01 / STATISTICAL SAMPLING
Softmax Entropy & Tail Sampling
Language models output unbounded logits $z_i$. Applying softmax with temperature produces $P(w_i) = \frac{e^{z_i/\tau}}{\sum e^{z_j/\tau}}$. When $\tau > 0.7$, the probability distribution flattens. Even when a factual token has highest probability, sampling draws from the probability tail where factually erroneous but grammatically plausible tokens live.
02 / ATTENTION MECHANICS
Context Fading & Attention Sinks
As generation proceeds, dot-product attention scores $\text{Softmax}\left(\frac{Q K^T}{\sqrt{d}}\right)V$ diffuse. Models develop "attention sinks" where massive probability mass clusters on recent punctuation or common connective tokens. The semantic constraint of the user's initial prompt decays, allowing generative drift.
03 / CONFABULATION CASCADE
Autoregressive Error Amplification
Transformers predict token $t_n$ conditioned strictly on $[t_1, \dots, t_{n-1}]$. When an incorrect token is sampled at step $k$, it permanently joins the conditioning prompt. The model cannot backtrack; its attention heads now treat its own hallucination as verified premise, making subsequent confabulation mathematically optimal.