You have written SIMD acronym Single Instruction, Multiple Data — one CPU instruction operating on several packed values at once. Then → now: you knew this as vector instructions (MMX/SSE). Same idea, wider registers (512 bits now), and the ML world calls the packed values a vector too — overloaded word, §1 untangles it. code that adds eight floats in one instruction. You already have the right mental model for a vector; the ML field just loads extra meaning onto the word. Let’s separate the three senses so nothing is ambiguous later.

A vector is, first, an ordered list of numbers definition An element of ℝⁿ: n real numbers in a fixed order. The order carries meaning — position i is a specific coordinate. — a point in ℝⁿ. That’s the algebraic sense. Second, it’s a direction and magnitude — the geometric sense, an arrow from the origin. Third, in your SIMD code, it’s just a register’s worth of lanes. These coincide on purpose: the hardware vector holds the coordinates of the algebraic vector, and the algebraic vector is the geometric arrow. One object, three vocabularies.

Why does direction carry the meaning and not, say, the raw coordinates? Because the operations we’ll build — similarity, attention scores, quantization distortion — are all rotation-friendly: they care about the angles and lengths between vectors, not the accident of which axis is “axis 0.” Hold that thought; it’s literally why rotation-based quantization forward ref A family of compression methods (RaBitQ, TurboQuant) that rotate vectors before quantizing, because rotation preserves dot products while equalizing per-coordinate variance. You'll meet this in Ch. 25. It only makes sense once §1.3 (norms) and Ch. 6 (high-dim geometry) are in hand. works at all (Ch. 25).