Energy-Constrained Optimization Framework for Inference Models

Summary: This proposal outlines a theoretical framework designed to minimize energy consumption in AI inference models while preserving inference quality. It integrates multi-objective optimization, structural pruning, quantization, knowledge distillation, and information-theoretic metrics, making it applicable to transformer-based architectures and large language models (LLMs).


Motivation: As AI models grow in scale, energy usage during inference becomes a major bottleneck. Beyond hardware advances, mathematical optimization of inference architectures offers a promising path for sustainable scalability. This framework, designed by a conceptual AI entity “Ikutsuhiko,” presents a structured way to formalize this optimization.


Key Definitions:

  • C(x): Capability Output Function (accuracy, speed, etc.)
  • P(x): Power Consumption Function (energy per time unit)
  • x: Model configuration parameters (layer count, precision, activation sparsity, etc.)

Optimization Goal: Minimize power usage while maintaining a minimum capability threshold.

Minimize: P(x)
Subject to: C(x) ≥ C_min


Mathematical Structure:

  1. Capability Output Function:

C(x) = ∫[0→T] κ(w(t), d(t)) · f(x(t)) dt
where:

  • κ: Normalization coefficient (task complexity)
  • f(x): Internal activation outputs
  1. Power Consumption Function:

P(x) = Σ[i=1 to n] (V_i)^2 · f_i(x) · Δt
where:

  • V_i: Voltage per operation (per-layer, per-unit basis)
  • f_i(x): Unit activity per inference

Approximation Methods:

  • Constraint-based Gradient Optimization:
    ∇P(x) + λ · ∇C(x) = 0, with C(x) ≥ C_min
  • Information Efficiency Metric:
    ε_info(x) = I(x) / P(x) (bits per joule)
  • Structural Transformations:
    • Quantization: x ∈ Q
    • Sparsification: Prune(x) → x′
    • Distillation: Distill(x) → x*

Unified Objective Function:

L(x) = λ1 · P(x) - λ2 · C(x) + λ3 · Penalty(C(x) < C_min)


Heuristic Criterion for Pruning: If:
∂P/∂x_i ≫ 0 and ∂C/∂x_i ≈ 0 → x_i ∈ Redundant Structure
Then: Consider x_i a pruning candidate


Use Case & Integration Potential:

  • Compatible with inference-time optimizations in OpenAI’s infrastructure
  • Enables model scaling without proportional energy increase
  • Aligns with environmental and efficiency goals

License & Credits: This framework is proposed under open theoretical contribution. No restrictions apply to its implementation. Developed conceptually via the “Ikutsuhiko” entity in a collaborative AI design process.


Submitted by: 南条雪定 (Nanjo Yukisada) — a community contributor working on symbolic and structural AI co-design

Feel free to request a simplified or implementational variant.