Bayes AI

Unit 10: Bayesian Neural Networks and Deep Learning

Vadim Sokolov
George Mason University
Spring 2025

Course Page, Slides

Bayes in Modern AI

Some Applications of Bayes Approaches in LLMs

  • Bayesian techniques are increasingly being used in the context of large language models (LLMs).
  • These developments highlight the growing synergy between Bayesian methods and large language models, offering improvements in model performance, uncertainty quantification, and interpretability.
  • Uncertainty Estimation: Bayesian Prompt Ensembles (BayesPE) have been proposed as a novel approach to obtain well-calibrated uncertainty estimates for black-box LLMs. This method uses a weighted ensemble of semantically equivalent prompts and applies Bayesian variational inference to estimate the weights.
  • Enhancing Bayesian Optimization: A new approach called LLAMBO integrates LLMs within Bayesian optimization frameworks. This method frames the optimization problem in natural language, allowing LLMs to propose and evaluate solutions based on historical data. LLAMBO has shown promise in improving surrogate modeling and candidate sampling, especially in early stages of search.

Some Applications of Bayes Approaches in LLMs

  • Probability Estimation: The BIRD framework incorporates abductive factors, LLM entailment, and learnable deductive Bayesian modeling to provide controllable and interpretable probability estimation for model decisions. This approach has demonstrated a 35% improvement over GPT-4 in aligning probability estimates with human judgments.
  • Natural Language Processing: Bayesian techniques have been applied to various NLP tasks, including word segmentation, syntax analysis, morphology, coreference resolution, and machine translation. These methods offer an elegant way to incorporate prior knowledge and manage uncertainty over parameters.
  • Deep Bayesian Learning: Researchers are exploring the integration of Bayesian principles with deep learning models for NLP applications. This includes the development of hierarchical Bayesian models, variational autoencoders, and (stochastic neural networks)[https://aclanthology.org/P19-4006/].
  • (Prompt Optimisation)[https://dl.acm.org/doi/10.1007/978-3-031-75623-8_28]

Bayesian Optimization

  • Bayesian optimization is a powerful tool for optimizing expensive-to-evaluate functions
  • RunAI was recently acquired by Nvidia for $700m