Entropy Bandwidth Y-Axis (EBY)

We introduce Entropy Bandwidth Y-Axis (EBY), a scalar diagnostic metric designed to quantify the behavioural quality of autoregressive language models during training. While conventional metrics such as cross-entropy loss and perplexity measure predictive accuracy, they provide no direct signal about the shape of the model’s output distribution specifically, the balance between diversity and confidence. EBY captures this balance by combining normalized Shannon entropy with top-k probability mass (sharpness), yielding a bounded signal in [0, 1]. Crucially, both degenerate regimes deterministic collapse and incoherent randomness map to low EBY values, while only balanced, human-like predictive behavior yields high EBY. We formalize EBY, analyse its asymptotic behaviour, introduce positional variants (EBY-Head and EBY-Tail) for temporal degradation detection, and describe a trend-based monitoring system suitable for online training. Empirical results from training a 381M-parameter Turkish language model demonstrate that EBY detects distributional collapse several hundred optimization steps before perplexity degradation becomes visible, enabling early corrective intervention. EBY thus provides a complementary behavioural axis for model diagnostics, orthogonal to loss- based metrics.