# LLM Processes: Numerical Predictive Distributions Conditioned on Natural Language

arXiv: https://arxiv.org/abs/2405.12856 · HTML: https://mlsanity.com/paper/2405.12856/

## Key facts

- Cited by 55 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2024.

## Built on by (most cited first, 30 of 55)

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- [Adaptive Acquisition Selection for Bayesian Optimization with Large Language Models](https://mlsanity.com/paper/2602.07904/) (2026)
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- [Revisiting LLMs as Zero-Shot Time-Series Forecasters: Small Noise Can Break Large Models](https://mlsanity.com/paper/2506.00457/) (2025)
- [Flipping Against All Odds: Reducing LLM Coin Flip Bias via Verbalized Rejection Sampling](https://mlsanity.com/paper/2506.09998/) (2025)
- [Text-Trained LLMs Can Zero-Shot Extrapolate PDE Dynamics, Revealing a Three-Stage In-Context Learning Mechanism](https://mlsanity.com/paper/2509.06322/) (2025)
- [Density estimation with LLMs: a geometric investigation of in-context learning trajectories](https://mlsanity.com/paper/2410.05218/) (2024)
- [Zero-shot Model-based Reinforcement Learning using Large Language Models](https://mlsanity.com/paper/2410.11711/) (2024)
- [ProMind-LLM: Proactive Mental Health Care via Causal Reasoning with Sensor Data](https://mlsanity.com/paper/2505.14038/) (2025)
- [LLMs as World Models: Data-Driven and Human-Centered Pre-Event Simulation for Disaster Impact Assessment](https://mlsanity.com/paper/2506.06355/) (2025)
- [Eliciting Numerical Predictive Distributions of LLMs Without Autoregression](https://mlsanity.com/paper/2603.02913/) (2026)
- [Agentic Bayesian Optimization through Surrogate-Augmented Autoresearch](https://mlsanity.com/paper/2608.00316/) (2026)
- [LAST SToP For Modeling Asynchronous Time Series](https://mlsanity.com/paper/2502.01922/) (2025)
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- [Overcoming the Modality Gap in Context-Aided Forecasting](https://mlsanity.com/paper/2603.12451/) (2026)
- [NumericJev: Jev-like LLM Numerical Decoding with Multiway Decision Trees](https://mlsanity.com/paper/2609.28587/) (2026)
- [CARL-GT: Evaluating Causal Reasoning Capabilities of Large Language Models](https://mlsanity.com/paper/2412.17970/) (2024)
- [Random Initialization Can't Catch Up: The Advantage of Language Model Transfer for Time Series Forecasting](https://mlsanity.com/paper/2506.21570/) (2025)
- [Equinox: Holistic Fair Scheduling in Serving Large Language Models](https://mlsanity.com/paper/2508.16646/) (2025)
- [Anticipatory Evaluation of Language Models: Predicting LLM Benchmark Scores from Descriptions](https://mlsanity.com/paper/2509.20645/) (2025)
- [RELISH: LLM REgression with a Latent Iterative State Head](https://mlsanity.com/paper/2604.01206/) (2026)
- [ForecastBench-Sim: A Simulated-World Forecasting Benchmark](https://mlsanity.com/paper/2606.18686/) (2026)

## Abstract (arXiv)

Machine learning practitioners often face significant challenges in formally integrating their prior knowledge and beliefs into predictive models, limiting the potential for nuanced and context-aware analyses. Moreover, the expertise needed to integrate this prior knowledge into probabilistic modeling typically limits the application of these models to specialists. Our goal is to build a regression model that can process numerical data and make probabilistic predictions at arbitrary locations, guided by natural language text which describes a user's prior knowledge. Large Language Models (LLMs) provide a useful starting point for designing such a tool since they 1) provide an interface where users can incorporate expert insights in natural language and 2) provide an opportunity for leveraging latent problem-relevant knowledge encoded in LLMs that users may not have themselves. We start by exploring strategies for eliciting explicit, coherent numerical predictive distributions from LLMs. We examine these joint predictive distributions, which we call LLM Processes, over arbitrarily-many quantities in settings such as forecasting, multi-dimensional regression, black-box optimization, and image modeling. We investigate the practical details of prompting to elicit coherent predictive distributions, and demonstrate their effectiveness at regression. Finally, we demonstrate the ability to usefully incorporate text into numerical predictions, improving predictive performance and giving quantitative structure that reflects qualitative descriptions. This lets us begin to explore the rich, grounded hypothesis space that LLMs implicitly encode.