Equation 8 · Part 7 · Model Systems in 2035: Four Scenarios, Their Signals, and What Would Falsify Them
subscript
subscript
What this part means
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
Its job in the formula
A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.
Full expression→subscript→Article meaning
The passage around this formula
with and the annual growth factors. When > , grows without bound, and the batch size required to keep the arithmetic units busy grows with it. Autoregressive decoding sits on the wrong side of this: generating one token requires streaming the weights and the accumulated key–value cache, so decode time is bounded below by . where W is the weight bytes touched and K the cache bytes. Pope and colleagues formalised the partitioning analysis behind this and showed how latency, throughput and cost trade against one another under different sharding layouts [ 12 ] . The mitigations are well documented and all attack the numerator or the batch: grouped-query…
Learn the underlying idea
A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.
Open the illustrated subscripts: which member of a family? guide →
Sources cited in the surrounding passage
- [12] Efficiently Scaling Transformer Inference ↗
- [14] GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints ↗
- [13] Efficient Memory Management for Large Language Model Serving with PagedAttention ↗
- [15] Fast Inference from Transformers via Speculative Decoding ↗
These citations provide research context; check each source for the exact claim it supports.