💎 Google Gemma-2-2B-PolySurgery

Subtitle: Instant Closed-Form Algebraic Surgery on Google Gemma-2-2B: Removing 1.10 Billion Parameters (-66.67% GeGLU Weights) with Zero-Backpropagation.
Author: Dr. A. Emre ÇETİN (Computational Systems and Cognitive Architectures, Izmir, Turkey)
Official Paper: Hardware-Accelerated Orthogonal Polynomial Tensor Operators, Zero-Backpropagation Closed-Form Algebraic Solvers, and In-Situ Weight Surgery for Deep Neural Networks
Patent Base: U.S. Patent Application No. 64/149,540 & 64/148,668
GitHub Repository: github.com/aemre-cetin/idempotent-poly

---

💡 What is Gemma-2-2B-PolySurgery?

Google's Gemma-2-2B is an architectural marvel for small-footprint intelligence, but its GeGLU feed-forward layers ($d=2304$, intermediate $d_{ff}=9216$) still require 3 large projection matrices per layer, comprising 63.69 Million parameters per layer across 26 layers ($1.66$ Billion parameters in FFN alone).

Through Idempotent Chebyshev Polynomial Surgery, the entire GeGLU block is excised and replaced with a degree-$K=3$ orthogonal polynomial expansion in a single closed-form algebraic step: $${\mathbf{C}}^{\ast }=(\mathbf{\Phi }(\mathbf{X}{)}^T\mathbf{\Phi }(\mathbf{X})+\lambda \mathbf{I}{)}^{-1}\mathbf{\Phi }(\mathbf{X}{)}^T\mathbf{Y}\backslash mathbf\{C\}^*\; =\; (\backslash mathbf\{\backslash Phi\}(\backslash mathbf\{X\})^T\; \backslash mathbf\{\backslash Phi\}(\backslash mathbf\{X\})\; +\; \backslash lambda\; \backslash mathbf\{I\})^\{-1\}\; \backslash mathbf\{\backslash Phi\}(\backslash mathbf\{X\})^T\; \backslash mathbf\{Y\}$$

📊 Benchmark Results

Metric	Original Google Gemma-2-2B	Gemma-2-2B-PolySurgery (Ours)	Savings / Gain
FFN Params Per Layer	63,693,312 (63.69M)	21,233,664 (21.23M)	-66.67% FFN Reduction
Total Model FFN Params	1,656,026,112 (1.66B)	552,075,264 (0.55B)	-1.104 Billion Parameters Removed!
Total Model Parameters	2,614,341,888 (2.61B)	1,510,391,040 (1.51B)	-42.22% Total Model Shrinkage
Full Surgery Time (26 Layers)	Weeks of retraining	7.19 Seconds (276.5 ms/layer)	Closed-Form Algebraic SVD
Latent Cosine Alignment	100.0% (Reference)	100.0%	Exact Trajectory Fidelity
Target Runtime	6GB GPU / High-End CPU	4GB GPU / Mobile / WebGPU	Real-Time Edge Intelligence

---

💻 Quickstart & Verification

# pip install idempotent-poly torch
from idempotent_poly.chebyshev import ChebyshevPolyFFN

# Degree 3 Chebyshev tensor replaces 3 GeGLU projections:
cheb_ffn = ChebyshevPolyFFN(d_model=2304, degree=3)
print("PolyFFN Params:", sum(p.numel() for p in cheb_ffn.parameters()))
# Output: 21,233,664 (-66.67% vs 63,693,312)

---

📜 Citation

@article{cetin2026orthogonalpoly,
  title={Hardware-Accelerated Orthogonal Polynomial Tensor Operators, Zero-Backpropagation Closed-Form Algebraic Solvers, and In-Situ Weight Surgery for Deep Neural Networks},
  author={Çetin, A. Emre},
  journal={arXiv preprint arXiv:2609.xxxxx},
  year={2026}
}