This paper proposes the use of "multicalibration": to yield interpretable and reliable confidence scores for outputs generated by large language models (LLMs). Multicalibration asks for calibration not just marginally, but simultaneously across various intersecting groupings of the data. We show how to form groupings for prompt/completion pairs that are correlated with the probability of correctness via two techniques: clustering within an embedding space, and "self-annotation" - querying the LLM by asking it various yes-or-no questions about the prompt. We also develop novel variants of multicalibration algorithms that offer performance improvements by reducing their tendency to overfit. Through systematic benchmarking across various question answering datasets and LLMs, we show how our techniques can yield confidence scores that provide substantial improvements in fine-grained measures of both calibration and accuracy compared to existing methods.

We present Fortuna, an open-source library for uncertainty quantification in deep learning. Fortuna supports a range of calibration techniques, such as conformal prediction that can be applied to any trained neural network to generate reliable uncertainty estimates, and scalable Bayesian inference methods that can be applied to deep neural networks trained from scratch for improved uncertainty quantification and accuracy. By providing a coherent framework for advanced uncertainty quantification methods, Fortuna simplifies the process of benchmarking and helps practitioners build robust AI systems.

Many recent invertible neural architectures are based on coupling block designs where variables are divided in two subsets which serve as inputs of an easily invertible (usually affine) triangular transformation. While such a transformation is invertible, its Jacobian is very sparse and thus may lack expressiveness. This work presents a simple remedy by noting that subdivision and (affine) coupling can be repeated recursively within the resulting subsets, leading to an efficiently invertible block with dense, triangular Jacobian. By formulating our recursive coupling scheme via a hierarchical architecture, HINT allows sampling from a joint distribution p(y,x) and the corresponding posterior p(x|y) using a single invertible network. We evaluate our method on some standard data sets and benchmark its full power for density estimation and Bayesian inference on a novel data set of 2D shapes in Fourier parameterization, which enables consistent visualization of samples for different dimensionalities.

Stein variational gradient descent (SVGD) was recently proposed as a general purpose nonparametric variational inference algorithm: it minimizes the Kullback–Leibler divergence between the target distribution and its approximation by implementing a form of functional gradient descent on a reproducing kernel Hilbert space [Liu & Wang, NIPS 2016]. In this paper, we accelerate and generalize the SVGD algorithm by including second-order information, thereby approximating a Newton-like iteration in function space. We also show how second-order information can lead to more effective choices of kernel. We observe significant computational gains over the original SVGD algorithm in multiple test cases.