← Mathematical compendium

Published equation contexts

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

Why this formula appears here

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…

Read the full article-specific guide →

Read the representative guide

SrequestS_{\mathrm{request}}

Symbol S_request

SrS_request is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Read this term in its guide →
ii

Symbol i

i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Read this term in its guide →
ii

Starting index or lower bound: i

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Read this term in its guide →

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

Research cited beside this formula

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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

Equation 2 · Edge AI & Electronics

Ten Failure Modes That Define Small and On-Device AI Deployments

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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…

Equation guide → · Article →