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Equation 1 · Part 4 · Ten Failure Modes That Define Small and On-Device AI Deployments

subscript

Srequest≤max⁡i(freei)S_{\mathrm{request}} \le \max_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

A device can report gigabytes of free memory and still kill the process that asks for a much smaller allocation, because the operating system’s out-of-memory killer does not care about total free memory — it cares about whether a single contiguous block large enough for the request exists. Large weight tensors and growing key-value caches on a constrained device fragment memory into scattered free regions faster than they fill it, and an allocation can fail against a device that is, in aggregate, nowhere near full. 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…

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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.

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Sources cited in the surrounding passage

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