computational science require not only accurate predictions but also reliable uncertainty quantification (UQ). Herein we investigate the UQ capabilities of tabular FMs in regression tasks through a comprehensive empirical study comparing Tabular Prior-Data Fitted Networks (TabPFN) against Gaussian processes (GPs). We systematically evaluate these two methods across a host of regression problems with varying complexity, dataset sizes, and input dimensionalities. We use a default setting to build all the GPs and for a fair comparison against TabPFN v2.5. Our findings highlight an important trade-off between explicit and learned priors: while TabPFN achieves highly competitive performance for complex, high-dimensional problems with sufficient data, GPs often provide superior predictive accuracy and UQ in data-scarce settings. Moreover, when the chosen kernel constitutes a good prior for the underlying function, GP performance can substantially exceed that of TabPFN. Our results can be reproduced from https://github.com/kianswarehouse/GPvsPFN.

Extending discrete-time causal Prior-data Fitted Networks for time series to continuous time invites writing the mechanism as a stochastic differential equation (SDE) -- but if the SDE is integrated \emph{once per observation gap}, the trajectory law depends on when it is observed, and the prior remains a discrete-time Markov model in SDE clothing. We propose a precise continuity criterion -- trajectory-law invariance to the observation schedule -- together with a three-tier taxonomy (discrete; naive observation-grid integration; fine-grid integration with decoupled observation) and a construction realising the top tier on a random DAG with OU or small-MLP nonlinear drifts, irregular observation schedules, and hard / soft / time-varying interventions. A $2 \times 2$ encoder $\times$ integrator ablation, run independently on a linear and a nonlinear prior, finds fine-grid integration beats naive on 8/8 cells (sign-consistency $p < 1/256$) with the gap growing as the eval grid refines; the encoder axis is null with fine integration but time-aware-leading with naive. We release the prior and a preliminary zero-shot protocol on pharmacokinetic and physical-system data.

Prior-data fitted networks (PFNs) have recently emerged as a powerful approach for Bayesian prediction tasks, approximating the posterior predictive distribution (PPD) through in-context learning. Despite their strong empirical performance and ability to go beyond point predictions, theoretical understandings of the algorithmic capability of transformers to learn distributions in context are still lacking. Focusing on Gaussian process regression problems, we show by construction that transformers can implement a gradient descent algorithm targeting the posterior predictive mean and variance, followed by nonlinear mappings that yield binned probabilities of PPD. We study the error bounds of the approximated PPD in terms of attention depth and bin resolution. Based on these results, we further demonstrate the key role of normalization and the choice of attention depth in enabling the extrapolation abilities of transformers beyond the pretraining sample size range. We conduct simulations that corroborate our findings, providing insight into the expressivity of PFNs targeting PPDs and how architectural choices may influence generalization capabilities.

Prior-data fitted networks (PFNs) have achieved exceptional performance on tabular classification tasks. However, like other classifiers, their performance can suffer under the effect of class imbalance, resulting in poor performance for rare classes. Several techniques exist which attempt to mitigate the deleterious effect of class imbalance on classification performance, but the in-context learning (ICL) dynamic of PFNs means that loss-based strategies are impossible, and other techniques are unproven. We have adapted several classical techniques addressing class imbalance and analyzed their performance on PFN classification. We observe that thresholding performs exceptionally well because of the calibration characteristics of PFNs, and downsampling performs comparably because of PFNs exceptional limited-data performance, with the additional benefit of reduced computation cost for inference.

Tabular foundation models based on pretrained prior-data fitted networks~(PFNs) have shown strong generalization on diverse tabular tasks, but they are typically designed for \emph{non-strategic} settings where data distributions are independent of deployed classifiers. In many real-world decision scenarios, however, individuals may strategically modify their features after deployment to obtain favorable outcomes, inducing a post-deployment distribution shift. This paper studies whether PFN-style tabular foundation models can generalize to such \emph{strategic} tabular data. We show that strategic manipulation creates a mismatch between the non-strategic prior learned during pretraining and the post-manipulation strategic prior, which leads to systematic prediction bias. To address this issue, we propose \textbf{Strategic Prior-data Fitted Network}~\textit{(SPN)}, an inference-time strategy-aware framework that adapts tabular foundation models to strategic environments without retraining. SPN constructs strategic in-context examples to approximate post-manipulation inputs and aligns PFN predictions with the induced strategic distribution. Experiments on real-world and synthetic tabular datasets show that SPN consistently improves robustness and predictive performance under strategic manipulation compared with both tabular foundation models and classical tabular methods.

Survival analysis provides a powerful statistical framework for modeling time-to-event outcomes in the presence of censoring. However, selecting an appropriate estimator from the many specialized survival approaches often requires substantial methodological and domain expertise. We introduce SurvivalPFN, a prior-data fitted network that amortizes Bayesian inference for censored observations through in-context learning. SurvivalPFN is pretrained on a diverse family of synthetic, identifiable, and right-censored data-generating processes, enabling it to amortize survival analysis in a single forward pass during inference. As a result, the model adapts to the effective complexity of each dataset without task-specific training or hyperparameter tuning, avoids restrictive parametric assumptions, and produces calibrated survival distributions. In a large-scale benchmark spanning 61 datasets, 21 methods, and 5 evaluation metrics, SurvivalPFN achieves strong predictive performance and often improves upon established survival models. These results suggest that SurvivalPFN offers a principled and practical foundation model for survival analysis, with potential applications in high-impact domains such as healthcare, finance, and engineering (https://github.com/rgklab/SurvivalPFN).

Thompson sampling is a widely used strategy for contextual bandits: at each round, it samples a reward function from a Bayesian posterior and acts greedily under that sample. Prior-data fitted networks (PFNs), such as TabPFN v2+ and TabICL v2, are attractive candidates for this purpose because they approximate Bayesian posterior predictive distributions in a single forward pass. However, PFNs predict noisy future rewards, while Thompson sampling requires uncertainty over the latent mean reward function. We propose PFN-TS, a Thompson sampling algorithm that converts PFN posterior predictives into mean-reward samples using a subsampled predictive central limit theorem. The method estimates posterior variance from a geometric grid of $O(\log n)$ dataset prefixes rather than the full $O(n)$ predictive sequence used in previous predictive-sequence approaches, and reuses TabICL's cached representations across rounds. We prove consistency of the subsampled variance estimator and give a Bayesian regret bound that decomposes PFN-TS regret into exact posterior-sampling regret under the PFN prior plus approximation terms. Empirically, PFN-TS achieves the best average rank across nonlinear synthetic and OpenML classification-to-bandit benchmarks, remains competitive on linear and BART-generated rewards, and attains the highest estimated policy value in an offline mobile-health evaluation. Code is available at https://anonymous.4open.science/r/PFN_TS-36ED/.

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.

Prior-Fitted Networks (PFNs) amortize Bayesian prediction by meta-learning over a synthetic task prior, but their standard output is a posterior predictive distribution over noisy observations. For sequential decision-making, such as active learning and Bayesian optimization, acquisition should prioritize epistemic uncertainty about the latent signal rather than irreducible aleatoric observation noise. We show that this epistemic--aleatoric split is not identifiable in general from the posterior predictive distribution alone, even when that distribution is known exactly. We then exploit a distinctive advantage of PFNs: because the synthetic data-generating process is under our control, each task can contain an explicit latent signal and noise function, and the generator can provide query-level labels for both the noiseless target and the observation-noise variance. We use these labels to train a decoupled PFN with separate latent-signal and aleatoric heads. The observation-level predictive is induced by convolving the latent signal distribution with the learned noise model. Empirically, epistemic-only acquisition mitigates the failure mode of total-variance exploration in noisy and heteroscedastic settings. In matched comparisons, decoupled models usually improve over tuned observation-level baselines, with the clearest gains in HPO; in broader sweeps, a decoupled model obtains the best average rank in both HPO and synthetic BO.

Accurate prediction of conversion from Mild Cognitive Impairment (MCI) to Alzheimers Diseases (AD) is essential for early intervention, however, developing reliable conversion predictive models is difficult to develop due to limited longitudinal data availability We evaluate TabPFN (Tabular Pre-Trained Foundation Network) against traditional machine learning methods for predicting 3 year MCI to AD conversion using the TADPOLE dataset derived from ADNI. Using multimodal biomarker features extracted from demographics, APOE4, MRI volumes, CSF markers, and PET imaging, we conducted an experimental comparison across varying training set sizes (N=50 to 1000) and models including XGBoost, Random Forest, LightGBM, and Logistic Regression. TabPFN achieved one the highest performance (AUC=0.892), outperforming LightGBM (AUC=0.860) and demonstrating advantages in low data settings. At N=50 training samples, TabPFN maintained strong AUC while the traditional machine learning models struggles at small training samples. These findings demonstrate that foundation models are promising for disease prediction in data limited scenarios, such as Alzheimers diseases.

We introduce Prior-Fitted Functional Flows, a generative foundation model for pharmacokinetics that enables zero-shot population synthesis and individual forecasting without manual parameter tuning. We learn functional vector fields, explicitly conditioned on the sparse, irregular data of an entire study population. This enables the generation of coherent virtual cohorts as well as forecasting of partially observed patient trajectories with calibrated uncertainty. We construct a new open-access literature corpus to inform our priors, and demonstrate state-of-the-art predictive accuracy on extensive real-world datasets.

Graph foundation models face several fundamental challenges including transferability across diverse domains and data scarcity, which calls into question the very feasibility of creating such models. However, despite similar challenges, the tabular domain has recently witnessed the emergence of the first successful foundation models such as TabPFN. These models are based on the prior-data fitted networks (PFN) framework, in which models are pretrained on carefully designed synthetic datasets to make predictions in an in-context learning setting. Recently, G2T-FM, a framework that converts graph node-level tasks into tabular tasks, has made the first step towards adopting PFNs for graphs, yet it is limited to hand-crafted features and was never pretrained on graph data. In this work, we make the next step by proposing GraphPFN, a PFN-based model designed and pretrained specifically for graph node-level tasks. Following the PFN framework, we first design a prior distribution of synthetic attributed graphs by using a novel combination of multi-level stochastic block models and a preferential attachment process for structure generation and graph-aware structured causal models for attribute generation. Then, we augment the tabular foundation model LimiX with attention-based graph neighborhood aggregation layers and train it on millions of synthetic graphs sampled from our prior. On diverse real-world graph datasets with node-level tasks, GraphPFN achieves state-of-the-art results in both in-context learning and finetuning regimes, outperforming G2T-FM, prior GFMs, and task-specific GNNs trained from scratch. More broadly, GraphPFN shows the potential of PFN-based models for building graph foundation models.