Beyond Text: Tapping Hidden Numerical Insights in Language Models

New research reveals that large language models possess surprisingly accurate numerical prediction capabilities encoded within their internal states, bypassing the need for traditional text generation.

![Trading activity in digitally-created “Biden Tokens” spiked around key political events, demonstrating how speculative fervor transforms symbolic capital into quantifiable market behavior and revealing the susceptibility of even novelty assets to emotionally-driven surges and declines-a pattern mirroring established financial bubbles driven by hope and fear rather than underlying value, as predictably encoded in [latex] P = f(E, S) [/latex], where price (P) is a function of events (E) and sentiment (S).](https://arxiv.org/html/2603.03152v1/2603.03152v1/biden_no_token_price_tx_vol_events.png)
![The shifting correlation between predictions in the Trump and Democrat-aligned forecasting markets demonstrates a dynamic relationship, revealing how consensus diverges and converges as events unfold-a pattern indicative of evolving perceptions rather than static alignment, and suggesting that even opposing systems momentarily share predictive signals before ultimately re-establishing independent trajectories-a phenomenon mirroring the inherent impermanence of all complex systems [latex] \Delta t \rightarrow \in fty [/latex].](https://arxiv.org/html/2603.03136v1/2603.03136v1/rolling_correlation_between_trump_and_dem_market.png)
![Model sensitivity, as measured by impulse responses at [latex]t-1[/latex], diverges across different optimization algorithms, highlighting the nuanced impact of each on system dynamics.](https://arxiv.org/html/2603.02620v1/2603.02620v1/figs/difference_adam_muon_t-1_transformer.jpeg)



![A transformation utilizing the score function maximizes the local Fisher information, enabling a detector-applied to the transformed data-to achieve a higher probability of detection, though estimates remain biased globally, while application to the original data yields globally unbiased estimates with a variance exceeding the Cramér-Rao lower bound [latex] CRLB [/latex].](https://arxiv.org/html/2603.01737v1/2603.01737v1/x2.png)