faresrafat3/semitic-scattering-law

Exploratory research on how root-scatter affects neural language model performance in Semitic morphology (Arabic, Hebrew, Amharic). # 🔬 The Scattering Law — Exploratory Research on Information Distribution in Semitic Morphology > An independent research project exploring how root-scatter affects neural language model performance in Semitic languages (Arabic, Hebrew, Amharic). --- ## 🌌 Overview For decades, the difficulty of Neural Language Models in processing Semitic languages has been commonly attributed to "data scarcity" or "tokenization issues." **This project investigates an alternative hypothesis**: that the difficulty stems, at least in part, from a structural property of root-and-pattern morphology — specifically, the spatial scatter of root radicals within a word. Through a systematic empirical study, we observed a pattern we call the **Scattering Law**: a roughly linear decay in a model's ability to perceive morphological boundaries as the distance between root radicals increases. This is treated here as an exploratory finding, not a finalized scientific claim. --- ## 📐 The Mathematical Formulation We define the **Scattering Degree (S)** as: $$S = (\text{span of root radicals}) - (\text{number of radicals})$$ Our preliminary empirical observations suggest that the **Neural Lift** (the gain in boundary detection over random chance) follows an approximately linear decay: $$\text{Lift} \approx \beta_0 - \beta_1 \cdot S$$ Where $\beta_1$ is what we informally call the **"Blindness Coefficient"**. When $S$ exceeds a critical threshold (empirically observed around $\approx 3.7$ in our experiments), the model's predictive power appears to drop sharply — a region we refer to as the **"Blind Zone"**. > ⚠️ **Important caveat**: The constants above ($\beta_0$, $\beta_1$, the 3.7 threshold) are empirical observations from our experiments, not universal constants. Independent replication is encouraged. --- ## 🌍 Cross-Language Observations We tested the Scattering Law hypothesis across three Semitic languages in our experiments: | Language | Observation | Correlation | |---|---|-- …