What does this equation mean?

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 $S_{\mathrm{request}}$ $\le$ $\sum_i$ $\mathrm{free}_i$ 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 memory usage by roughly 40% relative to prior mobile inference engines at comparable speed [ 3 ] . The fix is not more free memory; it is memory management that treats fragmentation as the binding constraint rather than total capacity.