AI Math Challenge
A — Quick energy math test (illustrative, step-by-step)
Goal: show a conservative example comparing energy per inference/token for a large LLM vs. a lean Turner/Sovara-style model.
Define variables (clear assumptions up front)
FLLMFLLM = FLOPs per token for the big LLM — assume 3×10113×1011 FLOPs/token (illustrative).
FTFT = FLOPs per inference for Turner model — assume 1×1081×108 FLOPs/inference (illustrative).
EperFLOP=1×10−9EperFLOP=1×10−9 joules per FLOP (1 nJ/FLOP — conservative order-of-magnitude).
1 kWh=3,600,0001 kWh=3,600,000 J.
Step 1 — Energy per token (joules)
LLM:
ELLM=FLLM×EperFLOP=3×1011×1×10−9.ELLM=FLLM×EperFLOP=3×1011×1×10−9.
Compute digit-by-digit:
3×1011×10−9=3×10(11−9)=3×1023×1011×10−9=3×10(11−9)=3×102.
So ELLM=300ELLM=300 joules per token.
Turner:
ET=FT×EperFLOP=1×108×1×10−
9.ET=FT×EperFLOP=1×108×1×10−9.
Compute:
1×108×10−9=1×10−11×108×10−9=1×10−1.
So ET=0.1ET=0.1 joules per inference.
Step 2 — Convert to kWh
LLM:
kWhLLM=300 J3,600,000 J/kWh.kWhLLM=3,600,000 J/kWh300 J.
Compute:
300/3,600,000=112,000=8.3333×10−5300/3,600,000=12,0001=8.3333×10−5 kWh per token.
Turner:
kWhT=0.1 J3,600,000 J/kWh.kWhT=3,600,000 J/kWh0.1 J.
Compute:
0.1/3,600,000=2.7778×10−80.1/3,600,000=2.7778×10−8 kWh per inference.
Step 3 — Ratio (how many × more energy)
Energy ratio (LLM : Turner) in joules:
3000.1=3000.0.1300=3000.
So in this illustrative example, the LLM costs ~3,000× more energy per token/inference than the Turner model.
Step 4 — Scale to useful units (1,000 tokens / 1 session)
Per 1000 tokens:
LLM: 300 J/token×1000=300,000300 J/token×1000=300,000 J → 300,000/3,600,000=0.08333300,000/3,600,000=0.08333 kWh.
Turner: 0.1 J×1000=1000.1 J×1000=100 J → 100/3,600,000=2.7778×10−5100/3,600,000=2.7778×10−5kWh.
So 1,000 tokens of big LLM ≈ 0.083 kWh vs Turner ≈ 0.0000278 kWh.
These numbers are illustrative and depend on the FLOPs-per-token and joules-per-FLOP assumptions. The point of the test is method, not the absolute number: show reviewers how to compute and compare, and force them to state their FLOPs and energy constants. If you want, we can replace my illustrative assumptions with measured numbers from Grok/LLM posts (or your Sovara telemetry) for a follow-up comparison.
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