A Block-Based Regularization Proposal for Neural Networks

Exploring Localized Weight Groupings as a Way to Control Overfitting

Introduction
I’m not an expert in machine learning. I've been studying the field out of curiosity and an almost irrational drive to understand if some things could be done differently. I ended up thinking about a simple idea — which might already exist in more sophisticated forms — but I thought it was worth sharing: a regularization strategy based on weight blocks.

The idea came as an attempt to simplify regularization processes. What if we grouped weights into trios forming structural subsets (blocks), and applied a smoothing average?

Core Idea: Block-Based Regularization

Apply regularization using local contrast smoothing, promoting continuity — a concept with two “filters” per unit.

Key detail: these blocks can be organized as sliding trios, like:

[w₀, w₁, w₂], [w₁, w₂, w₃], [w₂, w₃, w₄]...

That is, the blocks overlap, and each trio of adjacent weights becomes a regularized unit. The goal is to reduce abrupt contrasts, creating a form of structural continuity that smooths transitions between activations and helps prevent overfitting — without needing to eliminate features.

Each intermediate weight (like w₂) participates in multiple overlapping blocks, undergoing multiple smoothing passes. This creates an effect similar to an implicit smoothing hidden layer, acting in the weight space even before regular propagation and backpropagation — like an internal wire “stretching” the net's shape.

This approach also handles the extremes (w₀ and wₙ₊₁) using phantom blocks to ensure these edge weights are regularized fairly.

Simplified Mathematical Expression

${Loss}_{t o t a l} = {Loss}_{b a s e} + λ (∥ w_{0} ∥^{2} + N \sum i = 1 ∥ B_{i} ∥^{2} + ∥ w_{n + 1} ∥^{2})$

Where:

w₀ and wₙ₊₁ are edge weights;
Bᵢ is each block trio [wᵢ, wᵢ₊₁, wᵢ₊₂];
λ is the regularization coefficient;
N is the number of sliding blocks.

Why This Might Be Interesting

Encourages regularity within functional groups, reducing local spikes;
Acts as a form of lightweight modularization, especially in symbolic architectures;
Might reduce the need for complex preprocessing or handcrafted regularization tweaks;
Could complement or partially replace classic loss tweaks, like ½(y - ŷ)²;
Block size is adjustable depending on spike magnitude.

Limitations I Can Already Foresee

This might already exist under another name (Group Lasso? Modu

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