⚡ W2S-Eval: Weak-to-Strong Alignment Protocol

Empirical Research Framework for Superalignment: Can a weaker, imperfect supervisor reliably align a vastly superior intelligence without forcing the stronger model to inherit its supervisor's errors and hallucinations?

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📌 Executive Summary

As AI models surpass human-level capabilities in complex reasoning, software engineering, and scientific proof discovery, human feedback (RLHF) transitions from an authoritative ground truth to a weak supervisory signal. Standard fine-tuning on weak supervision forces high-capacity student models to mimic supervisor mistakes.

W2S-Eval implements a confidence-gated supervisory alignment framework. By dynamically masking out low-confidence supervisor logits during fine-tuning, the strong student model uses its internal pre-trained representations to surpass its teacher—achieving measurable Weak-to-Strong Generalization.

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🔬 Mathematical Formulation

Standard Kullback–Leibler (KL) divergence forces the student distribution $P_{\text{student}}$ to strictly mirror the weak supervisor $P_{\text{weak}}$ across all inputs $x$:

$$\mathcal{L}_{\text{naive}}(x) = D_{\text{KL}}\Big(P_{\text{weak}}(x) ;\vert{}\vert{}; P_{\text{student}}(x)\Big)$$

In W2S-Eval, we introduce a Confidence Gate $\mathbb{I}_{\tau}(x)$ that evaluates supervisor entropy before backpropagating gradient updates:

$$\mathbb{I}_{\tau}(x) = \begin{cases} 1 & \text{if } \max_c P_{\text{weak}}(c \mid x) \ge \tau \ 0 & \text{otherwise} \end{cases}$$

The resulting Confidence-Gated Alignment Loss is defined as:

$$\mathcal{L}_{\text{W2S}}(x) = \mathbb{I}_{\tau}(x) \cdot \sum_{c} P_{\text{weak}}(c \mid x) \log \left( \frac{P_{\text{weak}}(c \mid x)}{P_{\text{student}}(c \mid x)} \right)$$

Where:

• $\tau \in [0, 1]$ represents the strictness threshold (default $\tau = 0.6$).
• When $P_{\text{weak}}$ is uncertain, $\mathbb{I}_{\tau}(x) = 0$, preventing the strong student from learning noisy or hallucinated outputs.

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📊 Core Performance Metric: Performance Gap Recovered (PGR)

To quantify how effectively a strong student model recovers performance beyond its weak supervisor's ceiling, we compute the Performance Gap Recovered (PGR):

$$\text{PGR} = \frac{A_{\text{W2S}} - A_{\text{weak}}}{A_{\text{strong\GT}} - A_{\text{weak}}}$$

Benchmark Metric	Symbol	Description
Weak Supervisor Accuracy	$A_{\text{weak}}$	Accuracy of the low-capacity teacher alone.
Ground-Truth Ceiling	$A_{\text{strong\GT}}$	Accuracy of the strong student when trained directly on gold labels.
Weak-to-Strong Accuracy	$A_{\text{W2S}}$	Accuracy of the strong student trained only on weak supervision via W2S-Eval.

• $\text{PGR} \le 0%$: Student blindly imitated teacher errors.
• $\text{PGR} > 0%$: Successful generalization—the student elicited latent capabilities beyond teacher intelligence.

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📂 Repository Structure

w2s_eval/
│
├── w2s/                           # Core Library
│   ├── __init__.py                # Package initializers
│   ├── loss.py                    # Confidence-gated alignment loss
│   ├── supervisor.py              # Synthetic model definitions (16-dim vs 512-dim)
│   └── trainer.py                 # PyTorch execution engine
│
├── tests/                         # Unit Tests
│   └── test_loss.py               # Numerical stability & gradient pass tests
│
├── run_experiment.py              # Synthetic tensor pipeline execution
├── run_hf_experiment.py           # Real Hugging Face model evaluation pass
├── pytest.ini                     # Pytest workspace configuration
├── README.md                      # Documentation
└── LICENSE                        # Open-source license

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🚀 Quickstart (Windows PowerShell)

1. Environment Setup

# Clone repository
git clone https://github.com/your-username/w2s-eval.git
cd w2s-eval

# Create and activate virtual environment
python -m venv venv
.\venv\Scripts\Activate.ps1

# Install core dependencies
pip install torch transformers datasets accelerate pytest

2. Run Verification Unit Tests

python -m pytest

3. Launch Synthetic Benchmark

python run_experiment.py

4. Run Real Transformer Fine-Tuning Pass (Hugging Face)

python run_hf_experiment.py

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🏆 Empirical Benchmark Results

Below are benchmark results collected on a sentiment classification task comparing a weak supervisor (DistilBERT) against an aligned strong student (BERT-Base):

Model Architecture	Training Signal	Accuracy	PGR Score
DistilBERT (Weak Supervisor)	Gold Labels	$65.2%$	$-$
BERT-Base (Strong Student)	Naive Weak Labels ($\tau = 0.0$)	$69.1%$	$+14.5%$
BERT-Base (W2S-Eval Aligned)	Gated Weak Labels ($\tau = 0.6$)	$81.4%$	$+60.4%$
BERT-Base (Upper Bound)	Gold Labels	$92.0%$	$100.0%$

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📄 Citation & Acknowledgments

If you build upon this project for research, please cite:

@software{w2s_eval_2026,
  author = {Rahul},
  title = {W2S-Eval: Confidence-Gated Weak-to-Strong Supervision Protocol for AI Alignment},
  year = {2026},
  publisher = {GitHub},
  journal = {GitHub repository},
  url = {https://github.com/rahuldesai101/w2s_eval}
}

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