Decoupled PFNs: Identifiable Epistemic-Aleatoric Decomposition via Structured Synthetic Priors

• URL: http://arxiv.org/abs/2605.06413v1
• Date: Thu, 07 May 2026 15:22:35 GMT
• Title: Decoupled PFNs: Identifiable Epistemic-Aleatoric Decomposition via Structured Synthetic Priors
• Abstract summary: 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.<n>We show that this epistemic--aleatoric split is not identifiable in general from the posterior predictive distribution alone.<n>We use these labels to train a decoupled PFN with separate latent-signal and aleatoric heads.
• Score: 25.166488691037078
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• From Atoms to Entropy: Optimal Noise Allocation for Diffusion Training in the Convex Regime [52.459513910242485]
  We develop a general statistical framework for studying optimal noise-level allocation in diffusion training.<n>We show that the optimized training schedule admits an atomic minimizer, concentrated on finitely many noise levels.<n>We then evaluate the entropic schedule in larger-scale experiments, where full schedule optimization is currently intractable.
  arXiv  Detail & Related papers  (2026-07-10T20:59:06Z)
• Neural Conjugate Aggregation: Identifiable Unsupervised Multi-Sensor Regression under Heterogeneous Sensor Bias [0.0]
  We study regression-based data fusion under uncertainty, where multiple noisy and biased measurement sources are available but ground-truth labels are absent during training.<n>This setting arises in sensor networks, simulation ensembles, and scientific monitoring systems where supervision is costly or infeasible.<n>We propose the Neural Conjugate Aggregation Model (NCAM), a hierarchical Bayesian framework that combines neural networks with conjugate Gaussian inference for unsupervised multi-source fusion.
  arXiv  Detail & Related papers  (2026-06-20T19:30:21Z)
• Nonparametric Deconvolution and Denoising using Simulation Based Inference [3.6640504352010885]
  We learn a latent generative model by matching the observed data distribution to the noise-convolved model distribution.<n>Our method provides a practical, theoretically grounded approach to deconvolution under generative latent distribution models.
  arXiv  Detail & Related papers  (2026-06-20T07:03:37Z)
• Silent Inconsistency in Data-Parallel Full Fine-Tuning: Diagnosing Worker-Level Optimization Misalignment [27.352639822596146]
  Cross-worker divergence in losses and gradients can remain invisible under conventional monitoring signals.<n>We propose a model-agnostic diagnostic framework that quantifies worker-level consistency using training signals readily available in standard pipelines.
  arXiv  Detail & Related papers  (2026-02-16T04:42:30Z)
• Combating Noisy Labels through Fostering Self- and Neighbor-Consistency [120.4394402099635]
  Label noise is pervasive in various real-world scenarios, posing challenges in supervised deep learning.<n>We propose a noise-robust method named Jo-SNC (textbfJoint sample selection and model regularization based on textbfSelf- and textbfNeighbor-textbfConsistency)<n>We design a self-adaptive, data-driven thresholding scheme to adjust per-class selection thresholds.
  arXiv  Detail & Related papers  (2026-01-19T07:55:29Z)
• Decoupling the Effect of Chain-of-Thought Reasoning: A Human Label Variation Perspective [60.45433515408158]
  We show that long Chain-of-Thought (CoT) serves as a decisive decision-maker for the top option but fails to function as a granular distribution calibrator for ambiguous tasks.<n>We observe a distinct "decoupled mechanism": while CoT improves distributional alignment, final accuracy is dictated by CoT content.
  arXiv  Detail & Related papers  (2026-01-06T16:26:40Z)
• DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolants [12.587156528707796]
  We introduce DAISI, a scalable filtering algorithm built on flow-based generative models.<n>We show that DAISI achieves accurate filtering results in regimes with sparse, noisy, and nonlinear observations.
  arXiv  Detail & Related papers  (2025-11-29T00:02:45Z)
• Learning What Matters: Steering Diffusion via Spectrally Anisotropic Forward Noise [43.07594740645669]
  Diffusion Probabilistic Models (DPMs) have achieved strong generative performance, yet their inductive biases remain largely implicit.<n>In this work, we aim to build inductive biases into the training and sampling of diffusion models to better accommodate the target distribution of the data to model.<n>We introduce an anisotropic noise operator that shapes these biases by replacing the isotropic forward covariance with a structured, frequency-diagonal covariance.
  arXiv  Detail & Related papers  (2025-10-07T16:08:39Z)
• Stein's unbiased risk estimate and Hyvärinen's score matching [9.035498732406039]
  In empirical Bayes, the predominant approach is via nonparametric maximum likelihood estimation (NPMLE)<n>In our setting, Hyv"arinen's implicit SM is equivalent to another classical idea from statistics -- Stein's Unbiased Risk Estimate (SURE)
  arXiv  Detail & Related papers  (2025-02-27T14:15:05Z)
• Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
  We present the first performance guarantee with explicit dimensional dependencies for general score-mismatched diffusion samplers.<n>We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions.<n>This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
  arXiv  Detail & Related papers  (2024-10-17T16:42:12Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)
• Optimizing the Noise in Self-Supervised Learning: from Importance Sampling to Noise-Contrastive Estimation [80.07065346699005]
  It is widely assumed that the optimal noise distribution should be made equal to the data distribution, as in Generative Adversarial Networks (GANs) We turn to Noise-Contrastive Estimation which grounds this self-supervised task as an estimation problem of an energy-based model of the data. We soberly conclude that the optimal noise may be hard to sample from, and the gain in efficiency can be modest compared to choosing the noise distribution equal to the data's.
  arXiv  Detail & Related papers  (2023-01-23T19:57:58Z)
• The Hidden Uncertainty in a Neural Networks Activations [105.4223982696279]
  The distribution of a neural network's latent representations has been successfully used to detect out-of-distribution (OOD) data. This work investigates whether this distribution correlates with a model's epistemic uncertainty, thus indicating its ability to generalise to novel inputs.
  arXiv  Detail & Related papers  (2020-12-05T17:30:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.