Energy Complexity
CE(x;q,δ) = E*(x,q,δ)
Define the minimum expected energy required to solve a task at a specified quality and reliability level.
ENERGY-EFFICIENT ARTIFICIAL INTELLIGENCE
More Intelligence.
Less Energy.
LowJoule is a research initiative exploring the mathematical, algorithmic, and computational foundations of energy-efficient artificial intelligence.
CORE OPTIMIZATION OBJECTIVE
π* = arg maxπ E[ Q − λE ]
Maximize useful output quality while explicitly accounting for the energy required to produce it.
ADAPTIVE COMPUTATIONCONCEPTUAL MODEL
Adaptive allocationFixed allocation
01 / RESEARCH QUESTION
How much computation is
actually necessary?
Contemporary AI systems typically allocate substantial computation regardless of the intrinsic difficulty of a task. LowJoule studies whether computation can instead be allocated dynamically according to expected marginal utility.
02 / METRIC
Useful Intelligence per Joule
UI/J is a proposed framework for studying the relationship between useful model performance and the physical energy required to achieve it.
UI/J
Useful Intelligence
Energy Consumed
03 / MATHEMATICAL FOUNDATIONS
Energy as a first-class computational variable.
Marginal Computation
ρt = ΔQt / ct
Measure the expected quality improvement produced by an additional unit of energy.
Adaptive Policy
π* = arg max E[Q − λE]
Select computational actions dynamically instead of allocating the same computation to every task.
04 / CENTRAL HYPOTHESIS
If tasks have heterogeneous computational requirements, a sufficiently accurate adaptive policy can reduce expected energy consumption while maintaining a specified quality constraint.
E[Eadaptive] < E[Efixed]
subject to Qadaptive ≥ Qfixed − ε
subject to Qadaptive ≥ Qfixed − ε
05 / RESEARCH PROGRAM
01Task Complexity
02Optimal Stopping
03Dynamic Depth
04Conditional Routing
05Reasoning Reuse
06Energy-Aware Scheduling
06 / PUBLICATIONS
Research in progress.
Mathematical foundations, experimental protocols, benchmarks, and technical papers will be published as the LowJoule research program develops.