Not at all! You are still completely faithful to Guo et al. Your current implementation does **not** break their framework.

In fact, your setup matches the exact methodology of the paper. There is a common misconception about what Guo et al. mean when they caution against calculating the Hessian inverse, and understanding how your feature extraction relates to their theory explains why your code remains completely valid.

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## 1. What Guo et al. *Actually* Said

In the original paper (*"Certified Removal from Linear Models"*), Guo et al. state that explicitly calculating and inverting the Hessian matrix becomes prohibitively expensive when the parameter count $d$ scales up.

$$\text{Time Complexity to Invert } H = O(d^3)$$

However, the authors explicitly implemented and verified their approach on **linear classifiers** (like logistic regression) where the input feature dimension $d$ was small enough to handle directly.

When you strip out the heavy ResNet50 convolutional layers and turn the backbone into a static feature extractor, **you transform your deep network into a linear classifier.** ```
[Images] ──> [Frozen ResNet Backbone] ──> Extracted Feature Vector (d = 2048) ──> [Linear Head (model.fc)]


Because your feature vector is exactly 2,048 dimensions, your Hessian matrix is a modest $2048 \times 2048$. 

Inverting a $2048 \times 2048$ matrix takes your CPU less than **0.5 seconds** ($2048^3$ operations is tiny for a modern processor). You are executing the exact mathematics Guo et al. prescribed for linear systems. You haven't broken their implementation; you have successfully reduced a non-convex deep learning problem into their exact convex linear domain.


## 2. Where Hessian-Free Approximations (Like LiSSA) Apply

The reason alternative methods like LiSSA or Conjugate Gradient exist is for scenarios where you *cannot* reduce the model to a small linear head.

If you decided to apply Certified Removal to the **entire ResNet50 network** (all 23.5 million parameters open), then you would be forced to abandon your exact matrix calculation. Inverting a $23.5\text{M} \times 23.5\text{M}$ matrix is impossible. In that specific scenario, you would have to use a Hessian-free approximation method to avoid breaking the budget.

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## 3. The Core Alignment with the Paper

Your script implements the three pillars that define Guo et al.’s Certified Removal:

1. **The Optimization Target:** It uses an $L_2$-regularized objective function (`self.l2_reg`).
2. **The Newton Step:** It takes the exact second-order curvature correction ($H^{-1} \nabla$) to adjust the parameters.
3. **The Indistinguishability Guarantee:** It applies a privacy perturbation boundary check (`self.removal_bound`).

Your implementation is an elegant, academically sound adaptation of their linear model theory for a deep learning architecture. By handling the feature extraction step first, you made their exact algorithm run efficiently within a 4GB VRAM envelope.