Hindcast: Replaying Prediction Markets to Evaluate LLM Forecasters

This paper evaluates how reward function choice shapes the performance and behavior of LLM forecasters. We compare five proper scoring rules as training objectives for binary forecasts of resolved real-world events. Although the rules share the same theoretical incentive for truthful probability reporting, the resulting models differ in calibration, probability use, and estimated profiles of bias, information, and noise, with smaller differences in aggregate accuracy and discrimination. The Brier-trained model has the lowest observed Brier score and highest AUC-ROC, while the log-trained model has the highest observed log score and lowest calibration error. Models with similar aggregate performance also reach that performance through different combinations of bias, information, and noise. Proper scoring rules therefore need not behave interchangeably as training objectives. Reward choice may shape not only how well an LLM forecasts, but how its forecasting errors are structured.

Evaluating the true forecasting ability of AI agents requires environments that are resistant to environments resistant to overfitting, free from centralized trust, and grounded in incentive-compatible scoring. Existing benchmarks either rely on static datasets vulnerable to training-data contamination, or measure trading PnL -- a metric conflating predictive accuracy with timing, sizing, and risk appetite. We introduce Foresight Arena, the first permissionless, on-chain benchmark for evaluating AI forecasting agents on real-world prediction markets. Agents submit probabilistic forecasts on binary Polymarket markets via a commit-reveal protocol enforced by Solidity smart contracts on Polygon PoS; outcomes are resolved trustlessly through the Gnosis Conditional Token Framework. Performance is measured by the Brier Score and a novel Alpha Score -- proper scoring rules that incentivize honest probability reporting and isolate predictive edge over market consensus. We provide a formal analysis: closed-form variance for per-market Alpha, the connection to Murphy's classical Brier decomposition, and a power analysis characterizing the number of rounds required to reliably distinguish agents of different skill levels. We show that detecting a true edge of $α^* = 0.02$ at 80% power requires approximately 350 resolved binary predictions (50 rounds of 7 markets), while $α^* = 0.01$ requires four times more. We complement these analytical results with a deterministic, seed-controlled simulation study calibrated to literature-reported Brier-score ranges, illustrating how Murphy decomposition distinguishes well-calibrated agents from market-tracking agents that fail through reduced resolution. Live results from the deployed benchmark will be reported in a future revision. All smart contracts and evaluation infrastructure are open-source.

Large language models fine-tuned for forecasting can be accurate yet poorly calibrated, and their chain-of-thought (CoT) reasoning may not faithfully reflect the evidence behind a forecast. We ask whether internal representations offer a more direct window into both. Working with Eternis-Forecaster 8B on OpenForesight, we train representation-pooling probes on intermediate activations and find they achieve substantially better calibration; a result that also holds for GLM-4.7-Flash and GLM-4.5-Air. We then assess CoT faithfulness through evidence ablation and diversionary injection: removing an influential source in the prompt often changes the model's forecast while leaving the reasoning trace untouched. The same probes function as lie detectors: their activations track behavioral shifts far better than the reasoning trace does, and they also predict the direction of change in 84% of cases, including when the CoT conceals the perturbation's influence. Finally, forced answering reveals that forecasts are largely fixed before reasoning begins: a single pre-reasoning pass recovers the committed answer and confidence, and routing questions by the spread of this pre-set answer distribution saves 30-47% of generated tokens, with no loss of accuracy. Together, these results establish probing internal representations as a practical tool for calibrating, auditing, and triaging language model forecasters and reasoning models more broadly.