Effect of Data Noise on Representation Learning in Language Models

📝 Abstract

This research project investigates the Geometric and Information-Theoretical consequences of data corruption in Transformer-based Language Models. As Large Language Models (LLMs) are increasingly trained on uncurated, web-scale corpora, the impact of "noisy" tokens—whether stochastic (random replacement), syntactic (shuffling), or adversarial (gradient-optimized)—on the internal embedding manifold remains poorly understood.

This repository provides a rigorous, modular, and reproducible experimental framework to quantify Representation Degradation. We utilize elite-tier diagnostic features including Intrinsic Dimensionality (ID) analysis, Centered Kernel Alignment (CKA), and Bayesian Uncertainty Calibration via Monte Carlo (MC) Dropout. Our empirical findings reveal a catastrophic "dimensionality explosion" in early layers and a structural "filtering horizon" in deeper transformer blocks, providing novel evidence for the robustness-generalization trade-offs of state-of-the-art NLP architectures.

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🔬 Research Problem & Motivation

The Crisis of Web-Scale Training

Modern NLP models are trained on datasets like the Common Crawl, which contain significant levels of linguistic noise—typos, slang, misaligned labels, and adversarial "spam." While models are famously resilient at the output layer, our research asks: What happens to the internal Latent Space?

Core Research Questions

1. Manifold Saturation: Does data noise cause the latent manifold to "saturate," where the model loses the ability to distinguish between nuanced semantic vectors?
2. The Filtering Horizon: Does a transformer act as a "Denoising Filter" across layers, or do noise signals propagate and amplify toward the final output?
3. Epistemic Collapse: At what point ($p$) does the model's confidence decohere from its actual predictive accuracy?

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🛠️ Technical Methodology

Our project employs a multi-metric approach to analyze the "Health" of the representation space.

1. Geometric Diagnostics (Intrinsic Dimension)

We estimate the Intrinsic Dimensionality (ID) of the manifold using the Two-NN algorithm (Maximum Likelihood Estimator).

• Method: For each hidden state $Z_i$, we compute the ratio of distances to its first and second nearest neighbors ($\mu = r_2/r_1$).
• Interpretability: A higher ID in noisy regimes indicates that the model is being forced to represent stochastic patterns that have no semantic grounding (Representation Clutter).

2. Structural Alignment (Centered Kernel Alignment)

We utilize Linear CKA to measure the similarity between "Clean" and "Noisy" representation matrices across all transformer layers.

• Mathematical Bound: $CKA(K, L) = \frac{HSIC(K, L)}{\sqrt{HSIC(K, K) \cdot HSIC(L, L)}}$.
• Insight: This identifies the "Most Vulnerable Layer" (MVL) by showing where the latent features of a noisy sentence start to diverge from the clean manifold.

3. Adversarial Probing (FGSM)

To move beyond random "Stochastic Noise," we implement the Fast Gradient Sign Method (FGSM).

• The Experiment: We optimize a perturbation $\epsilon \cdot sign(\nabla_X L(\theta, X, y))$ to find the "Semantic Breakpoint" of the manifold.
• Result: We demonstrate that targeted adversarial noise causes a significantly higher manifold displacement than random token replacement.

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📊 Datasets & Experimental Context

We selected these datasets specifically for their contrasting noise profiles:

Dataset	Research Category	Utility
WikiText-2	Stability Baseline	Standard formal text used as the "Zero-Noise" control group.
Sentiment140	Natural Noise	Twitter Data: Typos, slang, user handles, and emojis. Perfect for testing "Real-world Noise."
AG News	Synthetic Noise	Used to test classification robustness under $10% \to 80%$ token corruption.
CLIP (VLM)	Multimodal Drift	Image-Text pairs used to study how text noise "infects" visual perception.

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🧬 Project Modules & Advanced Extensions

Pillar 1: Geometric Probing (advanced_research.py)

This module calculates the Intrinsic Dimension (ID) and generates Representation Sensitivity Maps. It compares how different noise levels "shred" the manifold.

Pillar 2: Multimodal Robustness (multimodal_research.py)

Using OpenAI’s CLIP, we analyze the Alignment Breakpoint. We study how Visual Noise (Gaussian/Salt-and-Pepper) cross-correlate with Text Noise to destroy image-retrieval performance.

Pillar 3: Uncertainty Calibration (uncertainty_calibration.py)

We implement MC Dropout and Predictive Entropy. High variance across dropout samples reveals "Epistemic Uncertainty," allowing us to detect noisy data points during inference.

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📉 Interpreting the Results

When running the suite, the metrics reflect the following research outcomes:

1. Low CKA (< 0.70): The representation layer has been "lost" to noise; the semantic signal is no longer recoverable.
2. High ID (> 80): The manifold is "over-saturated" with noise; the model is over-parametrizing stochastic patterns.
3. High Entropy (> 1.0): The model is "guessing" and has low confidence in its prediction due to data corruption.

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📂 Project Structure

/
├── data/
│   ├── loader.py         # Automated Kaggle/HF Dataset handlers
│   └── noise_injector.py # Stochastic, Shuffling, and Grammar noise logic
├── analysis/
│   ├── probing.py        # ID, CKA, MI, and Denoising Probe logic
│   └── visualize.py      # UMAP & Displacement plotting
├── main.py               # Baseline experiment runner
├── advanced_research.py   # Geometric, Adversarial, and Layer-wise mapping
├── multimodal_research.py # CLIP Image-Text alignment suite
└── uncertainty_calibration.py # MC Dropout & Entropy scaling suite

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🚀 Execution & Reproducibility for R&D

1. Environment Setup

# Clone the repository
git clone https://github.com/your-username/effect-of-noise-llm.git
cd effect-of-noise-llm

# Install dependencies (Tier-1 standard)
pip install -r requirements.txt

2. Run Geometric & Adversarial Probing

This script produces the Research Report and the CKA Propagation Map.

python advanced_research.py

3. Analyze Multimodal Sensitivity

Analyzes the decay of Image-Text alignment under Gaussian visual noise.

python multimodal_research.py

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🚀 Future Directions & Scalability

This repository acts as a foundation for advanced robustness research. Planned future extensions include:

• Denoising Fine-tuning: Training models to "re-stiffen" their semantic manifolds against stochastic noise during pre-training.
• Cross-Architectural Benchmarking: Comparing the "Filtering Horizon" of Mamba (SSM) and Transformer models under identical noise regimes.
• Automated Noise-Filtering Probes: Implementing a real-time module that dynamically filters noisy tokens before they reach the attention layers using Intrinsic Dimension thresholds.
• Large-Scale Multi-Modal Expansion: Investigating "Cross-Modal Infection" in massive VISION-TRANSFORMER (ViT) and Stable Diffusion latent spaces.

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Project maintained for Robust AI & Advanced Representation Learning Research - (C) 2026