Faced with complex problems, the human brain demonstrates a remarkable capacity to transcend sensory input and form latent understandings of perceived world patterns. However, this cognitive capacity is not explicitly considered or encoded in current large language models (LLMs). As a result, LLMs often struggle to capture latent structures and model uncertainty in complex compositional reasoning tasks. This work introduces a novel Bayesian prompting approach that facilitates training-free Bayesian inference with LLMs by using a verbalized Probabilistic Graphical Model (PGM). While traditional Bayesian approaches typically depend on extensive data and predetermined mathematical structures for learning latent factors and dependencies, our approach efficiently reasons latent variables and their probabilistic dependencies by prompting LLMs to adhere to Bayesian principles. We evaluated our model on several compositional reasoning tasks, both close-ended and open-ended. Our results indicate that the model effectively enhances confidence elicitation and text generation quality, demonstrating its potential to improve AI language understanding systems, especially in modeling uncertainty.

While deep learning models have achieved remarkable success across a range of medical image analysis tasks, deployment of these models in real clinical contexts requires that they be robust to variability in the acquired images. While many methods apply predefined transformations to augment the training data to enhance test-time robustness, these transformations may not ensure the model's robustness to the diverse variability seen in patient images. In this paper, we introduce a novel three-stage approach based on transformers coupled with conditional diffusion models, with the goal of improving model robustness to the kinds of imaging variability commonly encountered in practice without the need for pre-determined data augmentation strategies. To this end, multiple image encoders first learn hierarchical feature representations to build discriminative latent spaces. Next, a reverse diffusion process, guided by the latent code, acts on an informative prior and proposes prediction candidates in a generative manner. Finally, several prediction candidates are aggregated in a bi-level aggregation protocol to produce the final output. Through extensive experiments on medical imaging benchmark datasets, we show that our method improves upon state-of-the-art methods in terms of robustness and confidence calibration. Additionally, we introduce a strategy to quantify the prediction uncertainty at the instance level, increasing their trustworthiness to clinicians using them in clinical practice.