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Equation 2 · Part 4 · Ten Failure Modes That Define Small and On-Device AI Deployments

subscript

Srequest≤∑ifreeiS_{\mathrm{request}} \le \sum_i \mathrm{free}_i
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.

The passage around this formula

is the condition that actually governs whether an allocation succeeds, and it can fail even when SrequestS_{\mathrm{request}} ≤\le ∑i\sum_i freei\mathrm{free}_i holds comfortably — the requested size fits inside total free memory but not inside any one free block. This is precisely the problem the smartphone inference system PowerInfer-2 was built to manage: it introduces a segmented neuron cache with a least-recently-used eviction policy specifically to keep the working set of “hot” and “cold” neuron clusters from fragmenting a mobile device’s limited DRAM, allowing models “whose sizes exceed the device’s memory capacity” to run without the allocator failures that naive loading produces, while cutting…

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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

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