# CHAIN: Calibrated LLM Forecasting via Causal-Temporal Hypergraph Inference

arXiv: https://arxiv.org/abs/2609.36689 · HTML: https://mlsanity.com/paper/2609.36689/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 50 of its 72 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 30 of 50)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [From Local to Global: A Graph RAG Approach to Query-Focused Summarization](https://mlsanity.com/paper/2404.16130/) (2024)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Graph Retrieval-Augmented Generation: A Survey](https://mlsanity.com/paper/2408.08921/) (2024)
- [LightRAG: Simple and Fast Retrieval-Augmented Generation](https://mlsanity.com/paper/2410.05779/) (2024)
- [HippoRAG: Neurobiologically Inspired Long-Term Memory for Large Language Models](https://mlsanity.com/paper/2405.14831/) (2024)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)
- [Approaching Human-Level Forecasting with Language Models](https://mlsanity.com/paper/2402.18563/) (2024)
- [From News to Forecast: Integrating Event Analysis in LLM-Based Time Series Forecasting with Reflection](https://mlsanity.com/paper/2409.17515/) (2024)
- [Large language model validity via enhanced conformal prediction methods](https://mlsanity.com/paper/2406.09714/) (2024)
- [Stop Measuring Calibration When Humans Disagree](https://mlsanity.com/paper/2210.16133/) (2022)
- [HyperGraphRAG: Retrieval-Augmented Generation via Hypergraph-Structured Knowledge Representation](https://mlsanity.com/paper/2503.21322/) (2025)
- [Wisdom of the Silicon Crowd: LLM Ensemble Prediction Capabilities Rival Human Crowd Accuracy](https://mlsanity.com/paper/2402.19379/) (2024)
- [ConU: Conformal Uncertainty in Large Language Models with Correctness Coverage Guarantees](https://mlsanity.com/paper/2407.00499/) (2024)
- [Forecasting Future World Events with Neural Networks](https://mlsanity.com/paper/2206.15474/) (2022)
- [FutureX: An Advanced Live Benchmark for LLM Agents in Future Prediction](https://mlsanity.com/paper/2508.11987/) (2025)
- [Calibrating Language Models with Adaptive Temperature Scaling](https://mlsanity.com/paper/2409.19817/) (2024)
- [Calibrating the Confidence of Large Language Models by Eliciting Fidelity](https://mlsanity.com/paper/2404.02655/) (2024)
- [Temporal Knowledge Graph Forecasting Without Knowledge Using In-Context Learning](https://mlsanity.com/paper/2305.10613/) (2023)
- [GenTKG: Generative Forecasting on Temporal Knowledge Graph with Large Language Models](https://mlsanity.com/paper/2310.07793/) (2023)
- [Calibrating Reasoning in Language Models with Internal Consistency](https://mlsanity.com/paper/2405.18711/) (2024)
- [Consistency Checks for Language Model Forecasters](https://mlsanity.com/paper/2412.18544/) (2024)
- [Restoring Calibration for Aligned Large Language Models: A Calibration-Aware Fine-Tuning Approach](https://mlsanity.com/paper/2505.01997/) (2025)
- [GraphRAG-Bench: Challenging Domain-Specific Reasoning for Evaluating Graph Retrieval-Augmented Generation](https://mlsanity.com/paper/2506.02404/) (2025)
- [Pitfalls in Evaluating Language Model Forecasters](https://mlsanity.com/paper/2506.00723/) (2025)

## Abstract (arXiv)

Large language models have achieved significant progress in event forecasting, yet their probability outputs exhibit systematic calibration bias that varies heterogeneously across different domains and question types, undermining the trustworthiness of probabilistic outputs for decision-making under uncertainty. However, existing calibration methods typically correct probability outputs after prediction is complete, without modeling the structural sources of bias within the prediction process itself. To address this challenge, we decompose probabilistic prediction over causal-temporal hypergraphs into three stages, evidence weighting, evidence aggregation, and source fusion, and propose CHAIN, which designs stage-specific mechanisms to mitigate bias at each stage: (i) modulating the temporal decay function by causal topological distance, (ii) aggregating approximately independent causal chains via Noisy-OR after direction-aware deduplication, and (iii) driving adaptive fusion by causal coverage and directional balance. Experimental results on cross-domain forecasting benchmarks show CHAIN outperforms existing methods in expected calibration error, Brier score, and accuracy. Our project is available at https://github.com/QwenQKing/Chain.