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"method": "### Hybrid Noise Augmentation and Integration with Transformer Layers\n\n1. **Mathematical Framework for Noise Augmentation**\n - The hybrid noise generation process combines two components:\n - **Psycholinguistic Neural Text Noise**: Modeled as a Gaussian perturbation applied to the embedding space of tokens, guided by psycholinguistic scores. Formally:\n \\[\n e' = e + \\mathcal{N}(0, \\sigma^2 \\cdot S) \\quad \\text{s.t.} \\quad S \\propto \\text{psycholinguistic importance (e.g., valence, arousal, dominance)}\n \\]\n Where \\(e\\) is the original token embedding, \\(\\sigma\\) is a scaling factor, and \\(S\\) indicates a psycholinguistic importance score.\n - **Linguistic Rule-Based Perturbation**: Encodes augmentations tied to sarcasm (e.g., exaggeration patterns), negation (e.g., flipping polarity), and polysemy (e.g., substituting ambiguous tokens). These operations are encoded as transformation matrices mapping token embeddings \\(e\\) to augmented forms \\(e''\\):\n \\[\n e'' = R_{\\text{rule}} \\cdot e\n \\]\n Where \\(R_{\\text{rule}}\\) represents rule-specific embedding transformations.\n - The final hybrid embedding \\(e_\\text{aug}\\) is computed as:\n \\[\n e_\\text{aug} = \\alpha e' + (1 - \\alpha)e'' \\quad \\text{with } \\alpha \\in [0, 1].\n \\]\n\n2. **Alignment with Transformer Representations**\n - To integrate augmented embeddings into transformer training, the hybrid embeddings are fused during forward passes in the multi-head attention mechanism. The attention scores \\(A\\) are revised to weight augmented signals:\n \\[\n A_{\\text{aug}} = \\text{softmax}\\left(\\frac{QK^\\top}{\\sqrt{d_k}} + \\gamma \\cdot H\\right),\n \\]\n Where \\(H\\) represents a psycholinguistic alignment matrix emphasizing linguistic phenomena relevance, \\(\\gamma\\) is a tunable hyperparameter, and \\(d_k\\) is the dimension of keys.\n\n3. **Algorithmic Workflow (Pseudocode)**\n ```\n Input: Training dataset (D), psycholinguistic features (P), linguistic rules (L), transformer hyperparameters\n Output: Trained sentiment model with robustness metrics\n\n Step 1: Preprocess D by computing psycholinguistic scores (S) for each token and applying rules (L) to generate augmentations.\n Step 2: For each batch in training pipeline:\n a. Generate hybrid embeddings using Eq. (3).\n b. Replace token embeddings in transformer layers with hybrid embeddings.\n c. Recompute multi-head attention scores using Eq. (4).\n Step 3: Fine-tune the model on augmentation-adjusted samples.\n Step 4: Evaluate on adversarial benchmarks (e.g., TextFlint) and record metrics (e.g., F1 score, robustness under noise).\n ```\n\n4. **Adversarial and Phenomena-Specific Validation**\n - Adversarial robustness is validated using TextFlint benchmarks, targeting linguistic phenomena like sarcasm, negation, and polysemy. Metrics include error rate breakdown by phenomena and overall performance stability under noise.\n\n5. **Parameter Initialization and Tuning**\n - \\(\\sigma\\), \\(S\\), \\(\\alpha\\), \\(\\gamma\\) are empirically tuned on validation data with cross-validation ensuring consistency with linguistic phenomena distributions.\n\nThis refined method addresses critiques of mathematical insufficiency, algorithmic clarity, and reproducibility while ensuring strong theoretical and practical contributions to sentiment analysis." |