Understanding parameter functions helps elucidate the internal mechanisms of large language models (LLMs). However, how to connect parameters from different modules to verifiable output effects and further characterize the relationship between their functional organization and model capability remains to be explored.
To this end
we introduce the downstream vocabulary lens (DV-Lens), a parameter-level interpretability framework that links native parameter directions to their downstream vocabulary responses.
Specifically, we first estimate module-specific downstream Jacobians over a reference prompt set for attention query, key, value, and output (Q/K/V/O) projections and feed-forward networks (FFNs).
Second, we use these mappings to project native parameter columns into the final vocabulary space, obtaining signed readouts that characterize their average local output responses.
Third, we group parameter columns by their vocabulary readouts and introduce downstream vocabulary complexity (DV-Complexity), which quantifies within-group structural variation using normalized reconstruction residuals of the original weights.
At the parameter level, randomized controls and finite-difference tests show that DV-Lens readouts capture non-random vocabulary structure and predict local logit changes with 98.0% coordinate-orientation agreement across 720 cases from nine models.
These readouts further guide parameter ablation, steering, and swapping across 21 models, shifting target-token probabilities in the predicted directions under controlled conditions.
At the model level
the joint-parameter score of DV-Complexity achieves a Spearman correlation of 0.904 with benchmark-based capability rankings across 48 language models.
Together, these results provide intervention-based evidence for DV-Lens interpretations and reveal an association between DV-Complexity and model capability.