Recovering Event Probabilities from Large Language Model Embeddings via Axiomatic Constraints

• URL: http://arxiv.org/abs/2505.07883v1
• Date: Sat, 10 May 2025 19:04:56 GMT
• Title: Recovering Event Probabilities from Large Language Model Embeddings via Axiomatic Constraints
• Authors: Jian-Qiao Zhu, Haijiang Yan, Thomas L. Griffiths,
• Abstract summary: We propose enforcing axiomatic constraints, such as the additive rule of probability theory, in the latent space learned by an extended variational autoencoder.<n>This approach enables event probabilities to naturally emerge in the latent space as the VAE learns to both reconstruct the original embeddings and predict the embeddings of semantically related events.
• Score: 4.029252551781513
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Rational decision-making under uncertainty requires coherent degrees of belief in events. However, event probabilities generated by Large Language Models (LLMs) have been shown to exhibit incoherence, violating the axioms of probability theory. This raises the question of whether coherent event probabilities can be recovered from the embeddings used by the models. If so, those derived probabilities could be used as more accurate estimates in events involving uncertainty. To explore this question, we propose enforcing axiomatic constraints, such as the additive rule of probability theory, in the latent space learned by an extended variational autoencoder (VAE) applied to LLM embeddings. This approach enables event probabilities to naturally emerge in the latent space as the VAE learns to both reconstruct the original embeddings and predict the embeddings of semantically related events. We evaluate our method on complementary events (i.e., event A and its complement, event not-A), where the true probabilities of the two events must sum to 1. Experiment results on open-weight language models demonstrate that probabilities recovered from embeddings exhibit greater coherence than those directly reported by the corresponding models and align closely with the true probabilities.

Related papers

• Inv-Entropy: A Fully Probabilistic Framework for Uncertainty Quantification in Language Models [5.6672926445919165]
  Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ)<n>Existing UQ methods are often and lack a probabilistic foundation.<n>We propose a fully probabilistic framework based on an inverse model, which quantifies uncertainty by evaluating the diversity of the input space conditioned on a given output through systematic perturbations.
  arXiv  Detail & Related papers  (2025-06-11T13:02:17Z)
• Identification of Probabilities of Causation: A Complete Characterization [14.18654714001098]
  We propose a complete set of representative probabilities of causation and prove that they are sufficient to characterize all possible probabilities of causation within the framework of Structural Causal Models (SCMs)<n>We then formally derive tight bounds for these representative quantities using formal mathematical proofs.
  arXiv  Detail & Related papers  (2025-05-21T08:50:12Z)
• Exchangeable Sequence Models Quantify Uncertainty Over Latent Concepts [6.256239986541708]
  We show that pre-trained sequence models are naturally capable of probabilistic reasoning over exchangeable data points.<n>A sequence model learns the relationship between observations, which differs from typical Bayesian models.<n>We show the sequence prediction loss controls the quality of uncertainty quantification.
  arXiv  Detail & Related papers  (2024-08-06T17:16:10Z)
• To Believe or Not to Believe Your LLM [51.2579827761899]
  We explore uncertainty quantification in large language models (LLMs) We derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large. We conduct a series of experiments which demonstrate the advantage of our formulation.
  arXiv  Detail & Related papers  (2024-06-04T17:58:18Z)
• Intervention and Conditioning in Causal Bayesian Networks [23.225006087292765]
  We show that by making simple yet often realistic independence assumptions, it is possible to estimate the probability of an interventional formula. In many cases of interest, when the assumptions are appropriate, these probability estimates can be evaluated using observational data.
  arXiv  Detail & Related papers  (2024-05-23T15:55:38Z)
• Incoherent Probability Judgments in Large Language Models [4.307483901449801]
  We assess the coherence of probability judgments made by autoregressive Large Language Models (LLMs)<n>Our results show that the judgments produced by these models are often incoherent, displaying human-like systematic deviations from the rules of probability theory.
  arXiv  Detail & Related papers  (2024-01-30T00:40:49Z)
• Towards Characterizing Domain Counterfactuals For Invertible Latent Causal Models [15.817239008727789]
  In this work, we analyze a specific type of causal query called domain counterfactuals, which hypothesizes what a sample would have looked like if it had been generated in a different domain. We show that recovering the latent Structural Causal Model (SCM) is unnecessary for estimating domain counterfactuals. We also develop a theoretically grounded practical algorithm that simplifies the modeling process to generative model estimation.
  arXiv  Detail & Related papers  (2023-06-20T04:19:06Z)
• User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systems [49.75149094527068]
  We show that diffusion models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. We develop a probabilistic approximation scheme for the conditional score function which converges to the true distribution as the noise level decreases. We are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.
  arXiv  Detail & Related papers  (2023-06-13T03:42:03Z)
• Advancing Counterfactual Inference through Nonlinear Quantile Regression [77.28323341329461]
  We propose a framework for efficient and effective counterfactual inference implemented with neural networks. The proposed approach enhances the capacity to generalize estimated counterfactual outcomes to unseen data. Empirical results conducted on multiple datasets offer compelling support for our theoretical assertions.
  arXiv  Detail & Related papers  (2023-06-09T08:30:51Z)
• Dense Uncertainty Estimation via an Ensemble-based Conditional Latent Variable Model [68.34559610536614]
  We argue that the aleatoric uncertainty is an inherent attribute of the data and can only be correctly estimated with an unbiased oracle model. We propose a new sampling and selection strategy at train time to approximate the oracle model for aleatoric uncertainty estimation. Our results show that our solution achieves both accurate deterministic results and reliable uncertainty estimation.
  arXiv  Detail & Related papers  (2021-11-22T08:54:10Z)
• Multivariate Probabilistic Regression with Natural Gradient Boosting [63.58097881421937]
  We propose a Natural Gradient Boosting (NGBoost) approach based on nonparametrically modeling the conditional parameters of the multivariate predictive distribution. Our method is robust, works out-of-the-box without extensive tuning, is modular with respect to the assumed target distribution, and performs competitively in comparison to existing approaches.
  arXiv  Detail & Related papers  (2021-06-07T17:44:49Z)
• Tractable Inference in Credal Sentential Decision Diagrams [116.6516175350871]
  Probabilistic sentential decision diagrams are logic circuits where the inputs of disjunctive gates are annotated by probability values. We develop the credal sentential decision diagrams, a generalisation of their probabilistic counterpart that allows for replacing the local probabilities with credal sets of mass functions. For a first empirical validation, we consider a simple application based on noisy seven-segment display images.
  arXiv  Detail & Related papers  (2020-08-19T16:04:34Z)

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.