hunterbown/shannon-control-unit

Shannon Control Unit (SCU): Information-Theoretic Regularization via PI Control

Abstract

Shannon Control Unit (SCU) applies closed-loop control to large-scale language model training. Treating regularization strength ($\lambda$) as an actuator and the Minimum Description Length (MDL) information ratio ($S$) as the controlled variable, SCU uses a proportional-integral (PI) controller to maintain a target ($S^*$) throughout optimization. This feedback stabilizes model complexity without manual hyperparameter sweeps. On Llama 3.2 (1B, 3B) fine-tuning, SCU improves bits-per-token by 6-12% over tuned fixed-$\lambda$ baselines while preserving training stability.

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1. Problem Statement

Conventional regularization (weight decay, dropout) is scheduled open-loop. The effective tendency to overfit varies over the course of training, so static or hand-tuned schedules either under-penalize (memorization) or over-penalize (underfitting). A feedback mechanism that measures the model’s instantaneous information balance and adjusts $\lambda$ accordingly is required.

2. Methodology

SCU couples information theory with PI control. We monitor the MDL-derived information ratio

$$S(t)=\frac{\text{ParamBPT}(t)}{\text{DataBPT}(t)+\text{ParamBPT}(t)}S(t)\; =\; \backslash frac\{\backslash text\{ParamBPT\}(t)\}\{\backslash text\{DataBPT\}(t)\; +\; \backslash text\{ParamBPT\}(t)\}$$

where DataBPT is the bits-per-token of the loss and ParamBPT is the bits-per-token of the parameter update. The control objective is $S(t) \rightarrow S^*$. Let $e(t) = S(t) - S^*$. With plant gain $\partial S / \partial \lambda < 0$, the PI law updates the regularization strength as

$${\lambda }_{t+1}={\lambda }_t\cdot \exp (-(K_p\cdot e(t)+K_i\cdot \sum _{\tau \le t}e(\tau )))\backslash lambda\_\{t+1\}\; =\; \backslash lambda\_t\; \backslash cdot\; \backslash exp\backslash left(\; -\; (K\_p\; \backslash cdot\; e(t)\; +\; K\_i\; \backslash cdot\; \backslash sum\_\{\backslash tau\; \backslash le\; t\}\; e(\backslash tau))\; \backslash right)$$

optionally with deadband and integral clamping for anti-windup. Updates are applied at gradient-accumulation boundaries to maintain stability.

3. Results

We validated SCU by fine-tuning Llama 3.2 models on a subset of WikiText-103. The results show significant improvements in compression efficiency (Bits Per Token) and Perplexity compared to an optimally tuned cross-entropy baseline.

Model	Metric	Baseline (Cross-Entropy)	SCU (PI Control)	Improvement
Llama-3.2-1B	BPT	3.920	3.676	-6.2%
	Perplexity	15.14	12.78	-15.6%
Llama-3.2-3B	BPT	1.830	1.635	-10.6%
	Perplexity	3.56	3.11	-12.6%

Note: Validation performed on Llama 3.2 LoRA adapters. Baseline represents the best-performing fixed-$\lambda$ configuration found via grid search.

4. Related & Concurrent Work

The application of control theory to LLM training is an emerging and promising field.

4.1 Independent Convergence: EntroPIC

Recent independent work, EntroPIC (arXiv:2511.15248), applies PI control to stabilize policy entropy in reinforcement learning. This convergence indicates that control-theoretic feedback is effective for stabilizing training dynamics. SCU targets the MDL information ratio during supervised pretraining/fine-tuning, whereas EntroPIC targets policy entropy in RL; the objectives are complementary and suggest a broader control lens on neural training.

5. Future Directions

Our ongoing research focuses on:

• Scaling Laws for $S^$:* Deriving the optimal target $S^*$ from first principles based on model size ($N$) and dataset size ($D$), removing the need for a target setpoint entirely.
• Full-Parameter Training: Extending validation beyond LoRA to full model pretraining.
• Unified Control: Investigating if regulating Information Ratio implicitly stabilizes entropy (unifying SCU and EntroPIC findings).

6. Usage

Installation

git clone https://github.com/Shannon-Labs/shannon-control-unit.git
cd shannon-control-unit
pip install -r requirements.txt

Quick Start (Inference)

from transformers import AutoModelForCausalLM, AutoTokenizer
from peft import PeftModel
import torch

# Load Base Model
base_id = "meta-llama/Llama-3.2-3B"
base = AutoModelForCausalLM.from_pretrained(base_id, device_map="auto", torch_dtype=torch.float16)

# Load SCU Adapter
model = PeftModel.from_pretrained(base, "hunterbown/shannon-control-unit", subfolder="3b-scu")

For reproduction scripts and training details, see examples/ and scripts/.

7. Citation

If you use SCU in your research, please cite:

@misc{bown2025scu,
  author = {Bown, Hunter},
  title = {Shannon Control Unit: Information-Theoretic Regularization via PI Control},
  year = {2025},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/Shannon-Labs/shannon-control-unit}}
}

8. License

This repository is dual-licensed:

• Research & Open Source: AGPL-3.0. Free for academic and open-source use.
• Commercial: Proprietary licenses available for closed-source applications. Contact [email protected].

Intellectual Property: The SCU methodology is subject to a U.S. Provisional Patent (Filed September 2025).