← Back to article

Equation 11 · Comparing the Main Approaches to AI Memory Systems and the Bandwidth Wall

What does this equation mean?

WW

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

WW

Symbol W

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

Understand this part →

How to interpret it

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

What the article says around this equation

That capacity is not free. Sun and colleagues built the first comprehensive evaluation of real, shipping CXL memory devices — as opposed to the emulated-via-remote-NUMA-node substitute most earlier research used — across three commercial devices on a current-generation Intel Xeon platform, and their results are a useful correction to intuition built on emulation: true CXL memory can show up to 26 percent lower latency and 3 to 66 percent higher bandwidth efficiency than emulated CXL memory did in prior studies, meaning some of the pessimism in the earlier literature was measuring the wrong thing [ 6 ] . Their paper is also explicit about where the physical trade comes from: a CXL memory…
Read the full surrounding passage
That capacity is not free. Sun and colleagues built the first comprehensive evaluation of real, shipping CXL memory devices — as opposed to the emulated-via-remote-NUMA-node substitute most earlier research used — across three commercial devices on a current-generation Intel Xeon platform, and their results are a useful correction to intuition built on emulation: true CXL memory can show up to 26 percent lower latency and 3 to 66 percent higher bandwidth efficiency than emulated CXL memory did in prior studies, meaning some of the pessimism in the earlier literature was measuring the wrong thing [ 6 ] . Their paper is also explicit about where the physical trade comes from: a CXL memory device connects over PCIe rather than the DDR bus, at roughly three times fewer pins than a DDR5 interface, in exchange for a much longer link latency — on the order of 40 nanoseconds for a PCIe 4.0 hop versus under 1 nanosecond for a native DDR4 link [ 6 ] . That is the pin-versus-latency trade the earlier equation predicts: CXL keeps W narrow and serial, and pays in access time instead.

Read the equation in its article →

Sources cited in the surrounding passage

These citations give research context. Read each source to check which claims it supports.

Return to Comparing the Main Approaches to AI Memory Systems and the Bandwidth Wall

Browse the mathematical compendium →