Self-attention models content-dependent interactions between tokens but does not by itself encode token order. Position encoding addresses this limitation by introducing absolute coordinates, relative distances, or position-dependent rotations into Transformer representations and attention scores. This technical survey develops a unified account of sinusoidal and learned absolute position embeddings, Shaw-style relative position representations, Transformer-XL, T5 relative position bias, ALiBi, and Rotary Position Embeddings (RoPE). We derive how RoPE converts absolute position indices into relative phase differences in Query-Key inner products and compare these methods in terms of where position is injected, computational cost, compatibility with KV caching, and length extrapolation. We then examine long-context extensions, including Position Interpolation, RoPE scaling laws, NTK-aware scaling, Dynamic NTK, NTK-by-parts, YaRN, LongRoPE, and LongRoPE2, with emphasis on frequency allocation, attention rescaling, training length, and target context length. We also summarize implementation considerations, evaluation protocols, and position-encoding choices in representative large language models. A central conclusion is that the ability to compute positional features beyond the training length does not imply reliable long-context generalization; context extension must be evaluated through short-context retention, position-wise perplexity, retrieval, reasoning, and long-context code tasks.
We organize relative-position mechanisms in attention as a learnable Fourier-Jet-Affine position space. The starting point is lag-shift dynamics: a relative-position kernel is a response function of the lag \(d=i-j\), and the one-step shift \((Ef)(d)=f(d+1)\) gives a compact classification of finite structured responses through constant-coefficient difference modules. In this view, RoPE supplies simple Fourier roots, Jordan-RoPE thickens these roots into finite Fourier jets, and ALiBi supplies the repeated unit-root affine direction. NTK-aware RoPE scaling fits the same structure as a spectral flow of simple Fourier roots: moving the frequency grid generates first Fourier-jet tangent directions, while higher Taylor directions generate higher jets. PJ-RoPE makes these jet directions explicit and learnable, and uses the resulting space to measure task-level sector selection. The framework separates scalar PJ-bias kernels from exact PJ-rotary feature transforms, introduces sector-gate, effective-mass, functional-energy, and leave-one-order-out diagnostics, and stabilizes high-order coordinates with LC/rapidity compactification. Controlled probes recover designed sectors; synthetic teachers show trainable use; small byte-level language runs favor NTK-aware RoPE plus affine recency; symbolic music-token streams keep LC/affine variants strong with measurable high-order corrections; and LC diagnostics quantify the stability-resolution tradeoff.