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+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0099", "section": "A. Details of Baseline", "page_start": 11, "page_end": 11, "type": "Text", "text": "Shared Notations: We first define the universal notations used across all baseline methods for consistency:", "source": "marker_v2", "marker_block_id": "/page/10/Text/2"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0100", "section": "A. Details of Baseline", "page_start": 11, "page_end": 11, "type": "ListGroup", "text": "x: Input text sample for membership inference detection. {x1, x2, . . . , x N }: Token sequence of input text sample x, where N denotes the total number of tokens in the text. x<t: Prefix token sequence of the t-th token xt, i.e., x<t = {x1, . . . , xt−1}. θ: Trainable parameters of the pre-trained language model. p(· | ·; θ): Conditional probability distribution parameterized by the model parameters θ. k%: Percentage threshold for selecting low-probability outlier tokens (used in Min-k% and Min-k%++).", "source": "marker_v2", "marker_block_id": "/page/10/ListGroup/597"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0101", "section": "A.1. PPL", "page_start": 11, "page_end": 11, "type": "Text", "text": "Perplexity (PPL) is a classic global likelihood-based metric that measures the model's uncertainty in predicting a given text, with lower PPL indicating higher text familiarity (more likely to be a member sample). First, the text is tokenized into a sequence of tokens {x1, x2, . . . , x N }. Then, the log-likelihood of each token is calculated conditional on the preceding tokens, and the final PPL is derived by normalizing the sum of log-likelihoods by the token sequence length and performing an exponential transformation.", "source": "marker_v2", "marker_block_id": "/page/10/Text/10"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0102", "section": "A.1. PPL", "page_start": 11, "page_end": 11, "type": "Equation", "text": "PPL = \\exp\\left(-\\frac{1}{N} \\sum_{i=1}^{N} \\log p(x_i|x_1, ..., x_{x-1}; \\theta)\\right) (16)", "source": "marker_v2", "marker_block_id": "/page/10/Equation/11"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0103", "section": "A.2. Zlib", "page_start": 11, "page_end": 11, "type": "Text", "text": "Zlib is a compression-based global likelihood-related method that leverages compression entropy to distinguish member and non-member samples, which calibrates the loss using the input's Zlib entropy. For an input text sample x and a pre-trained model M, the Zlib score is defined as the ratio of the loss related to the text and model to the Zlib compression entropy of the input text:", "source": "marker_v2", "marker_block_id": "/page/10/Text/13"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0104", "section": "A.2. Zlib", "page_start": 11, "page_end": 11, "type": "Equation", "text": "Zlib Score = \\frac{L(x, M)}{\\text{zlib}(x)} (17)", "source": "marker_v2", "marker_block_id": "/page/10/Equation/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0105", "section": "A.2. Zlib", "page_start": 11, "page_end": 11, "type": "Text", "text": "where L(x, M) denotes the loss value associated with the input text x under the model M and zlib(x) represents the Zlib compression entropy of the input text x, which is derived from the length of the text after Zlib compression.", "source": "marker_v2", "marker_block_id": "/page/10/Text/15"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0106", "section": "A.3. Min-k%", "page_start": 11, "page_end": 11, "type": "Text", "text": "Min-k% is a local likelihood-based method that mitigates global word frequency interference by focusing on low-probability outlier tokens. For an input text token sequence x = {x1, x2, . . . , x N } (where N denotes the total number of tokens), it first calculates the conditional log-likelihood of each token x i given its preceding context:", "source": "marker_v2", "marker_block_id": "/page/10/Text/17"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0107", "section": "A.3. Min-k%", "page_start": 11, "page_end": 11, "type": "Equation", "text": "\\log p(x_i \\mid x_1, x_2, \\dots, x_{i-1}; \\theta)", "source": "marker_v2", "marker_block_id": "/page/10/Equation/18"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0108", "section": "A.3. Min-k%", "page_start": 11, "page_end": 11, "type": "Text", "text": "Subsequently, it sorts all token conditional probabilities in ascending order, selects the bottom k% tokens (i.e., the k% tokens with the smallest conditional probabilities) to form the low-probability set Tmin(k%) = Min-K%(x). The final Min-k% score is defined as the average conditional log-likelihood of tokens in Tmin(k%):", "source": "marker_v2", "marker_block_id": "/page/10/Text/19"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0109", "section": "A.3. Min-k%", "page_start": 11, "page_end": 11, "type": "Equation", "text": "Min-k% Score(x) = \\frac{1}{|T_{\\min(k\\%)}|} \\sum_{x_i \\in T_{\\min(k\\%)}} \\log p(x_i \\mid x_1, \\dots, x_{i-1}; \\theta) (18)", "source": "marker_v2", "marker_block_id": "/page/10/Equation/20"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0110", "section": "A.3. Min-k%", "page_start": 11, "page_end": 11, "type": "Text", "text": "where |Tmin(k%)| = ⌊k% × N⌋ denotes the cardinality of the low-probability token set (rounded down to the nearest integer). During detection, a threshold is set on Min-k% Score(x): text with a score below the threshold is classified as a member sample (since member samples tend to contain more low-probability outlier tokens), and vice versa.", "source": "marker_v2", "marker_block_id": "/page/10/Text/21"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0111", "section": "A.4. Min-k%++", "page_start": 12, "page_end": 12, "type": "Text", "text": "Min-k%++ is an optimized variant of Min-k% that enhances detection robustness by integrating vocabulary-level probability statistics, addressing the text-length dependency and short-text fluctuation issues of the original method. For an input text token sequence x = \\{x_1, x_2, \\dots, x_N\\} , it first computes the normalized conditional log-likelihood for each token x_t (given prefix x_{< t} = \\{x_1, \\dots, x_{t-1}\\} ) by normalizing with the vocabulary-wide log-probability statistics of the prefix x_{< t} .", "source": "marker_v2", "marker_block_id": "/page/11/Text/2"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0112", "section": "Core Token-Level Score Calculation", "page_start": 12, "page_end": 12, "type": "Text", "text": "For each token x_t , the token-level Min-k%++ score is defined as:", "source": "marker_v2", "marker_block_id": "/page/11/Text/4"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0113", "section": "Core Token-Level Score Calculation", "page_start": 12, "page_end": 12, "type": "Equation", "text": "Min-k\\% + +_{token}(x_{< t}, x_t) = \\frac{\\log p(x_t \\mid x_{< t}; \\theta) - \\mu_{x_{< t}}}{\\sigma_{x_{< t}}} (19)", "source": "marker_v2", "marker_block_id": "/page/11/Equation/5"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0114", "section": "Core Token-Level Score Calculation", "page_start": 12, "page_end": 12, "type": "Text", "text": "where \\mu_{x_{< t}} = \\mathbb{E}_{z \\sim p(\\cdot \\mid x_{< t}; \\theta)} [\\log p(z \\mid x_{< t}; \\theta)] : Expectation of the next-token log-likelihood over the model's vocabulary, given prefix x_{< t} ; \\sigma_{x_{< t}} = \\sqrt{\\mathbb{E}_{z \\sim p(\\cdot \\mid x_{< t}; \\theta)} \\left[ (\\log p(z \\mid x_{< t}; \\theta) - \\mu_{x_{< t}})^2 \\right]} : Standard deviation of the next-token log-likelihood over the vocabulary, given prefix x_{< t} .", "source": "marker_v2", "marker_block_id": "/page/11/Text/6"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0115", "section": "Core Token-Level Score Calculation", "page_start": 12, "page_end": 12, "type": "Text", "text": "Both \\mu_{x_{< t}} and \\sigma_{x_{< t}} can be computed analytically using the model's output logits (since p(\\cdot \\mid x_{< t}; \\theta) follows a categorical distribution), requiring no additional computational overhead beyond standard LLM inference.", "source": "marker_v2", "marker_block_id": "/page/11/Text/7"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0116", "section": "Final Sequence-Level Score Calculation", "page_start": 12, "page_end": 12, "type": "Text", "text": "Similar to Min-k%, Min-k%++ selects the bottom k% tokens with the smallest Min-k%++<sub>token</sub> scores to form the low-probability set T_{\\min(k\\%)}^+ . The final sequence-level score is the average of the token-level scores in this set:", "source": "marker_v2", "marker_block_id": "/page/11/Text/9"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0117", "section": "Final Sequence-Level Score Calculation", "page_start": 12, "page_end": 12, "type": "Equation", "text": "Min-k\\% ++ Score(x) = \\frac{1}{|T_{\\min(k\\%)}^+|} \\sum_{(x_{< t}, x_t) \\in T_{\\min(k\\%)}^+} Min-k\\% ++_{token}(x_{< t}, x_t) (20)", "source": "marker_v2", "marker_block_id": "/page/11/Equation/10"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0118", "section": "Final Sequence-Level Score Calculation", "page_start": 12, "page_end": 12, "type": "Text", "text": "where |T_{\\min(k\\%)}^+| = \\lfloor k\\% \\times N \\rfloor denotes the cardinality of the low-probability token set. During detection, a threshold is applied: text with a lower Min-k%++ score is more likely to be a member sample, as the normalized score better distinguishes low-probability outlier tokens of member samples from non-member ones.", "source": "marker_v2", "marker_block_id": "/page/11/Text/11"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0119", "section": "A.5. FSD", "page_start": 12, "page_end": 12, "type": "Text", "text": "Fine-tuned Score Deviation (FSD) is a fine-tuning enhanced method that leverages score discrepancies between pre-trained and fine-tuned models for member sample detection. Its core workflow includes two key steps: first, constructing a domain-matched non-member fine-tuning dataset (using post-model-release unseen data), then performing self-supervised next-token prediction fine-tuning on the pre-trained model. Finally, it calculates the score difference between the pre-trained and fine-tuned models to distinguish member and non-member samples. The self-supervised fine-tuning loss is defined as:", "source": "marker_v2", "marker_block_id": "/page/11/Text/13"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0120", "section": "A.5. FSD", "page_start": 12, "page_end": 12, "type": "Equation", "text": "\\mathcal{L}_{\\text{fine-tuning}}(x) = -\\frac{1}{n} \\sum_{i=1}^{n} \\log f_{\\theta}(x_i \\mid x_1, \\dots, x_{i-1}) (21)", "source": "marker_v2", "marker_block_id": "/page/11/Equation/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0121", "section": "A.5. FSD", "page_start": 12, "page_end": 12, "type": "Text", "text": "The final FSD score is the deviation between the sample scores obtained from the pre-trained model f_{\\theta} and the fine-tuned model f_{\\theta'} (with parameters \\theta' ):", "source": "marker_v2", "marker_block_id": "/page/11/Text/15"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0122", "section": "A.5. FSD", "page_start": 12, "page_end": 12, "type": "Equation", "text": "FSD(x; f_{\\theta}, f_{\\theta'}) = S(x; f_{\\theta}) - S(x; f_{\\theta'}) (22)", "source": "marker_v2", "marker_block_id": "/page/11/Equation/16"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0123", "section": "A.5. FSD", "page_start": 12, "page_end": 12, "type": "Text", "text": "where S(\\cdot) represents a base scoring function (e.g., Perplexity, Min-k%). A large FSD score indicates the sample is likely a non-member (fine-tuning reduces non-member perplexity significantly), while a small score suggests a member sample (fine-tuning has negligible impact on member perplexity). A validation-set optimized threshold \\varepsilon is used for final classification.", "source": "marker_v2", "marker_block_id": "/page/11/Text/17"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0124", "section": "A.6. Experimental Settings", "page_start": 12, "page_end": 12, "type": "Text", "text": "We use the PEFT library (Mangrulkar et al., 2022) for LoRA-based (Hu et al., 2022) gradient feature extraction without parameter updates. The base model is initialized from pre-trained checkpoints, and for LoRA configuration, we adopt", "source": "marker_v2", "marker_block_id": "/page/11/Text/19"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0125", "section": "A.6. Experimental Settings", "page_start": 13, "page_end": 13, "type": "Text", "text": "default settings with rank r = 16, LoRA scaling factor α = 32, and dropout set to 0 since we only focus on gradients from a single backpropagation step and no parameter updates are required. Target modules include all submodules of attention and FFN, including query, key, value, output, gate, up, and down projections. For different datasets, we select the tokenizer sequence length based on the overall length distribution: 256 for the WikiMIA dataset and 512 for all other datasets. When training the MLP classifier, the dataset is uniformly split into training and validation sets at a ratio of 3:7. The MLP classifier is configured with two hidden layers of dimensions 128 and 64, respectively, and uses the default Adam optimizer with a learning rate of 0.001. An early stopping strategy is implemented to avoid overfitting.", "source": "marker_v2", "marker_block_id": "/page/12/Text/1"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0126", "section": "B. Motivation Experiment Supplementary Details", "page_start": 13, "page_end": 13, "type": "Text", "text": "To verify the parameter update law driven by the training process, we conduct LoRA fine-tuning with 8 epochs on LLaMA-7B using the unseen set of BookMIA dataset, counting LoRA matrix parameter updates per epoch to extract dynamic change curves of target features. Experiments are performed under three learning rates (1e − 5, 3e − 5, 5e − 5). We present the variation trends of the four feature categories across different modules and layers under each learning rate.", "source": "marker_v2", "marker_block_id": "/page/12/Text/3"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0127", "section": "B. Motivation Experiment Supplementary Details", "page_start": 13, "page_end": 13, "type": "Text", "text": "We present the variation trends of the four feature categories across different modules and layers under each learning rate. Across all learning rates, ∆Θ t and S t exhibit clear epoch-wise patterns: ∆Θ t continuously decreases with training epochs, while S t gradually increases. For Et, distinct opposite trends are observed between the ATT and MLP modules—the update positions of the ATT module tend to be centralized, whereas those of the MLP module tend to be marginalized. Despite this divergence, E t values of both modules converge to the same stable range across the three learning rates. In contrast, T10,t shows a different dynamic: under large learning rates, it first increases and then decreases, yet remains stably around 0.27 throughout training. Notably, the inflection point of T10,t decline coincides with the stage when E t stabilizes. This aligns with our core hypothesis: during training, the model identifies core parameters correlated with the input data and performs concentrated updates on them; once this process is completed, the overall parameter update dynamics tend to stabilize. Regarding different hierarchical levels, only E t shows noticeable discrepancies, while all other features follow the same evolutionary laws.", "source": "marker_v2", "marker_block_id": "/page/12/Text/4"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0128", "section": "B. Motivation Experiment Supplementary Details", "page_start": 13, "page_end": 13, "type": "FigureGroup", "text": "Figure 6. Feature Dynamic Changes During LoRA Fine-Tuning (Learning Rate 1e−5). Top row: Features in ATT/MLP modules; Bottom row: Features in low/middle/high layers.", "source": "marker_v2", "marker_block_id": "/page/12/FigureGroup/363"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0129", "section": "B. Motivation Experiment Supplementary Details", "page_start": 14, "page_end": 14, "type": "FigureGroup", "text": "Figure 7. Feature Dynamic Changes During LoRA Fine-Tuning (Learning Rate 3e − 5).", "source": "marker_v2", "marker_block_id": "/page/13/FigureGroup/236"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0130", "section": "B. Motivation Experiment Supplementary Details", "page_start": 14, "page_end": 14, "type": "FigureGroup", "text": "Figure 8. Feature Dynamic Changes During LoRA Fine-Tuning (Learning Rate 5e − 5).", "source": "marker_v2", "marker_block_id": "/page/13/FigureGroup/237"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0131", "section": "C. Ablation Experiments on Sub-features and Sub-modules", "page_start": 15, "page_end": 15, "type": "Text", "text": "To further explore the discriminative power of fine-grained components in our method, we conduct two additional ablation experiments: sub-feature category ablation (8 sub-features) and sub-module ablation (7 sub-modules). All experiments follow the same configuration as the main text (LLaMA-7B model, WikiMIA/ArxivTection datasets), with AUC and TPR@5% FPR as evaluation metrics.", "source": "marker_v2", "marker_block_id": "/page/14/Text/12"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0132", "section": "C.1. Sub-feature Category Ablation Experiment", "page_start": 15, "page_end": 15, "type": "Text", "text": "The four core feature categories are decomposed into 8 sub-features, as follows:", "source": "marker_v2", "marker_block_id": "/page/14/Text/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0133", "section": "C.1. Sub-feature Category Ablation Experiment", "page_start": 15, "page_end": 15, "type": "ListGroup", "text": "Magnitude Distribution Features: Abs Mean, Std Core Contribution Features: 10p Ratio, Sparsity Position Offset Features: Row Ecc, Col Ecc Row-Dimension Consistency Features: Row Mean Max, Row Mean Std", "source": "marker_v2", "marker_block_id": "/page/14/ListGroup/372"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0134", "section": "C.1. Sub-feature Category Ablation Experiment", "page_start": 15, "page_end": 15, "type": "Text", "text": "Ablation is performed by removing one sub-feature at a time (retaining the other 7), and the results are shown in Table 8.", "source": "marker_v2", "marker_block_id": "/page/14/Text/19"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0135", "section": "C.1. Sub-feature Category Ablation Experiment", "page_start": 15, "page_end": 15, "type": "TableGroup", "text": "Table 8. Ablation Experiment Results of Sub-features (AUC Scores). Dataset Sub-feature (Ablation Variant) -Abs Mean -Std -10p Ratio -Sparsity -Row Ecc -Col Ecc -Row Max -Row Std WikiMIA 0.95/0.71 0.95/0.72 0.95/0.70 0.94/0.67 0.95/0.70 0.93/0.62 0.95/0.73 0.95/0.72 0.96/0.84 ArxivTection 0.96/0.82 0.96/0.81 0.96/0.83 0.96/0.82 0.96/0.83 0.95/0.78 0.96/0.83 0.96/0.83 0.97/0.85", "source": "marker_v2", "marker_block_id": "/page/14/TableGroup/370"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0136", "section": "C.1. Sub-feature Category Ablation Experiment", "page_start": 15, "page_end": 15, "type": "Text", "text": "The sub-feature ablation results verify that all sub-features contribute to detection performance, with their combination achieving optimal AUC and TPR scores across both datasets. Among these sub-features, Col Ecc (a Position Offset Feature) is the most critical: its removal leads to the sharpest performance decline (AUC drops to 0.93 on WikiMIA and 0.95 on ArxivTection, with TPR falling to 0.62 and 0.78 respectively). In contrast, removing Abs Mean, Std, 10p Ratio, Row Ecc, Row Max, or Row Std induces only mild performance degradation, with AUC remaining above 0.95 on both datasets, indicating their relatively moderate importance; Sparsity also shows a slight impact on WikiMIA, with its ablation resulting in an AUC of 0.94. Overall, the fine-grained sub-feature design is rational, as each component provides complementary discriminative information for pre-training data detection.", "source": "marker_v2", "marker_block_id": "/page/14/Text/22"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0137", "section": "C.2. Sub-module Ablation Experiment", "page_start": 15, "page_end": 15, "type": "Text", "text": "The ATT and FFN modules are decomposed into 7 sub-modules based on Transformer architecture details:", "source": "marker_v2", "marker_block_id": "/page/14/Text/24"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0138", "section": "C.2. Sub-module Ablation Experiment", "page_start": 15, "page_end": 15, "type": "ListGroup", "text": "ATT-related sub-modules: Q-Proj, K-Proj, V-Proj, Out-Proj FFN-related sub-modules: Gate-Proj, Up-Proj, Down-Proj", "source": "marker_v2", "marker_block_id": "/page/14/ListGroup/373"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0139", "section": "C.2. Sub-module Ablation Experiment", "page_start": 15, "page_end": 15, "type": "Text", "text": "Ablation is performed by removing one sub-module's features at a time, and the results are shown in Table 9.", "source": "marker_v2", "marker_block_id": "/page/14/Text/27"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0140", "section": "C.2. Sub-module Ablation Experiment", "page_start": 15, "page_end": 15, "type": "TableGroup", "text": "Table 9. Ablation Experiment Results of Sub-modules (AUC / TPR@5% FPR Scores). Dataset Sub-module (Ablation Variant) -Q-Proj -K-Proj -V-Proj -Out-Proj -Gate-Proj -Up-Proj -Down-Proj WikiMIA 0.95/0.72 0.95/0.71 0.94/0.69 0.94/0.67 0.95/0.69 0.94/0.65 0.94/0.61 0.96/0.84 ArxivTection 0.96/0.80 0.96/0.82 0.95/0.79 0.96/0.80 0.96/0.82 0.95/0.78 0.96/0.82 0.97/0.85", "source": "marker_v2", "marker_block_id": "/page/14/TableGroup/371"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0141", "section": "C.2. Sub-module Ablation Experiment", "page_start": 15, "page_end": 15, "type": "Text", "text": "The sub-module ablation results demonstrate that all sub-modules provide complementary gradient information, as singlesub-module ablation consistently leads to performance degradation while integrating all sub-modules' features achieves", "source": "marker_v2", "marker_block_id": "/page/14/Text/30"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0142", "section": "C.2. Sub-module Ablation Experiment", "page_start": 16, "page_end": 16, "type": "FigureGroup", "text": "Figure 9. Impact Analysis of Training Set Size on WikiMIA. The abscissa denotes the training-validation set ratio, the ordinate represents the scores of two metrics, yellow indicates the AUROC score, and blue indicates the TPR@5% FPR.", "source": "marker_v2", "marker_block_id": "/page/15/FigureGroup/236"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0143", "section": "C.2. Sub-module Ablation Experiment", "page_start": 16, "page_end": 16, "type": "Text", "text": "the optimal AUC and TPR@5% FPR scores across both datasets. Though the performance differences between individual ablation variants are mild, ATT-related sub-modules show slightly stronger discriminative power than FFN-related ones, with K-Proj performing prominently among ATT sub-modules; in contrast, among FFN sub-modules, Down-Proj and Gate-Proj contribute more to detection performance than Up-Proj, as retaining the former two yields slightly higher AUC and TPR scores. The performance gap between single-sub-module variants and the full model further confirms the necessity of multi-sub-module feature fusion, which enables the capture of comprehensive gradient patterns across the Transformer architecture. It can be seen from this that our method also achieves excellent performance with smaller LoRA adaptation parameters and lower computational complexity.", "source": "marker_v2", "marker_block_id": "/page/15/Text/3"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0144", "section": "C.3. Low-Data Scenarios", "page_start": 16, "page_end": 16, "type": "Text", "text": "To evaluate the data efficiency of our method in scenarios with limited training data, we adjust the training-testing split ratio of the WikiMIA dataset to five settings: 1:9, 2:8, 3:7 and 4:6, while keeping the total sample size fixed. Figure Y shows AUC and TPR@5% FPR scores across different split ratios.", "source": "marker_v2", "marker_block_id": "/page/15/Text/5"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0145", "section": "C.3. Low-Data Scenarios", "page_start": 16, "page_end": 16, "type": "Text", "text": "Figure 9 show our method's performance improves steadily with increasing training set size. Notably, it achieves an AUC of 0.9 even with only 10% of data, accompanied by a TPR@5% FPR of 0.48, confirming that it can also achieve excellent performance with a small amount of data.", "source": "marker_v2", "marker_block_id": "/page/15/Text/6"}

icml26/9346049b-7104-494c-9378-955a2d7393ed/appendix_text_v3.txt

@@ -0,0 +1,140 @@
+[p. 11 | section: A. Details of Baseline | type: Text]
+Shared Notations: We first define the universal notations used across all baseline methods for consistency:
+
+[p. 11 | section: A. Details of Baseline | type: ListGroup]
+x: Input text sample for membership inference detection. {x1, x2, . . . , x N }: Token sequence of input text sample x, where N denotes the total number of tokens in the text. x<t: Prefix token sequence of the t-th token xt, i.e., x<t = {x1, . . . , xt−1}. θ: Trainable parameters of the pre-trained language model. p(· | ·; θ): Conditional probability distribution parameterized by the model parameters θ. k%: Percentage threshold for selecting low-probability outlier tokens (used in Min-k% and Min-k%++).
+
+[p. 11 | section: A.1. PPL | type: Text]
+Perplexity (PPL) is a classic global likelihood-based metric that measures the model's uncertainty in predicting a given text, with lower PPL indicating higher text familiarity (more likely to be a member sample). First, the text is tokenized into a sequence of tokens {x1, x2, . . . , x N }. Then, the log-likelihood of each token is calculated conditional on the preceding tokens, and the final PPL is derived by normalizing the sum of log-likelihoods by the token sequence length and performing an exponential transformation.
+
+[p. 11 | section: A.1. PPL | type: Equation]
+PPL = \exp\left(-\frac{1}{N} \sum_{i=1}^{N} \log p(x_i|x_1, ..., x_{x-1}; \theta)\right) (16)
+
+[p. 11 | section: A.2. Zlib | type: Text]
+Zlib is a compression-based global likelihood-related method that leverages compression entropy to distinguish member and non-member samples, which calibrates the loss using the input's Zlib entropy. For an input text sample x and a pre-trained model M, the Zlib score is defined as the ratio of the loss related to the text and model to the Zlib compression entropy of the input text:
+
+[p. 11 | section: A.2. Zlib | type: Equation]
+Zlib Score = \frac{L(x, M)}{\text{zlib}(x)} (17)
+
+[p. 11 | section: A.2. Zlib | type: Text]
+where L(x, M) denotes the loss value associated with the input text x under the model M and zlib(x) represents the Zlib compression entropy of the input text x, which is derived from the length of the text after Zlib compression.
+
+[p. 11 | section: A.3. Min-k% | type: Text]
+Min-k% is a local likelihood-based method that mitigates global word frequency interference by focusing on low-probability outlier tokens. For an input text token sequence x = {x1, x2, . . . , x N } (where N denotes the total number of tokens), it first calculates the conditional log-likelihood of each token x i given its preceding context:
+
+[p. 11 | section: A.3. Min-k% | type: Equation]
+\log p(x_i \mid x_1, x_2, \dots, x_{i-1}; \theta)
+
+[p. 11 | section: A.3. Min-k% | type: Text]
+Subsequently, it sorts all token conditional probabilities in ascending order, selects the bottom k% tokens (i.e., the k% tokens with the smallest conditional probabilities) to form the low-probability set Tmin(k%) = Min-K%(x). The final Min-k% score is defined as the average conditional log-likelihood of tokens in Tmin(k%):
+
+[p. 11 | section: A.3. Min-k% | type: Equation]
+Min-k% Score(x) = \frac{1}{|T_{\min(k\%)}|} \sum_{x_i \in T_{\min(k\%)}} \log p(x_i \mid x_1, \dots, x_{i-1}; \theta) (18)
+
+[p. 11 | section: A.3. Min-k% | type: Text]
+where |Tmin(k%)| = ⌊k% × N⌋ denotes the cardinality of the low-probability token set (rounded down to the nearest integer). During detection, a threshold is set on Min-k% Score(x): text with a score below the threshold is classified as a member sample (since member samples tend to contain more low-probability outlier tokens), and vice versa.
+
+[p. 12 | section: A.4. Min-k%++ | type: Text]
+Min-k%++ is an optimized variant of Min-k% that enhances detection robustness by integrating vocabulary-level probability statistics, addressing the text-length dependency and short-text fluctuation issues of the original method. For an input text token sequence x = \{x_1, x_2, \dots, x_N\} , it first computes the normalized conditional log-likelihood for each token x_t (given prefix x_{< t} = \{x_1, \dots, x_{t-1}\} ) by normalizing with the vocabulary-wide log-probability statistics of the prefix x_{< t} .
+
+[p. 12 | section: Core Token-Level Score Calculation | type: Text]
+For each token x_t , the token-level Min-k%++ score is defined as:
+
+[p. 12 | section: Core Token-Level Score Calculation | type: Equation]
+Min-k\% + +_{token}(x_{< t}, x_t) = \frac{\log p(x_t \mid x_{< t}; \theta) - \mu_{x_{< t}}}{\sigma_{x_{< t}}} (19)
+
+[p. 12 | section: Core Token-Level Score Calculation | type: Text]
+where \mu_{x_{< t}} = \mathbb{E}_{z \sim p(\cdot \mid x_{< t}; \theta)} [\log p(z \mid x_{< t}; \theta)] : Expectation of the next-token log-likelihood over the model's vocabulary, given prefix x_{< t} ; \sigma_{x_{< t}} = \sqrt{\mathbb{E}_{z \sim p(\cdot \mid x_{< t}; \theta)} \left[ (\log p(z \mid x_{< t}; \theta) - \mu_{x_{< t}})^2 \right]} : Standard deviation of the next-token log-likelihood over the vocabulary, given prefix x_{< t} .
+
+[p. 12 | section: Core Token-Level Score Calculation | type: Text]
+Both \mu_{x_{< t}} and \sigma_{x_{< t}} can be computed analytically using the model's output logits (since p(\cdot \mid x_{< t}; \theta) follows a categorical distribution), requiring no additional computational overhead beyond standard LLM inference.
+
+[p. 12 | section: Final Sequence-Level Score Calculation | type: Text]
+Similar to Min-k%, Min-k%++ selects the bottom k% tokens with the smallest Min-k%++<sub>token</sub> scores to form the low-probability set T_{\min(k\%)}^+ . The final sequence-level score is the average of the token-level scores in this set:
+
+[p. 12 | section: Final Sequence-Level Score Calculation | type: Equation]
+Min-k\% ++ Score(x) = \frac{1}{|T_{\min(k\%)}^+|} \sum_{(x_{< t}, x_t) \in T_{\min(k\%)}^+} Min-k\% ++_{token}(x_{< t}, x_t) (20)
+
+[p. 12 | section: Final Sequence-Level Score Calculation | type: Text]
+where |T_{\min(k\%)}^+| = \lfloor k\% \times N \rfloor denotes the cardinality of the low-probability token set. During detection, a threshold is applied: text with a lower Min-k%++ score is more likely to be a member sample, as the normalized score better distinguishes low-probability outlier tokens of member samples from non-member ones.
+
+[p. 12 | section: A.5. FSD | type: Text]
+Fine-tuned Score Deviation (FSD) is a fine-tuning enhanced method that leverages score discrepancies between pre-trained and fine-tuned models for member sample detection. Its core workflow includes two key steps: first, constructing a domain-matched non-member fine-tuning dataset (using post-model-release unseen data), then performing self-supervised next-token prediction fine-tuning on the pre-trained model. Finally, it calculates the score difference between the pre-trained and fine-tuned models to distinguish member and non-member samples. The self-supervised fine-tuning loss is defined as:
+
+[p. 12 | section: A.5. FSD | type: Equation]
+\mathcal{L}_{\text{fine-tuning}}(x) = -\frac{1}{n} \sum_{i=1}^{n} \log f_{\theta}(x_i \mid x_1, \dots, x_{i-1}) (21)
+
+[p. 12 | section: A.5. FSD | type: Text]
+The final FSD score is the deviation between the sample scores obtained from the pre-trained model f_{\theta} and the fine-tuned model f_{\theta'} (with parameters \theta' ):
+
+[p. 12 | section: A.5. FSD | type: Equation]
+FSD(x; f_{\theta}, f_{\theta'}) = S(x; f_{\theta}) - S(x; f_{\theta'}) (22)
+
+[p. 12 | section: A.5. FSD | type: Text]
+where S(\cdot) represents a base scoring function (e.g., Perplexity, Min-k%). A large FSD score indicates the sample is likely a non-member (fine-tuning reduces non-member perplexity significantly), while a small score suggests a member sample (fine-tuning has negligible impact on member perplexity). A validation-set optimized threshold \varepsilon is used for final classification.
+
+[p. 12 | section: A.6. Experimental Settings | type: Text]
+We use the PEFT library (Mangrulkar et al., 2022) for LoRA-based (Hu et al., 2022) gradient feature extraction without parameter updates. The base model is initialized from pre-trained checkpoints, and for LoRA configuration, we adopt
+
+[p. 13 | section: A.6. Experimental Settings | type: Text]
+default settings with rank r = 16, LoRA scaling factor α = 32, and dropout set to 0 since we only focus on gradients from a single backpropagation step and no parameter updates are required. Target modules include all submodules of attention and FFN, including query, key, value, output, gate, up, and down projections. For different datasets, we select the tokenizer sequence length based on the overall length distribution: 256 for the WikiMIA dataset and 512 for all other datasets. When training the MLP classifier, the dataset is uniformly split into training and validation sets at a ratio of 3:7. The MLP classifier is configured with two hidden layers of dimensions 128 and 64, respectively, and uses the default Adam optimizer with a learning rate of 0.001. An early stopping strategy is implemented to avoid overfitting.
+
+[p. 13 | section: B. Motivation Experiment Supplementary Details | type: Text]
+To verify the parameter update law driven by the training process, we conduct LoRA fine-tuning with 8 epochs on LLaMA-7B using the unseen set of BookMIA dataset, counting LoRA matrix parameter updates per epoch to extract dynamic change curves of target features. Experiments are performed under three learning rates (1e − 5, 3e − 5, 5e − 5). We present the variation trends of the four feature categories across different modules and layers under each learning rate.
+
+[p. 13 | section: B. Motivation Experiment Supplementary Details | type: Text]
+We present the variation trends of the four feature categories across different modules and layers under each learning rate. Across all learning rates, ∆Θ t and S t exhibit clear epoch-wise patterns: ∆Θ t continuously decreases with training epochs, while S t gradually increases. For Et, distinct opposite trends are observed between the ATT and MLP modules—the update positions of the ATT module tend to be centralized, whereas those of the MLP module tend to be marginalized. Despite this divergence, E t values of both modules converge to the same stable range across the three learning rates. In contrast, T10,t shows a different dynamic: under large learning rates, it first increases and then decreases, yet remains stably around 0.27 throughout training. Notably, the inflection point of T10,t decline coincides with the stage when E t stabilizes. This aligns with our core hypothesis: during training, the model identifies core parameters correlated with the input data and performs concentrated updates on them; once this process is completed, the overall parameter update dynamics tend to stabilize. Regarding different hierarchical levels, only E t shows noticeable discrepancies, while all other features follow the same evolutionary laws.
+
+[p. 13 | section: B. Motivation Experiment Supplementary Details | type: FigureGroup]
+Figure 6. Feature Dynamic Changes During LoRA Fine-Tuning (Learning Rate 1e−5). Top row: Features in ATT/MLP modules; Bottom row: Features in low/middle/high layers.
+
+[p. 14 | section: B. Motivation Experiment Supplementary Details | type: FigureGroup]
+Figure 7. Feature Dynamic Changes During LoRA Fine-Tuning (Learning Rate 3e − 5).
+
+[p. 14 | section: B. Motivation Experiment Supplementary Details | type: FigureGroup]
+Figure 8. Feature Dynamic Changes During LoRA Fine-Tuning (Learning Rate 5e − 5).
+
+[p. 15 | section: C. Ablation Experiments on Sub-features and Sub-modules | type: Text]
+To further explore the discriminative power of fine-grained components in our method, we conduct two additional ablation experiments: sub-feature category ablation (8 sub-features) and sub-module ablation (7 sub-modules). All experiments follow the same configuration as the main text (LLaMA-7B model, WikiMIA/ArxivTection datasets), with AUC and TPR@5% FPR as evaluation metrics.
+
+[p. 15 | section: C.1. Sub-feature Category Ablation Experiment | type: Text]
+The four core feature categories are decomposed into 8 sub-features, as follows:
+
+[p. 15 | section: C.1. Sub-feature Category Ablation Experiment | type: ListGroup]
+Magnitude Distribution Features: Abs Mean, Std Core Contribution Features: 10p Ratio, Sparsity Position Offset Features: Row Ecc, Col Ecc Row-Dimension Consistency Features: Row Mean Max, Row Mean Std
+
+[p. 15 | section: C.1. Sub-feature Category Ablation Experiment | type: Text]
+Ablation is performed by removing one sub-feature at a time (retaining the other 7), and the results are shown in Table 8.
+
+[p. 15 | section: C.1. Sub-feature Category Ablation Experiment | type: TableGroup]
+Table 8. Ablation Experiment Results of Sub-features (AUC Scores). Dataset Sub-feature (Ablation Variant) -Abs Mean -Std -10p Ratio -Sparsity -Row Ecc -Col Ecc -Row Max -Row Std WikiMIA 0.95/0.71 0.95/0.72 0.95/0.70 0.94/0.67 0.95/0.70 0.93/0.62 0.95/0.73 0.95/0.72 0.96/0.84 ArxivTection 0.96/0.82 0.96/0.81 0.96/0.83 0.96/0.82 0.96/0.83 0.95/0.78 0.96/0.83 0.96/0.83 0.97/0.85
+
+[p. 15 | section: C.1. Sub-feature Category Ablation Experiment | type: Text]
+The sub-feature ablation results verify that all sub-features contribute to detection performance, with their combination achieving optimal AUC and TPR scores across both datasets. Among these sub-features, Col Ecc (a Position Offset Feature) is the most critical: its removal leads to the sharpest performance decline (AUC drops to 0.93 on WikiMIA and 0.95 on ArxivTection, with TPR falling to 0.62 and 0.78 respectively). In contrast, removing Abs Mean, Std, 10p Ratio, Row Ecc, Row Max, or Row Std induces only mild performance degradation, with AUC remaining above 0.95 on both datasets, indicating their relatively moderate importance; Sparsity also shows a slight impact on WikiMIA, with its ablation resulting in an AUC of 0.94. Overall, the fine-grained sub-feature design is rational, as each component provides complementary discriminative information for pre-training data detection.
+
+[p. 15 | section: C.2. Sub-module Ablation Experiment | type: Text]
+The ATT and FFN modules are decomposed into 7 sub-modules based on Transformer architecture details:
+
+[p. 15 | section: C.2. Sub-module Ablation Experiment | type: ListGroup]
+ATT-related sub-modules: Q-Proj, K-Proj, V-Proj, Out-Proj FFN-related sub-modules: Gate-Proj, Up-Proj, Down-Proj
+
+[p. 15 | section: C.2. Sub-module Ablation Experiment | type: Text]
+Ablation is performed by removing one sub-module's features at a time, and the results are shown in Table 9.
+
+[p. 15 | section: C.2. Sub-module Ablation Experiment | type: TableGroup]
+Table 9. Ablation Experiment Results of Sub-modules (AUC / TPR@5% FPR Scores). Dataset Sub-module (Ablation Variant) -Q-Proj -K-Proj -V-Proj -Out-Proj -Gate-Proj -Up-Proj -Down-Proj WikiMIA 0.95/0.72 0.95/0.71 0.94/0.69 0.94/0.67 0.95/0.69 0.94/0.65 0.94/0.61 0.96/0.84 ArxivTection 0.96/0.80 0.96/0.82 0.95/0.79 0.96/0.80 0.96/0.82 0.95/0.78 0.96/0.82 0.97/0.85
+
+[p. 15 | section: C.2. Sub-module Ablation Experiment | type: Text]
+The sub-module ablation results demonstrate that all sub-modules provide complementary gradient information, as singlesub-module ablation consistently leads to performance degradation while integrating all sub-modules' features achieves
+
+[p. 16 | section: C.2. Sub-module Ablation Experiment | type: FigureGroup]
+Figure 9. Impact Analysis of Training Set Size on WikiMIA. The abscissa denotes the training-validation set ratio, the ordinate represents the scores of two metrics, yellow indicates the AUROC score, and blue indicates the TPR@5% FPR.
+
+[p. 16 | section: C.2. Sub-module Ablation Experiment | type: Text]
+the optimal AUC and TPR@5% FPR scores across both datasets. Though the performance differences between individual ablation variants are mild, ATT-related sub-modules show slightly stronger discriminative power than FFN-related ones, with K-Proj performing prominently among ATT sub-modules; in contrast, among FFN sub-modules, Down-Proj and Gate-Proj contribute more to detection performance than Up-Proj, as retaining the former two yields slightly higher AUC and TPR scores. The performance gap between single-sub-module variants and the full model further confirms the necessity of multi-sub-module feature fusion, which enables the capture of comprehensive gradient patterns across the Transformer architecture. It can be seen from this that our method also achieves excellent performance with smaller LoRA adaptation parameters and lower computational complexity.
+
+[p. 16 | section: C.3. Low-Data Scenarios | type: Text]
+To evaluate the data efficiency of our method in scenarios with limited training data, we adjust the training-testing split ratio of the WikiMIA dataset to five settings: 1:9, 2:8, 3:7 and 4:6, while keeping the total sample size fixed. Figure Y shows AUC and TPR@5% FPR scores across different split ratios.
+
+[p. 16 | section: C.3. Low-Data Scenarios | type: Text]
+Figure 9 show our method's performance improves steadily with increasing training set size. Notably, it achieves an AUC of 0.9 even with only 10% of data, accompanied by a TPR@5% FPR of 0.48, confirming that it can also achieve excellent performance with a small amount of data.

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+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0000", "section": "Abstract", "page_start": 1, "page_end": 1, "type": "Text", "text": "Pre-training data detection for LLMs is essential for addressing copyright concerns and mitigating benchmark contamination. Existing methods mainly focus on the likelihood-based statistical features or heuristic signals before and after finetuning, but the former are susceptible to word frequency bias in corpora, and the latter strongly depend on the similarity of fine-tuning data. From an optimization perspective, we observe that during training, samples transition from unfamiliar to familiar in a manner reflected by systematic differences in gradient behavior. Familiar samples exhibit smaller update magnitudes, distinct update locations in model components, and more sharply activated neurons. Based on this insight, we propose GDS, a method that identifies pre-training data by probing Gradient Deviation Scores of target samples. Specifically, we first represent each sample using gradient profiles that capture the magnitude, location, and concentration of parameter updates across FFN and Attention modules, revealing consistent distinctions between member and non-member data. These features are then fed into a lightweight classifier to perform binary membership inference. Experiments on five public datasets show that GDS achieves state-ofthe-art performance with significantly improved cross-dataset transferability over strong baselines. Further interpretability analyse show gradient feature distribution differences, enabling practical and scalable pre-training data detection.", "source": "marker_v2", "marker_block_id": "/page/0/Text/4"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0001", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "Large language models (LLMs) performance scales with the size and quality of pre-training data (Kaplan et al., 2020) .", "source": "marker_v2", "marker_block_id": "/page/0/Text/6"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0002", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "FigureGroup", "text": "Figure 1. Heat maps of gradient matrices from the unfamiliar stage (epochs 0–1, panels a, c) to the familiar stage (epochs 6–7, panels b, d). Panels a and b display the update magnitude of the FFN module in layer 30, while panels c and d illustrate the update positions, with white for sparse and blue for core updates.", "source": "marker_v2", "marker_block_id": "/page/0/FigureGroup/453"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0003", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "As pre-training corpora expand to trillions of tokens and become increasingly proprietary and non-transparent, they raise significant concerns, such as unauthorized copyright, biased or harmful content, and contamination of evaluation benchmarks (Balloccu et al., 2024; Grynbaum & Mac, 2023) . These challenges motivate a specialized task of membership inference attacks, named pre-training data detection: determining whether a given text sample was included in a model's pre-training corpus (Carlini et al., 2021) .", "source": "marker_v2", "marker_block_id": "/page/0/Text/11"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0004", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "Recent studies (Carlini et al., 2021; Li; Shi et al., 2024; Zhang et al., 2025) primarily use likelihood-based statistical features to detect pre-training samples. For example, the Min-K method (Shi et al., 2024; Zhang et al., 2025) examines the k% of tokens with the lowest predicted probabilities, assuming non-member texts contain more low-likelihood tokens. However, these approaches are susceptible to word frequency bias in pre-training corpora, specifically for rare words or short texts scenarios. To improve detection accuracy, other researchers (Zhang et al.; Choi et al.) propose to analyze heuristic signals before and after fine-tuning, leveraging the fact that fine-tuning impacts member and non-member samples differently. For example, KDS (Choi et al.) shows that non-member datasets exhibit much larger embedding changes, while FSD (Zhang et al.) finds that their loss reductions are also significantly greater. Neverthe-", "source": "marker_v2", "marker_block_id": "/page/0/Text/12"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0005", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "less, these methods rely on the strong assumption that finetuning data closely match the target samples' distribution, requiring additional training on similar non-member data and thereby limiting cross-dataset generalization. Therefore, how to achieve highly generalizable pre-training data detection remains an open problem.", "source": "marker_v2", "marker_block_id": "/page/1/Text/1"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0006", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "Pretraining can be viewed as a gradual shift from unfamiliarity to familiarity with data. Optimization theory (Ruder, 2016; Frankle et al.; Wang et al., 2024) suggests that training drives parameters toward data-specific structure, reflected in consistent update patterns across magnitude, location, and concentration. As shown in Figure 1 and Section 3, we observe the following trends:", "source": "marker_v2", "marker_block_id": "/page/1/Text/2"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0007", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "ListGroup", "text": "1. Decay of update magnitude. Figure 1( a,b) shows that parameter updates are strongly attenuated as data grows familiar, consistent with loss-convergence theory (Bottou, 2010; Ruder, 2016) . 2. Gradually stabilizing of update locations. Figure 1( c,d) shows that parameter updates evolve from broad activation regions to a stable core set of neurons, consistent with the sparse activation behavior of LLMs (Liu et al., 2024) . 3. Increasing update sparsity. Figure 1( a,b) and Figures 2( b,c) show that during training, an increasing fraction of updates concentrates in the top 10% of neurons, consistent with Hessian spectrum reshaping during loss convergence (Gur-Ari et al., 2018) . Familiar data yields sparse, concentrated updates, whereas unfamiliar data leads to more distributed updates.", "source": "marker_v2", "marker_block_id": "/page/1/ListGroup/529"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0008", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "These observations reflect the evolutionary dynamics of neural network training, highlighting phase differences in parameter updates induced by identical samples. Together, they offer both theoretical motivation and empirical support for our detection method based on gradient deviation scores.", "source": "marker_v2", "marker_block_id": "/page/1/Text/6"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0009", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "Based on this insight, we propose GDS, a novel pretraining data detection method that infers pre-training data by probing Gradient Deviation Scores of target samples without fine-tuning. GDS exploits gradient differences between member and non-member samples to train a lightweight classifier with strong generalization. Specifically, within the LoRA framework, we collect per-sample gradients across layers during backpropagation, encoding them as eightdimensional features that capture the magnitude, location, and concentration of updates in attention and FFN modules. Compared to non-members, member samples show smaller matrix-level and row-wise update magnitudes, lower FFN but higher attention eccentricity, greater variability in matrixlevel and row-wise updates, a higher share of top gradients, and fewer sparse neurons. Then, we extract discriminative", "source": "marker_v2", "marker_block_id": "/page/1/Text/7"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0010", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "statistics from the signals to build fixed-dimensional feature vectors, which are fed to a lightweight MLP for binary membership classification.", "source": "marker_v2", "marker_block_id": "/page/1/Text/8"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0011", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "Extensive experiments on five benchmark datasets show that GDS is effective and generalizable, improving AUC by 6.5% and achieving a 67.3% TPR@5%FPR, substantially outperforming strong baselines. Further interpretability analyses reveal distributional differences in gradient features between member and non-member samples, offering intuitive evidence of training data imprints on the model and validating our methodology. 1 Our contributions are as follows:", "source": "marker_v2", "marker_block_id": "/page/1/Text/9"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0012", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "ListGroup", "text": "From a training optimization perspective, we analyze how LLMs evolve from unfamiliarity to familiarity with data and propose using stage-wise parameter update dynamics to identify pretraining data, offering a novel direction to solve this task. We propose gradient deviation features capturing magnitude, location, and concentration, and introduce a gradient deviation score–based method for pretraining data detection without fine-tuning. Extensive experiments across diverse datasets and backbone models validate the effectiveness and generalization of GDS, while interpretability analyses reveal clear gradient differences between member and nonmember samples, supporting its validity.", "source": "marker_v2", "marker_block_id": "/page/1/ListGroup/530"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0013", "section": "2. Related Work", "page_start": 2, "page_end": 2, "type": "Text", "text": "Likelihood-Based Scoring Methods. Early works distinguish member and non-member samples by capturing static statistical metrics in token-level likelihood distributions. Global-likelihood–based methods, such as PPL (Li) , Zlib (Carlini et al., 2021) , and Lowercase (Carlini et al., 2021) , perform discrimination by exploiting global probability features, compression entropy, and case-conversion ratios. However, global likelihood is highly sensitive to wordfrequency effects, leading to unstable performance. Mink% (Shi et al., 2024) and Min-k%++ (Zhang et al., 2025) mitigate global dependence by focusing on low-probability outlier tokens or target–candidate probability comparisons, with k and text length jointly determining the analyzed token subset. However, the fixed choice of k lacks adaptivity, causing severe score fluctuations in short texts with lowfrequency words. Although PC-PDD (Zhang et al., 2024) approximates the word-frequency distribution of pretraining corpora using public datasets, these references lack fidelity due to limited domain coverage.", "source": "marker_v2", "marker_block_id": "/page/1/Text/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0014", "section": "2. Related Work", "page_start": 2, "page_end": 2, "type": "Text", "text": "Fine-tuning Enhanced Methods. To address the instability of static statistical indicators, recent studies (Zhang et al.;", "source": "marker_v2", "marker_block_id": "/page/1/Text/15"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0015", "section": "2. Related Work", "page_start": 2, "page_end": 2, "type": "Footnote", "text": "1 Code in", "source": "marker_v2", "marker_block_id": "/page/1/Footnote/16"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0016", "section": "2. Related Work", "page_start": 3, "page_end": 3, "type": "FigureGroup", "text": "Figure 2. Dynamic curves of four parameter update characteristics defined in the Motivation section. i → j denotes the epoch interval. Ordinate shows values of predefined characteristics, with orange and blue representing Attention and FFN modules.", "source": "marker_v2", "marker_block_id": "/page/2/FigureGroup/764"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0017", "section": "2. Related Work", "page_start": 3, "page_end": 3, "type": "Text", "text": "Choi et al.) adopt lightweight fine-tuning to actively amplify asymmetric differences between member and non-member samples. KDS (Choi et al.) evaluates dataset contamination by comparing kernel similarity matrices of embeddings before and after fine-tuning, assuming non-member datasets undergo larger embedding changes than member datasets. However, it only estimates dataset-level contamination and cannot reliably detect contamination at the sample-level. Another representative method FSD (Zhang et al.) detects membership by comparing loss before and after fine-tuning, assuming non-member samples experience a larger loss reduction than member samples. Nevertheless, these methods assume that fine-tuning data closely matches the target distribution, requiring additional tuning on similar non-member data, which limits cross-dataset generalization.", "source": "marker_v2", "marker_block_id": "/page/2/Text/3"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0018", "section": "3. Motivation", "page_start": 3, "page_end": 3, "type": "Text", "text": "Inspired by optimization theory (Ruder, 2016; Bottou, 2010) , we examine how LLMs transition from unfamiliarity to familiarity with data, and how this cognitive shift relates to the dynamic evolution of model parameters during training. To evaluate it, we fine-tune LLaMA-7B with LoRA on the unseen split of BookMIA dataset and track LoRA parameter updates over 7 epochs. Stage-wise analysis in Figure 2 reveals the dynamic evolution of gradient features.", "source": "marker_v2", "marker_block_id": "/page/2/Text/5"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0019", "section": "3.1. Decay of Update Magnitude", "page_start": 3, "page_end": 3, "type": "Text", "text": "Model training aims to minimize the loss function L(θ), with update magnitude determined by the gradient norm ∥∇L(θ)∥. According to optimization convergence theory (Ruder, 2016) , as the parameters θ t approach the optimum θ ∗ , the gradient norm of the loss function vanishes, i.e.,limθ→ θ ∗ ∥∇L(θt)∥ = 0. This causes the parameter update magnitude to decrease synchronously. Therefore, we use ∆θ t as the core indicator of the average update magnitude across all trainable parameters at iteration t:", "source": "marker_v2", "marker_block_id": "/page/2/Text/7"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0020", "section": "3.1. Decay of Update Magnitude", "page_start": 3, "page_end": 3, "type": "Equation", "text": "\\Delta \\theta_{t} = \\frac{1}{N} \\sum_{i=1}^{N} |\\theta_{t,i} - \\theta_{t-1,i}|, \\qquad (1)", "source": "marker_v2", "marker_block_id": "/page/2/Equation/8"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0021", "section": "3.1. Decay of Update Magnitude", "page_start": 3, "page_end": 3, "type": "Text", "text": "where N denotes the total number of trainable parameters.", "source": "marker_v2", "marker_block_id": "/page/2/Text/9"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0022", "section": "3.1. Decay of Update Magnitude", "page_start": 3, "page_end": 3, "type": "Text", "text": "As training progresses, both the loss L(θt) and gradient norm ∥∇L(θt)∥ decrease, reducing the update magnitude ∆θ t and slowing its decay as parameters converge to the optimum θ ∗ . Eventually, L(θt) stabilizes near its minimum, parameter updates ∆θ t become negligible. As shown in Figure 2a, the mean update magnitude decreases monotonically with training, with the largest changes occurring in the first two epochs, consistent with loss convergence.", "source": "marker_v2", "marker_block_id": "/page/2/Text/10"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0023", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 3, "page_end": 3, "type": "Text", "text": "Existing studies (Liu et al., 2024; Tang et al., 2025) have shown that neural activations occur at different locations when processing member samples and non-member samples. Inspired by this, we adopt the parameter update eccentricity as the core indicator, which quantifies the deviation of the top-10% parameter update positions from the global parameter centroid. We first define the global centroid as:", "source": "marker_v2", "marker_block_id": "/page/2/Text/12"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0024", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 3, "page_end": 3, "type": "Equation", "text": "\\theta_c = \\frac{1}{N} \\sum_{i=1}^{N} \\theta_i, \\tag{2}", "source": "marker_v2", "marker_block_id": "/page/2/Equation/13"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0025", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 3, "page_end": 3, "type": "Text", "text": "where θ i is the coordinate of the i-th parameter.", "source": "marker_v2", "marker_block_id": "/page/2/Text/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0026", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 3, "page_end": 3, "type": "Text", "text": "The update eccentricity at iteration t is then defined as:", "source": "marker_v2", "marker_block_id": "/page/2/Text/15"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0027", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 3, "page_end": 3, "type": "Equation", "text": "E_{t} = \\frac{1}{\\operatorname{card}(U_{10,t})} \\sum_{\\theta_{i} \\in U_{10,t}} \\|\\theta_{i} - \\theta_{c}\\|_{2}, (3)", "source": "marker_v2", "marker_block_id": "/page/2/Equation/16"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0028", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 3, "page_end": 3, "type": "Text", "text": "where card(·) denotes the number of elements in a set, U10,t = {∥∆θt,i∥ 1 ∈ Top10%(∥∆θt∥1)}, ∥ · ∥ 1 denotes the ℓ 1 norm and ∥ · ∥ 2 denotes the ℓ 2 norm.", "source": "marker_v2", "marker_block_id": "/page/2/Text/17"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0029", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 3, "page_end": 3, "type": "Text", "text": "In the initial training stage, activation patterns are unstable, leading to scattered U10,t and thus random large values of Et. As training proceeds, the model identifies core parameters related to data features: θ t stabilizes to the optimal subset θ ∗ , and U10,t converges to the core parameter region, resulting in E t gradually stabilizing at a low level. Figure 2d shows that the eccentricity of parameter update evolves to a relatively stable value, consistent with the evolution of the", "source": "marker_v2", "marker_block_id": "/page/2/Text/18"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0030", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 4, "page_end": 4, "type": "FigureGroup", "text": "Figure 3. Overview of Gradient Deviation Scores method.", "source": "marker_v2", "marker_block_id": "/page/3/FigureGroup/643"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0031", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 4, "page_end": 4, "type": "Text", "text": "neuron activation pattern, suggesting that training identifies the core parameters and stabilizes updates around them.", "source": "marker_v2", "marker_block_id": "/page/3/Text/4"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0032", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Text", "text": "The Hessian spectrum (Gur-Ari et al., 2018; Frankle et al.) is a core metric characterizing the loss function's curvature, directly determining the direction and efficiency of parameter updates. For the loss function L(θ), its Hessian matrix H(θ) = ∇2L(θ) describes the local curvature of the loss landscape, with eigenvalue decomposition:", "source": "marker_v2", "marker_block_id": "/page/3/Text/6"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0033", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Equation", "text": "\\mathcal{H}(\\theta) = U\\Lambda U^T,\\tag{4}", "source": "marker_v2", "marker_block_id": "/page/3/Equation/7"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0034", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Text", "text": "where U is the orthogonal eigenvector matrix (principal curvature directions), Λ = diag(λ1, . . . , λd) is the diagonal eigenvalue matrix (curvature magnitudes). During training, the Hessian spectrum changes from an almost uniform λ i ≈ c in the early stage to a late-stage structure with a few large eigenvalues and most near zero.", "source": "marker_v2", "marker_block_id": "/page/3/Text/8"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0035", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Text", "text": "This reshaping leads to concentrated updates, focusing on directions with large eigenvalues while leaving most others nearly unchanged. Consequently, update energy is confined to a small subset of parameters, motivating the selection of two joint indicators. S t measures the fraction of parameters with negligible updates (absolute value < 10 − 6 ) at iteration t, while T10,t measures the fraction of total update magnitude contributed by the top 10% largest updates.", "source": "marker_v2", "marker_block_id": "/page/3/Text/9"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0036", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Equation", "text": "S_t = \\frac{\\operatorname{card}\\left(i \\mid |\\Delta \\theta_{t,i}| < 10^{-6}\\right)}{N},\\tag{5}", "source": "marker_v2", "marker_block_id": "/page/3/Equation/10"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0037", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Equation", "text": "T_{10,t} = \\frac{\\sum_{|\\Delta\\theta_{t,i}| \\in U_{10,t}} |\\Delta\\theta_{t,i}|}{||\\Delta\\theta_t||_1}. (6)", "source": "marker_v2", "marker_block_id": "/page/3/Equation/11"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0038", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Text", "text": "As training progresses, parameter updates increasingly concentrate along core directions, with most parameters receiving negligible changes. Consequently, S t gradually", "source": "marker_v2", "marker_block_id": "/page/3/Text/12"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0039", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Text", "text": "increases, while T10,t remains relatively large and stable(0.26–0.27), indicating that update energy is consistently dominated by a small subset of parameters. Figures 2b and 2c confirm this growing sparsity and stable Top 10% contribution, reflecting update energy aggregation driven by Hessian spectrum reshaping. Further details on the variation trends of the three metrics are provided in the appendix B.", "source": "marker_v2", "marker_block_id": "/page/3/Text/13"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0040", "section": "4.1. Task Definition", "page_start": 4, "page_end": 4, "type": "Text", "text": "Given a target text x and a target LLM f θ pre-trained on a corpus D, the goal of pre-training data detection task is to construct a detector h(x, fθ)to determine whether x belongs to D. This task can be formalized as a binary classification problem: h(x, fθ) → {0, 1} where \"1\" indicates x ∈ D as member and \"0\" indicates x /∈ D as non-member.", "source": "marker_v2", "marker_block_id": "/page/3/Text/16"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0041", "section": "4.1. Task Definition", "page_start": 4, "page_end": 4, "type": "Text", "text": "As illustrated in Figure 3, GDS comprises three stages: gradient matrix acquisition, feature vector extraction and light Multilayer Perceptron(MLP) training. For each training sample, we perform inference and backpropagation to obtain LoRA gradients across l layers and m sub-modules, yielding l × m gradient matrices G. From these matrices, we extract eight-dimensional features to form a gradient feature vector V l×m×8 , which is used to train a lightweight MLP classifier for binary membership prediction. During inference, the same feature extraction process is applied to a target sample x ∗ , and the resulting feature vector is fed into the trained MLP to produce the final classification result.", "source": "marker_v2", "marker_block_id": "/page/3/Text/17"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0042", "section": "4.2. Gradient Matrix Acquisition", "page_start": 4, "page_end": 4, "type": "Text", "text": "Given the target model f θ and training sample x, we first initialize f θ with LoRA, yielding l × m LoRA matrices L. We then feed a single sample x into f θ for forward", "source": "marker_v2", "marker_block_id": "/page/3/Text/19"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0043", "section": "4.2. Gradient Matrix Acquisition", "page_start": 5, "page_end": 5, "type": "Text", "text": "inference and backpropagation, obtaining LoRA gradient matrices \\mathbb{G} = \\nabla_{\\mathbb{L}} \\mathcal{L}_{\\text{CLM}}(f_{\\theta}(x)) , where \\mathcal{L}_{\\text{CLM}} denotes the causal language modeling loss of the pre-trained LLM. Since the LoRA_B matrices are fully initialized to zero, a single round of gradient propagation leads to zero gradients for the LoRA_A matrices. Thus, we only collect the gradient matrices of LoRA_B for subsequent processing.", "source": "marker_v2", "marker_block_id": "/page/4/Text/2"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0044", "section": "4.3. Feature Vector Extraction", "page_start": 5, "page_end": 5, "type": "Text", "text": "Given the gradient matrices \\mathbb{G} , we extract features based on the three parameter update trends introduced in Section 3.", "source": "marker_v2", "marker_block_id": "/page/4/Text/4"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0045", "section": "4.3.1. MAGNITUDE", "page_start": 5, "page_end": 5, "type": "Text", "text": "We propose two magnitude indicators to measure the overall scale of gradient updates in the LoRA parameter space.", "source": "marker_v2", "marker_block_id": "/page/4/Text/6"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0046", "section": "4.3.1. MAGNITUDE", "page_start": 5, "page_end": 5, "type": "Text", "text": "(1) Absolute Mean : The mean of the absolute values of all elements in the gradient matrix, which characterizes the overall parameter update strength:", "source": "marker_v2", "marker_block_id": "/page/4/Text/7"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0047", "section": "4.3.1. MAGNITUDE", "page_start": 5, "page_end": 5, "type": "Equation", "text": "Abs\\_Mean = \\frac{1}{r \\cdot h} \\sum_{i=1}^{r} \\sum_{j=1}^{h} |\\mathbb{G}_{i,j}|, (7)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/8"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0048", "section": "4.3.1. MAGNITUDE", "page_start": 5, "page_end": 5, "type": "Text", "text": "where \\mathbb{G}_{i,j} denotes the element in the i -th row and j -th column of the gradient matrix with r rows and h columns.", "source": "marker_v2", "marker_block_id": "/page/4/Text/9"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0049", "section": "4.3.1. MAGNITUDE", "page_start": 5, "page_end": 5, "type": "Text", "text": "(2) Max Row Mean: The mean of each row in the LoRA matrix and take the maximum value, which characterizes the most sample-responsive local optimal response dimension with the largest parameter update magnitude:", "source": "marker_v2", "marker_block_id": "/page/4/Text/10"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0050", "section": "4.3.1. MAGNITUDE", "page_start": 5, "page_end": 5, "type": "Equation", "text": "Row\\_Mean\\_Max = \\max_{1 \\le i \\le r} \\left( \\frac{1}{h} \\sum_{j=1}^{h} |\\mathbb{G}_{i,j}| \\right). (8)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/11"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0051", "section": "4.3.2. Position", "page_start": 5, "page_end": 5, "type": "Text", "text": "Screen the top 10% of gradient elements by absolute value from \\mathbb{G} and calculate their offset from this matrix center, capturing offset characteristics of core gradient positions for (1) Row Eccentricity and (2) Column Eccentricity, respectively:", "source": "marker_v2", "marker_block_id": "/page/4/Text/13"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0052", "section": "4.3.2. Position", "page_start": 5, "page_end": 5, "type": "Equation", "text": "Row\\_Ecc = \\frac{1}{\\operatorname{card}(S)} \\sum_{(i,j) \\in S} \\left| \\frac{2i - (r+1)}{r-1} \\right|, \\quad (9)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0053", "section": "4.3.2. Position", "page_start": 5, "page_end": 5, "type": "Equation", "text": "Col\\_Ecc = \\frac{1}{\\operatorname{card}(S)} \\sum_{(i,j) \\in S} \\left| \\frac{2j - (h+1)}{h-1} \\right|, \\quad (10)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/15"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0054", "section": "4.3.2. Position", "page_start": 5, "page_end": 5, "type": "Text", "text": "where S = \\{(i,j) \\mid |\\mathbb{G}_{i,j}| \\in \\text{Top10\\%}(|\\mathbb{G}|)\\} denotes the set of indices for the top 10% of elements in the gradient matrix \\mathbb{G} ranked by absolute gradient value. Top gradients near the center correspond to an eccentricity of 0, while those near the edge correspond to a score of 1.", "source": "marker_v2", "marker_block_id": "/page/4/Text/16"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0055", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Text", "text": "We propose four indicators to measure the concentration of gradient distributions.", "source": "marker_v2", "marker_block_id": "/page/4/Text/18"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0056", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Text", "text": "(1) Top-10% Ratio : The ratio of the sum of the top 10% largest gradient magnitudes to the total update magnitude of the gradient matrix, which quantifies the contribution ratio of core gradients:", "source": "marker_v2", "marker_block_id": "/page/4/Text/19"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0057", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Equation", "text": "10p\\_Ratio = \\frac{\\sum_{(i,j)\\in S} |\\mathbb{G}_{i,j}|}{\\|\\mathbb{G}\\|_1}, \\tag{11}", "source": "marker_v2", "marker_block_id": "/page/4/Equation/20"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0058", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Text", "text": "(2) Sparsity : The proportion of gradient elements with absolute values less than 10^{-6} , which quantifies the sparsity degree of gradient distributions:", "source": "marker_v2", "marker_block_id": "/page/4/Text/21"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0059", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Equation", "text": "Sparsity = \\frac{\\operatorname{card}\\left(\\left\\{\\left(i,j\\right) \\mid |\\mathbb{G}_{i,j}| < 10^{-6}\\right\\}\\right)}{r \\cdot h}. (12)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/22"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0060", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Text", "text": "(3) Standard Deviation : The standard deviation of the elements in the gradient matrix, which quantifies the dispersion degree of parameter updates:", "source": "marker_v2", "marker_block_id": "/page/4/Text/23"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0061", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Equation", "text": "Std = \\sqrt{\\frac{1}{r \\cdot h} \\sum_{i=1}^{r} \\sum_{j=1}^{h} (|\\mathbb{G}_{i,j}| - \\text{Abs\\_mean})^2}. (13)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/24"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0062", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Text", "text": "(4) Row Mean Standard Deviation: The mean of each row in the LoRA matrix and take the standard deviation, which quantifies the consistency of update strength across all rows:", "source": "marker_v2", "marker_block_id": "/page/4/Text/25"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0063", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Equation", "text": "Row\\_Mean\\_Std = \\sqrt{\\frac{1}{r} \\sum_{i=1}^{r} \\left(\\bar{\\mathbb{G}}_i - \\mu_{\\bar{\\mathbb{G}}}\\right)^2}, \\quad (14)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/26"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0064", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Text", "text": "where \\bar{\\mathbb{G}}_i = \\frac{1}{h} \\sum_{j=1}^h |\\mathbb{G}_{i,j}| denotes the i -th row's absolute mean, \\mu_{\\bar{\\mathbb{G}}} = \\frac{1}{r} \\sum_{i=1}^r \\bar{\\mathbb{G}}_i denotes t the mean of row means.", "source": "marker_v2", "marker_block_id": "/page/4/Text/27"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0065", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Text", "text": "We compute the aforementioned eight feature values from all gradient matrices to derive a feature vector \\mathbb{V}^{l\\times m\\times 8} \\triangleq [Abs_Mean, Row_Mean_Max, 10p_Ratio, Sparsity, Std, Row_Mean_Std, Row_Ecc, Col_Ecc] per sample, which is then used for subsequent MLP training and inference.", "source": "marker_v2", "marker_block_id": "/page/4/Text/28"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0066", "section": "4.4. Light MLP Training", "page_start": 5, "page_end": 5, "type": "Text", "text": "Given the feature vectors \\mathbb{V}_i from all training samples vectors \\mathbb{V}_s , we feed them into a lightweight MLP for training. The target output corresponds to the binary label \\{0,1\\} for each sample, where 0 denotes non-member and 1 denotes member. The training loss is defined as follows:", "source": "marker_v2", "marker_block_id": "/page/4/Text/30"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0067", "section": "4.4. Light MLP Training", "page_start": 5, "page_end": 5, "type": "Equation", "text": "\\mathcal{L} = -\\frac{1}{N} \\sum_{i=1}^{N} \\left[ y_i \\log \\hat{y}_i + (1 - y_i) \\log(1 - \\hat{y}_i) \\right], \\quad (15)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/31"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0068", "section": "4.4. Light MLP Training", "page_start": 5, "page_end": 5, "type": "Text", "text": "where N denotes the number of training samples, y_i \\in \\{0,1\\} is the ground-truth label of the i-th sample, and \\hat{y}_i is the predicted probability output by the MLP.", "source": "marker_v2", "marker_block_id": "/page/4/Text/32"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0069", "section": "4.4. Light MLP Training", "page_start": 6, "page_end": 6, "type": "TableGroup", "text": "Table 1. Comparison(AUROC/TPR@5%FPR) on 4 Datasets across 5 target models. Target models are denoted as 2.7B/6B/6.7B/6.9B/7B, corresponding to Neo-2.7B/GPT-J-6b/OPT-6.7b/Pythia-6.9b/LLaMA-7B respectively. The best result is bold. WikiMIA ArXivTection Method 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B PPL 0.61/0.13 0.64/0.13 0.60/0.12 0.63/0.13 0.69/0.14 0.62/0.13 0.64/0.13 0.60/0.12 0.63/0.13 0.70/0.14 ZLib 0.58/0.10 0.60/0.11 0.58/0.10 0.59/0.10 0.71/0.22 0.58/0.10 0.60/0.11 0.58/0.09 0.59/0.11 0.71/0.22 Min-k 0.65/0.17 0.67/0.19 0.63/0.15 0.67/0.19 0.73/0.18 0.65/0.17 0.68/0.19 0.63/0.15 0.67/0.19 0.72/0.18 Min-k++ 0.67/0.15 0.69/0.19 0.65/0.11 0.70/0.18 0.82/0.22 0.67/0.15 0.69/0.19 0.65/0.10 0.70/0.17 0.83/0.22 FSD 0.92/0.77 0.95/0.78 0.90/0.63 0.90/0.66 0.92/0.41 0.91/0.65 0.96/0.79 0.89/0.63 0.95/0.66 0.94/0.81 Ours 0.90/0.60 0.93/0.66 0.94/0.67 0.92/0.63 0.96/0.84 0.94/0.73 0.97/0.86 0.94/0.75 0.95/0.83 0.97/0.85 BookTection BookMIA Method 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B PPL 0.69/0.15 0.74/0.25 0.64/0.13 0.73/0.25 0.71/0.25 0.29/0.02 0.22/0.13 0.23/0.01 0.59/0.19 0.56/0.21 ZLib 0.56/0.16 0.58/0.20 0.55/0.14 0.58/0.19 0.57/0.19 0.20/0.02 0.38/0.13 0.15/0.00 0.49/0.17 0.48/0.18 Min-k 0.71/0.18 0.75/0.27 0.67/0.15 0.74/0.26 0.71/0.25 0.45/0.05 0.60/0.20 0.40/0.03 0.62/0.20 0.60/0.21 Min-k++ 0.64/0.13 0.67/0.18 0.61/0.11 0.66/0.19 0.63/0.15 0.54/0.13 0.64/0.29 0.49/0.09 0.60/0.23 0.58/0.20 FSD 0.92/0.53 0.91/0.52 0.96/0.77 0.93/0.59 0.92/0.55 0.98/0.93 0.97/0.89 0.98/0.96 0.98/0.93 0.98/0.91 Ours 0.96/0.84 0.97/0.88 0.98/0.92 0.96/0.83 0.98/0.92 0.99/0.98 0.99/0.99 0.99/0.99 0.99/0.98 0.99/0.99 Table 2. Performance Comparison on Mimir datasets with 7 subsets across 5 target models using AUROC scores.", "source": "marker_v2", "marker_block_id": "/page/5/TableGroup/510"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0070", "section": "4.4. Light MLP Training", "page_start": 6, "page_end": 6, "type": "Table", "text": "Wikipedia Github Pile CC PubMed Central Method 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B PPL 0.56 0.57 0.56 0.56 0.56 0.78 0.79 0.78 0.90 0.83 0.56 0.57 0.56 0.56 0.52 0.78 0.79 0.78 0.78 0.72 ZLib 0.62 0.65 0.59 0.65 0.58 0.90 0.91 0.79 0.91 0.86 0.55 0.55 0.55 0.55 0.52 0.78 0.78 0.73 0.77 0.71 Min-k 0.66 0.68 0.65 0.68 0.63 0.88 0.89 0.76 0.90 0.83 0.56 0.57 0.56 0.56 0.52 0.81 0.80 0.74 0.79 0.72 Min-k++ 0.65 0.68 0.60 0.69 0.56 0.84 0.86 0.56 0.86 0.73 0.54 0.55 0.54 0.56 0.51 0.71 0.72 0.60 0.70 0.59 FSD 0.61 0.67 0.60 0.65 0.60 0.77 0.80 0.62 0.77 0.72 0.55 0.55 0.54 0.55 0.52 0.71 0.79 0.63 0.56 0.63 Ours 0.63 0.64 0.65 0.65 0.64 0.90 0.92 0.88 0.92 0.91 0.59 0.59 0.59 0.57 0.59 0.84 0.85 0.84 0.79 0.82 ArXiv DM Mathematics HackerNews Average Method 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B PPL 0.78 0.79 0.65 0.78 0.70 0.78 0.79 0.65 0.91 0.31 0.65 0.62 0.59 0.62 0.59 0.64 0.66 0.62 0.73 0.59 ZLib 0.77 0.78 0.68 0.77 0.71 0.82 0.81 0.80 0.81 0.23 0.68 0.60 0.58 0.60 0.58 0.65 0.67 0.63 0.72 0.58 Min-k 0.78 0.79 0.65 0.78 0.70 0.93 0.93 0.92 0.92 0.32 0.65 0.62 0.59 0.62 0.59 0.71 0.73 0.69 0.75 0.60 Min-k++ 0.60 0.64 0.53 0.70 0.57 0.77 0.79 0.67 0.75 0.22 0.53 0.57 0.51 0.60 0.53 0.60 0.63 0.56 0.67 0.53 FSD 0.72 0.78 0.55 0.70 0.52 0.58 0.85 0.60 0.74 0.53 0.61 0.60 0.57 0.56 0.51 0.61 0.66 0.59 0.62 0.55 Ours 0.78 0.79 0.78 0.78 0.77 0.95 0.95 0.94 0.95 0.95 0.58 0.60 0.60 0.57 0.58 0.73 0.75 0.74 0.76 0.70", "source": "marker_v2", "marker_block_id": "/page/5/Table/5"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0071", "section": "5.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "Datasets Following prior work, we evaluate on five prevalent datasets: WikiMIA, BookMIA (Shi et al., 2024) ,ArxivTection, BookTection (Duarte et al.) , and MIMIR (Duan et al.) , a widely recognized challenging benchmark for pretraining data detection.", "source": "marker_v2", "marker_block_id": "/page/5/Text/8"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0072", "section": "5.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "Target Models We evaluate five open-source LLMs with diverse architectures: Neo-2.7B (Black et al., 2021) , GPT-J-6B (Wang & Komatsuzaki, 2021) , OPT-6.7B (Zhang et al., 2022) , Pythia-6.9B (Biderman et al., 2023) , and LLaMA-7B (Touvron et al., 2023) from Hugging Face.", "source": "marker_v2", "marker_block_id": "/page/5/Text/9"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0073", "section": "5.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "Comparison Methods We select five representative stateof-the-art baselines. Four scoring function–based methods", "source": "marker_v2", "marker_block_id": "/page/5/Text/10"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0074", "section": "5.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "include PPL (Carlini et al., 2021) , ZLib (Carlini et al., 2021) , Min-k (Shi et al., 2024) , and Min-k++ (Zhang et al., 2025) . The fine-tuning–enhanced method includes FSD (Zhang et al.) . More details are shown in Appendix A.", "source": "marker_v2", "marker_block_id": "/page/5/Text/11"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0075", "section": "5.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "Evaluation Metrics Two metrics evaluate the binary pretraining data detection task: AUROC measures overall discriminative performance, and TPR@5%FPR captures practical effectiveness by assessing detection rate under a 5% false positive constraint.", "source": "marker_v2", "marker_block_id": "/page/5/Text/12"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0076", "section": "5.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "Implementation Details We use the PEFT library (Man grulkar et al., 2022) for LoRA-based (Hu et al., 2022) gradient feature extraction without parameter updates. The MLP is trained on 30% of the data, with the remaining 70% used for inference evaluation under FSD settings. More Details can be seen in Appendix A.6.", "source": "marker_v2", "marker_block_id": "/page/5/Text/13"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0077", "section": "5.1. Experimental Setup", "page_start": 7, "page_end": 7, "type": "FigureGroup", "text": "Figure 4. Distribution differences of eight gradient features between member(red) and non-member(blue) samples. Dashed lines indicate distribution means. The x-axis represents feature values, and the y-axis denotes probability density.", "source": "marker_v2", "marker_block_id": "/page/6/FigureGroup/466"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0078", "section": "5.1. Experimental Setup", "page_start": 7, "page_end": 7, "type": "TableGroup", "text": "Table 3. Ablation results using AUROC on WikiMIA and Arxiv-Tection. - denotes the removal of related features. Dataset -Magnitude -Concentration -Position WikiMIA 0.94 (↓0.02) 0.94 (↓0.02) 0.93 (↓0.03) ArxivTection 0.96 (↓0.01) 0.95 (↓0.02) 0.95 (↓0.02) Table 4. Ablation results using AUROC and TPR@5%FPR. ATT-Only refers to performance validation using only attention module.", "source": "marker_v2", "marker_block_id": "/page/6/TableGroup/467"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0079", "section": "5.1. Experimental Setup", "page_start": 7, "page_end": 7, "type": "Table", "text": "Dataset ATT-Only FFN-Only Origin WikiMIA 0.94 / 0.68 0.93 / 0.64 0.96 / 0.84 ArxivTection 0.95 / 0.76 0.93 / 0.72 0.97 / 0.85", "source": "marker_v2", "marker_block_id": "/page/6/Table/6"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0080", "section": "5.2. Main Results", "page_start": 7, "page_end": 7, "type": "Text", "text": "Table 1 shows detection performance on WikiMIA, Arxiv-Tection, BookTection, and BookMIA. Specifically, when tested on WikiMIA with LLaMA-7B, GDS achieves an AUC score of 0.96, which is an improvement of 0.04 compared to the best baseline FSD and significantly higher than score-function-based methods such as Min-k++. GDS outperforms the best baseline in most settings, with especially large gains in TPR@5%FPR on BookTection and Book-MIA. Notably, with LLaMA-7B, BookTection performance improves by nearly 67.3%.", "source": "marker_v2", "marker_block_id": "/page/6/Text/8"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0081", "section": "5.2. Main Results", "page_start": 7, "page_end": 7, "type": "Text", "text": "Table 2 reports results on seven MIMIR subsets. Although all methods degrade due to similar data distributions, GDS achieves the best average improvements +2.8%, +2.7%, +7.2%, +1.3%, +16.6% across different models, and shows clear advantages on PubMed Central, DM Mathematics, and GitHub. Using the LLaMA model, the three subsets achieve AUC scores of 0.82, 0.95, and 0.91. Our method shows the most stable performance across models, with AUC variations mostly within 0.04, demonstrating strong generalization across different models.", "source": "marker_v2", "marker_block_id": "/page/6/Text/9"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0082", "section": "5.3. Ablation Study", "page_start": 7, "page_end": 7, "type": "Text", "text": "We perform two ablation studies: (1) removing each gradient feature category individually, and (2) using features from only the Attention or FFN module. Table 3 shows that all feature categories contribute to performance, with Position Offset and Magnitude being the most important. Concentration features have smaller effects, and the full combination performs best, highlighting the complementary nature of multi-dimensional features (see Appendix C for sub-feature ablations). Table 4 shows that Attention features are more discriminative than FFN features. Both single-module variants underperform the full model, indicating that Attention and FFN capture complementary gradient patterns and must be combined for optimal performance.", "source": "marker_v2", "marker_block_id": "/page/6/Text/11"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0083", "section": "5.4.1. FEATURE DISTRIBUTION", "page_start": 7, "page_end": 7, "type": "Text", "text": "To explain the classifier's effectiveness, we quantify feature distributions across all layers and sub-modules for member and non-member samples. Figure 4 shows the eight features with the largest discrepancies. Member samples exhibit smaller Abs Mean and Row Mean Max, indicating lower gradient magnitudes due to higher data familiarity, along with higher Sparsity, smaller Std and Row Mean Std, reflecting more concentrated and stable gradients. They also maintain a consistently higher 10p Ratio, occupying the core of gradient propagation. For locations Row Ecc and Col Ecc, member samples cluster at lower values, while non-members shift higher, suggesting that member-related parameters lie more centrally in weight matrices.", "source": "marker_v2", "marker_block_id": "/page/6/Text/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0084", "section": "5.4.1. FEATURE DISTRIBUTION", "page_start": 7, "page_end": 7, "type": "Text", "text": "We collect sub-features with the largest distribution differences between the two sample types and analyze their overall distribution patterns. Figure 5 show that discriminative sub-features are predominantly concentrated in low layers, while middle and high layers contribute far less. Among sub-modules, attention-related modules are the main sources", "source": "marker_v2", "marker_block_id": "/page/6/Text/15"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0085", "section": "5.4.1. FEATURE DISTRIBUTION", "page_start": 8, "page_end": 8, "type": "TableGroup", "text": "Table 5. Performance Comparison between LoRA and Full-Parameter Update using AUROC on WikiMIA and ArxivTection. Dataset Metric LLaMA-7B GPT-J-6B OPT-6.7B Pythia-6.9B Neo-2.7B LoRA Full LoRA Full LoRA Full LoRA Full LoRA Full WikiMIA AUC 0.96 0.96 0.93 0.90 0.94 0.92 0.92 0.89 0.90 0.88 TPR@5% FPR 0.84 0.79 0.66 0.58 0.67 0.56 0.63 0.50 0.60 0.51 ArxivTection AUC 0.97 0.96 0.97 0.96 0.94 0.93 0.95 0.94 0.94 0.94 TPR@5% FPR 0.85 0.84 0.86 0.79 0.75 0.67 0.83 0.73 0.73 0.75", "source": "marker_v2", "marker_block_id": "/page/7/TableGroup/516"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0086", "section": "5.4.1. FEATURE DISTRIBUTION", "page_start": 8, "page_end": 8, "type": "FigureGroup", "text": "Figure 5. Distribution Difference Statistics of Discriminative Features. The y-axis shows the statistical count.", "source": "marker_v2", "marker_block_id": "/page/7/FigureGroup/517"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0087", "section": "5.4.1. FEATURE DISTRIBUTION", "page_start": 8, "page_end": 8, "type": "Text", "text": "of discriminative features, with obvious differences in contribution across modules. In terms of gradient features, grad sparsity exhibits the strongest discriminative power, significantly outperforming other indicators.", "source": "marker_v2", "marker_block_id": "/page/7/Text/6"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0088", "section": "5.4.2. FULL PARAMETER TRAINING", "page_start": 8, "page_end": 8, "type": "Text", "text": "In LoRA training, only FFN and MLP modules are updated, while LayerNorm, despite containing meaningful training dynamics, is excluded. To account for this, we evaluate our method under full-parameter training on two small-scale datasets, BookMIA and ArxivTection, for computational feasibility. As shown in Table 5, although full-parameter updates cause a slight performance drop compared to LoRA, our method still outperforms most baselines. We attribute this gap to reduced gradient magnitudes in full training, which weaken discriminative signals between sample types.", "source": "marker_v2", "marker_block_id": "/page/7/Text/8"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0089", "section": "5.4.3. WIKIMIA MODIFICATION", "page_start": 8, "page_end": 8, "type": "Text", "text": "Dataset partitioning can introduce distribution shifts or dataset-specific artifacts. For example, WikiMIA is split by publication time, with all non-member samples labeled as 2023. To ensure our method does not exploit such artifacts, we remove all timestamp tokens and reevaluate all methods. As shown in Table 6, although token removal degrades performance, our method suffers a much smaller drop than the strongest baseline, FSD, and still achieves SOTA results.", "source": "marker_v2", "marker_block_id": "/page/7/Text/10"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0090", "section": "5.4.3. WIKIMIA MODIFICATION", "page_start": 8, "page_end": 8, "type": "TableGroup", "text": "Table 6. Comparison of Temporal Feature Perturbation via AU-ROC. Deletion denotes the removal of all year timestamps. Method Origin Deletion PPL 0.69 0.62 Min-k 0.73 0.63 Min-k++ 0.82 0.59 FSD 0.92 0.76 Ours 0.96 0.84 Table 7. Cross-Dataset Generalization Performance using AU-ROC. Wiki(arXiv) indicates training on ArxivTection with test on WikiMIA, while Mix indicates mixed datasets.", "source": "marker_v2", "marker_block_id": "/page/7/TableGroup/518"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0091", "section": "5.4.3. WIKIMIA MODIFICATION", "page_start": 8, "page_end": 8, "type": "Table", "text": "Method Wiki (arXiv) arXiv (Wiki) Mix FSD 0.52 0.58 0.92 Ours 0.66 0.68 0.95", "source": "marker_v2", "marker_block_id": "/page/7/Table/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0092", "section": "5.4.4. TRANSFERABILITY", "page_start": 8, "page_end": 8, "type": "Text", "text": "Although our method shares the same feature extraction framework, it requires dataset-specific classifiers. To examine whether a unified classifier is feasible, we train classifiers on WikiMIA and ArXiv separately and evaluate crossdataset generalization, as well as train a unified classifier on mixed data. Table 7 shows that cross-dataset transfer leads to notable performance degradation due to dataset shifts (e.g., distribution, difficulty, and pre-training differences), which cause classifiers to overfit dataset-specific gradient features. In contrast, the unified classifier performs well on mixed data, indicating that our method can capture universal feature discrepancies arising from model familiarity.", "source": "marker_v2", "marker_block_id": "/page/7/Text/16"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0093", "section": "6. Conclusion", "page_start": 8, "page_end": 8, "type": "Text", "text": "We revisit pre-training data detection from an optimization and training-dynamics perspective and introduce GDS, a fine-tuning–free method for inferring pre-training membership. By analyzing how models transition from unfamiliarity to familiarity, we show that member and non-member samples exhibit stable, interpretable differences in gradient magnitude, location, and concentration across datasets and architectures. Experiments show that GDS is effective and generalizable, outperforming strong baselines. Future work can focus on developing more generalizable detectors by contrastive learning or deeper feature extraction.", "source": "marker_v2", "marker_block_id": "/page/7/Text/18"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0094", "section": "Limitations", "page_start": 9, "page_end": 9, "type": "Text", "text": "This work investigates pre-training data detection, a form of membership inference that determines whether a given sample was included in a LLM's pre-training corpus. While our proposed GDS method improves detection accuracy and generalization without fine-tuning, it also raises important ethical concerns. Pre-training data detection methods could be misused to probe proprietary or confidential training corpora, potentially revealing sensitive information about data sources or collection practices. Although GDS does not reconstruct or expose training samples directly, it contributes to capabilities that may be exploited if applied irresponsibly. Our primary motivation is to support transparency, accountability, and safety. As pre-training datasets become increasingly large and opaque, tools like GDS can help researchers, auditors, and regulators verify data usage claims, identify potential copyright violations, and detect benchmark contamination. In this sense, GDS is intended as a diagnostic and auditing mechanism rather than a data extraction attack. We release code and models to promote reproducibility while encouraging responsible deployment. Overall, we hope this work advances trustworthy and transparent large-scale model development while highlighting the need for careful governance of pre-training data.", "source": "marker_v2", "marker_block_id": "/page/8/Text/2"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0095", "section": "References", "page_start": 9, "page_end": 9, "type": "ListGroup", "text": "Balloccu, S., Schmidtova, P., Lango, M., and Du ´ sek, O. ˇ Leak, cheat, repeat: Data contamination and evaluation malpractices in closed-source llms. In Proceedings of the 18th Conference of the European Chapter of the Asso ciation for Computational Linguistics (Volume 1: Long Papers) , pp. 67–93, 2024. Biderman, S., Schoelkopf, H., Anthony, Q. G., Bradley, H., O'Brien, K., Hallahan, E., Khan, M. A., Purohit, S., Prashanth, U. S., Raff, E., et al. Pythia: A suite for analyzing large language models across training and scaling. In International Conference on Machine Learning , pp. 2397–2430. PMLR, 2023. Black, S., Leo, G., Wang, P., Leahy, C., and Biderman, S. Gpt-neo: Large scale autoregressive language modeling with mesh-tensorflow. Zenodo , 2021. Bottou, L. Large-scale machine learning with stochastic gradient descent. In Proceedings of COMPSTAT'2010: 19th International Conference on Computational Statis ticsParis France, August 22-27, 2010 Keynote, Invited and Contributed Papers , pp. 177–186. Springer, 2010. Carlini, N., Tramer, F., Wallace, E., Jagielski, M., Herbert-Voss, A., Lee, K., Roberts, A., Brown, T., Song, D., Erlingsson, U., et al. Extracting training data from large", "source": "marker_v2", "marker_block_id": "/page/8/ListGroup/507"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0096", "section": "References", "page_start": 9, "page_end": 9, "type": "ListGroup", "text": "language models. In 30th USENIX security symposium (USENIX Security 21) , pp. 2633–2650, 2021. Choi, H. K., Khanov, M., Wei, H., and Li, Y. How contaminated is your benchmark? measuring dataset leakage in large language models with kernel divergence. In Forty second International Conference on Machine Learning . Duan, M., Suri, A., Mireshghallah, N., Min, S., Shi, W., Zettlemoyer, L., Tsvetkov, Y., Choi, Y., Evans, D., and Hajishirzi, H. Do membership inference attacks work on large language models? In First Conference on Language Modeling . Duarte, A. V., Zhao, X., Oliveira, A. L., and Li, L. Decop: Detecting copyrighted content in language models training data. In Forty-first International Conference on Machine Learning . Frankle, J., Schwab, D. J., and Morcos, A. S. The early phase of neural network training. In International Con ference on Learning Representations . Grynbaum, M. M. and Mac, R. The times sues openai and microsoft over ai use of copyrighted work. The New York Times , 27(1), 2023. Gur-Ari, G., Roberts, D. A., and Dyer, E. Gradient descent happens in a tiny subspace. arXiv preprint arXiv:1812.04754 , 2018. Hu, E. J., Shen, Y., Wallis, P., Allen-Zhu, Z., Li, Y., Wang, S., Wang, L., Chen, W., et al. Lora: Low-rank adaptation of large language models. ICLR , 1(2):3, 2022. Kaplan, J., McCandlish, S., Henighan, T., Brown, T. B., Chess, B., Child, R., Gray, S., Radford, A., Wu, J., and Amodei, D. Scaling laws for neural language models. arXiv preprint arXiv:2001.08361 , 2020. Li, Y. Estimating contamination via perplexity: Quantifying memorisation in language model evaluation. In The Future of Machine Learning Data Practices and Reposi tories at ICLR 2025 . Liu, Z., Zhu, T., Tan, C., Liu, B., Lu, H., and Chen, W. Probing language models for pre-training data detection. In Proceedings of the 62nd Annual Meeting of the Asso ciation for Computational Linguistics (Volume 1: Long Papers) , pp. 1576–1587, 2024. Mangrulkar, S., Gugger, S., Debut, L., Belkada, Y., Paul, S., and Bossan, B. Peft: State-of-the-art parameter-efficient fine-tuning methods. 2022. Ruder, S. An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747 , 2016.", "source": "marker_v2", "marker_block_id": "/page/8/ListGroup/508"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0097", "section": "References", "page_start": 10, "page_end": 10, "type": "Text", "text": "Shi, W., Ajith, A., Xia, M., Huang, Y., Liu, D., Blevins, T., Chen, D., and Zettlemoyer, L. Detecting pretraining data from large language models. In 12th International Conference on Learning Representations, ICLR 2024 , 2024.", "source": "marker_v2", "marker_block_id": "/page/9/Text/280"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0098", "section": "References", "page_start": 10, "page_end": 10, "type": "ListGroup", "text": "Tang, H., Zhu, Z., and Yang, Y. Identifying pre-training data in llms: A neuron activation-based detection framework. In Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing , pp. 18738– 18751, 2025. Touvron, H., Lavril, T., Izacard, G., Martinet, X., Lachaux, M.-A., Lacroix, T., Roziere, B., Goyal, N., Hambro, E., ` Azhar, F., et al. Llama: Open and efficient foundation language models. arXiv preprint arXiv:2302.13971 , 2023. Wang, B. and Komatsuzaki, A. Gpt-j-6b: A 6 billion parameter autoregressive language model, 2021. Wang, H., Ma, S., Wang, R., and Wei, F. Q-sparse: All large language models can be fully sparsely-activated. arXiv preprint arXiv:2407.10969 , 2024. Zhang, H., Zhang, S., Jing, B., and Wei, H. Fine-tuning can help detect pretraining data from large language models. In The Thirteenth International Conference on Learning Representations . Zhang, J., Sun, J., Yeats, E., Ouyang, Y., Kuo, M., Zhang, J., Yang, H. F., and Li, H. Min-k%++: Improved baseline for pre-training data detection from large language models. In The Thirteenth International Conference on Learning Representations , 2025. Zhang, S., Roller, S., Goyal, N., Artetxe, M., Chen, M., Chen, S., Dewan, C., Diab, M., Li, X., Lin, X. V., et al. Opt: Open pre-trained transformer language models. arXiv preprint arXiv:2205.01068 , 2022. Zhang, W., Zhang, R., Guo, J., Rijke, M., Fan, Y., and Cheng, X. Pretraining data detection for large language models: A divergence-based calibration method. In Pro ceedings of the 2024 Conference on Empirical Methods in Natural Language Processing , pp. 5263–5274, 2024.", "source": "marker_v2", "marker_block_id": "/page/9/ListGroup/279"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0099", "section": "A. Details of Baseline", "page_start": 11, "page_end": 11, "type": "Text", "text": "Shared Notations: We first define the universal notations used across all baseline methods for consistency:", "source": "marker_v2", "marker_block_id": "/page/10/Text/2"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0100", "section": "A. Details of Baseline", "page_start": 11, "page_end": 11, "type": "ListGroup", "text": "x: Input text sample for membership inference detection. {x1, x2, . . . , x N }: Token sequence of input text sample x, where N denotes the total number of tokens in the text. x<t: Prefix token sequence of the t-th token xt, i.e., x<t = {x1, . . . , xt−1}. θ: Trainable parameters of the pre-trained language model. p(· | ·; θ): Conditional probability distribution parameterized by the model parameters θ. k%: Percentage threshold for selecting low-probability outlier tokens (used in Min-k% and Min-k%++).", "source": "marker_v2", "marker_block_id": "/page/10/ListGroup/597"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0101", "section": "A.1. PPL", "page_start": 11, "page_end": 11, "type": "Text", "text": "Perplexity (PPL) is a classic global likelihood-based metric that measures the model's uncertainty in predicting a given text, with lower PPL indicating higher text familiarity (more likely to be a member sample). First, the text is tokenized into a sequence of tokens {x1, x2, . . . , x N }. Then, the log-likelihood of each token is calculated conditional on the preceding tokens, and the final PPL is derived by normalizing the sum of log-likelihoods by the token sequence length and performing an exponential transformation.", "source": "marker_v2", "marker_block_id": "/page/10/Text/10"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0102", "section": "A.1. PPL", "page_start": 11, "page_end": 11, "type": "Equation", "text": "PPL = \\exp\\left(-\\frac{1}{N} \\sum_{i=1}^{N} \\log p(x_i|x_1, ..., x_{x-1}; \\theta)\\right) (16)", "source": "marker_v2", "marker_block_id": "/page/10/Equation/11"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0103", "section": "A.2. Zlib", "page_start": 11, "page_end": 11, "type": "Text", "text": "Zlib is a compression-based global likelihood-related method that leverages compression entropy to distinguish member and non-member samples, which calibrates the loss using the input's Zlib entropy. For an input text sample x and a pre-trained model M, the Zlib score is defined as the ratio of the loss related to the text and model to the Zlib compression entropy of the input text:", "source": "marker_v2", "marker_block_id": "/page/10/Text/13"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0104", "section": "A.2. Zlib", "page_start": 11, "page_end": 11, "type": "Equation", "text": "Zlib Score = \\frac{L(x, M)}{\\text{zlib}(x)} (17)", "source": "marker_v2", "marker_block_id": "/page/10/Equation/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0105", "section": "A.2. Zlib", "page_start": 11, "page_end": 11, "type": "Text", "text": "where L(x, M) denotes the loss value associated with the input text x under the model M and zlib(x) represents the Zlib compression entropy of the input text x, which is derived from the length of the text after Zlib compression.", "source": "marker_v2", "marker_block_id": "/page/10/Text/15"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0106", "section": "A.3. Min-k%", "page_start": 11, "page_end": 11, "type": "Text", "text": "Min-k% is a local likelihood-based method that mitigates global word frequency interference by focusing on low-probability outlier tokens. For an input text token sequence x = {x1, x2, . . . , x N } (where N denotes the total number of tokens), it first calculates the conditional log-likelihood of each token x i given its preceding context:", "source": "marker_v2", "marker_block_id": "/page/10/Text/17"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0107", "section": "A.3. Min-k%", "page_start": 11, "page_end": 11, "type": "Equation", "text": "\\log p(x_i \\mid x_1, x_2, \\dots, x_{i-1}; \\theta)", "source": "marker_v2", "marker_block_id": "/page/10/Equation/18"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0108", "section": "A.3. Min-k%", "page_start": 11, "page_end": 11, "type": "Text", "text": "Subsequently, it sorts all token conditional probabilities in ascending order, selects the bottom k% tokens (i.e., the k% tokens with the smallest conditional probabilities) to form the low-probability set Tmin(k%) = Min-K%(x). The final Min-k% score is defined as the average conditional log-likelihood of tokens in Tmin(k%):", "source": "marker_v2", "marker_block_id": "/page/10/Text/19"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0109", "section": "A.3. Min-k%", "page_start": 11, "page_end": 11, "type": "Equation", "text": "Min-k% Score(x) = \\frac{1}{|T_{\\min(k\\%)}|} \\sum_{x_i \\in T_{\\min(k\\%)}} \\log p(x_i \\mid x_1, \\dots, x_{i-1}; \\theta) (18)", "source": "marker_v2", "marker_block_id": "/page/10/Equation/20"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0110", "section": "A.3. Min-k%", "page_start": 11, "page_end": 11, "type": "Text", "text": "where |Tmin(k%)| = ⌊k% × N⌋ denotes the cardinality of the low-probability token set (rounded down to the nearest integer). During detection, a threshold is set on Min-k% Score(x): text with a score below the threshold is classified as a member sample (since member samples tend to contain more low-probability outlier tokens), and vice versa.", "source": "marker_v2", "marker_block_id": "/page/10/Text/21"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0111", "section": "A.4. Min-k%++", "page_start": 12, "page_end": 12, "type": "Text", "text": "Min-k%++ is an optimized variant of Min-k% that enhances detection robustness by integrating vocabulary-level probability statistics, addressing the text-length dependency and short-text fluctuation issues of the original method. For an input text token sequence x = \\{x_1, x_2, \\dots, x_N\\} , it first computes the normalized conditional log-likelihood for each token x_t (given prefix x_{< t} = \\{x_1, \\dots, x_{t-1}\\} ) by normalizing with the vocabulary-wide log-probability statistics of the prefix x_{< t} .", "source": "marker_v2", "marker_block_id": "/page/11/Text/2"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0112", "section": "Core Token-Level Score Calculation", "page_start": 12, "page_end": 12, "type": "Text", "text": "For each token x_t , the token-level Min-k%++ score is defined as:", "source": "marker_v2", "marker_block_id": "/page/11/Text/4"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0113", "section": "Core Token-Level Score Calculation", "page_start": 12, "page_end": 12, "type": "Equation", "text": "Min-k\\% + +_{token}(x_{< t}, x_t) = \\frac{\\log p(x_t \\mid x_{< t}; \\theta) - \\mu_{x_{< t}}}{\\sigma_{x_{< t}}} (19)", "source": "marker_v2", "marker_block_id": "/page/11/Equation/5"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0114", "section": "Core Token-Level Score Calculation", "page_start": 12, "page_end": 12, "type": "Text", "text": "where \\mu_{x_{< t}} = \\mathbb{E}_{z \\sim p(\\cdot \\mid x_{< t}; \\theta)} [\\log p(z \\mid x_{< t}; \\theta)] : Expectation of the next-token log-likelihood over the model's vocabulary, given prefix x_{< t} ; \\sigma_{x_{< t}} = \\sqrt{\\mathbb{E}_{z \\sim p(\\cdot \\mid x_{< t}; \\theta)} \\left[ (\\log p(z \\mid x_{< t}; \\theta) - \\mu_{x_{< t}})^2 \\right]} : Standard deviation of the next-token log-likelihood over the vocabulary, given prefix x_{< t} .", "source": "marker_v2", "marker_block_id": "/page/11/Text/6"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0115", "section": "Core Token-Level Score Calculation", "page_start": 12, "page_end": 12, "type": "Text", "text": "Both \\mu_{x_{< t}} and \\sigma_{x_{< t}} can be computed analytically using the model's output logits (since p(\\cdot \\mid x_{< t}; \\theta) follows a categorical distribution), requiring no additional computational overhead beyond standard LLM inference.", "source": "marker_v2", "marker_block_id": "/page/11/Text/7"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0116", "section": "Final Sequence-Level Score Calculation", "page_start": 12, "page_end": 12, "type": "Text", "text": "Similar to Min-k%, Min-k%++ selects the bottom k% tokens with the smallest Min-k%++<sub>token</sub> scores to form the low-probability set T_{\\min(k\\%)}^+ . The final sequence-level score is the average of the token-level scores in this set:", "source": "marker_v2", "marker_block_id": "/page/11/Text/9"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0117", "section": "Final Sequence-Level Score Calculation", "page_start": 12, "page_end": 12, "type": "Equation", "text": "Min-k\\% ++ Score(x) = \\frac{1}{|T_{\\min(k\\%)}^+|} \\sum_{(x_{< t}, x_t) \\in T_{\\min(k\\%)}^+} Min-k\\% ++_{token}(x_{< t}, x_t) (20)", "source": "marker_v2", "marker_block_id": "/page/11/Equation/10"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0118", "section": "Final Sequence-Level Score Calculation", "page_start": 12, "page_end": 12, "type": "Text", "text": "where |T_{\\min(k\\%)}^+| = \\lfloor k\\% \\times N \\rfloor denotes the cardinality of the low-probability token set. During detection, a threshold is applied: text with a lower Min-k%++ score is more likely to be a member sample, as the normalized score better distinguishes low-probability outlier tokens of member samples from non-member ones.", "source": "marker_v2", "marker_block_id": "/page/11/Text/11"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0119", "section": "A.5. FSD", "page_start": 12, "page_end": 12, "type": "Text", "text": "Fine-tuned Score Deviation (FSD) is a fine-tuning enhanced method that leverages score discrepancies between pre-trained and fine-tuned models for member sample detection. Its core workflow includes two key steps: first, constructing a domain-matched non-member fine-tuning dataset (using post-model-release unseen data), then performing self-supervised next-token prediction fine-tuning on the pre-trained model. Finally, it calculates the score difference between the pre-trained and fine-tuned models to distinguish member and non-member samples. The self-supervised fine-tuning loss is defined as:", "source": "marker_v2", "marker_block_id": "/page/11/Text/13"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0120", "section": "A.5. FSD", "page_start": 12, "page_end": 12, "type": "Equation", "text": "\\mathcal{L}_{\\text{fine-tuning}}(x) = -\\frac{1}{n} \\sum_{i=1}^{n} \\log f_{\\theta}(x_i \\mid x_1, \\dots, x_{i-1}) (21)", "source": "marker_v2", "marker_block_id": "/page/11/Equation/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0121", "section": "A.5. FSD", "page_start": 12, "page_end": 12, "type": "Text", "text": "The final FSD score is the deviation between the sample scores obtained from the pre-trained model f_{\\theta} and the fine-tuned model f_{\\theta'} (with parameters \\theta' ):", "source": "marker_v2", "marker_block_id": "/page/11/Text/15"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0122", "section": "A.5. FSD", "page_start": 12, "page_end": 12, "type": "Equation", "text": "FSD(x; f_{\\theta}, f_{\\theta'}) = S(x; f_{\\theta}) - S(x; f_{\\theta'}) (22)", "source": "marker_v2", "marker_block_id": "/page/11/Equation/16"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0123", "section": "A.5. FSD", "page_start": 12, "page_end": 12, "type": "Text", "text": "where S(\\cdot) represents a base scoring function (e.g., Perplexity, Min-k%). A large FSD score indicates the sample is likely a non-member (fine-tuning reduces non-member perplexity significantly), while a small score suggests a member sample (fine-tuning has negligible impact on member perplexity). A validation-set optimized threshold \\varepsilon is used for final classification.", "source": "marker_v2", "marker_block_id": "/page/11/Text/17"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0124", "section": "A.6. Experimental Settings", "page_start": 12, "page_end": 12, "type": "Text", "text": "We use the PEFT library (Mangrulkar et al., 2022) for LoRA-based (Hu et al., 2022) gradient feature extraction without parameter updates. The base model is initialized from pre-trained checkpoints, and for LoRA configuration, we adopt", "source": "marker_v2", "marker_block_id": "/page/11/Text/19"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0125", "section": "A.6. Experimental Settings", "page_start": 13, "page_end": 13, "type": "Text", "text": "default settings with rank r = 16, LoRA scaling factor α = 32, and dropout set to 0 since we only focus on gradients from a single backpropagation step and no parameter updates are required. Target modules include all submodules of attention and FFN, including query, key, value, output, gate, up, and down projections. For different datasets, we select the tokenizer sequence length based on the overall length distribution: 256 for the WikiMIA dataset and 512 for all other datasets. When training the MLP classifier, the dataset is uniformly split into training and validation sets at a ratio of 3:7. The MLP classifier is configured with two hidden layers of dimensions 128 and 64, respectively, and uses the default Adam optimizer with a learning rate of 0.001. An early stopping strategy is implemented to avoid overfitting.", "source": "marker_v2", "marker_block_id": "/page/12/Text/1"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0126", "section": "B. Motivation Experiment Supplementary Details", "page_start": 13, "page_end": 13, "type": "Text", "text": "To verify the parameter update law driven by the training process, we conduct LoRA fine-tuning with 8 epochs on LLaMA-7B using the unseen set of BookMIA dataset, counting LoRA matrix parameter updates per epoch to extract dynamic change curves of target features. Experiments are performed under three learning rates (1e − 5, 3e − 5, 5e − 5). We present the variation trends of the four feature categories across different modules and layers under each learning rate.", "source": "marker_v2", "marker_block_id": "/page/12/Text/3"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0127", "section": "B. Motivation Experiment Supplementary Details", "page_start": 13, "page_end": 13, "type": "Text", "text": "We present the variation trends of the four feature categories across different modules and layers under each learning rate. Across all learning rates, ∆Θ t and S t exhibit clear epoch-wise patterns: ∆Θ t continuously decreases with training epochs, while S t gradually increases. For Et, distinct opposite trends are observed between the ATT and MLP modules—the update positions of the ATT module tend to be centralized, whereas those of the MLP module tend to be marginalized. Despite this divergence, E t values of both modules converge to the same stable range across the three learning rates. In contrast, T10,t shows a different dynamic: under large learning rates, it first increases and then decreases, yet remains stably around 0.27 throughout training. Notably, the inflection point of T10,t decline coincides with the stage when E t stabilizes. This aligns with our core hypothesis: during training, the model identifies core parameters correlated with the input data and performs concentrated updates on them; once this process is completed, the overall parameter update dynamics tend to stabilize. Regarding different hierarchical levels, only E t shows noticeable discrepancies, while all other features follow the same evolutionary laws.", "source": "marker_v2", "marker_block_id": "/page/12/Text/4"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0128", "section": "B. Motivation Experiment Supplementary Details", "page_start": 13, "page_end": 13, "type": "FigureGroup", "text": "Figure 6. Feature Dynamic Changes During LoRA Fine-Tuning (Learning Rate 1e−5). Top row: Features in ATT/MLP modules; Bottom row: Features in low/middle/high layers.", "source": "marker_v2", "marker_block_id": "/page/12/FigureGroup/363"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0129", "section": "B. Motivation Experiment Supplementary Details", "page_start": 14, "page_end": 14, "type": "FigureGroup", "text": "Figure 7. Feature Dynamic Changes During LoRA Fine-Tuning (Learning Rate 3e − 5).", "source": "marker_v2", "marker_block_id": "/page/13/FigureGroup/236"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0130", "section": "B. Motivation Experiment Supplementary Details", "page_start": 14, "page_end": 14, "type": "FigureGroup", "text": "Figure 8. Feature Dynamic Changes During LoRA Fine-Tuning (Learning Rate 5e − 5).", "source": "marker_v2", "marker_block_id": "/page/13/FigureGroup/237"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0131", "section": "C. Ablation Experiments on Sub-features and Sub-modules", "page_start": 15, "page_end": 15, "type": "Text", "text": "To further explore the discriminative power of fine-grained components in our method, we conduct two additional ablation experiments: sub-feature category ablation (8 sub-features) and sub-module ablation (7 sub-modules). All experiments follow the same configuration as the main text (LLaMA-7B model, WikiMIA/ArxivTection datasets), with AUC and TPR@5% FPR as evaluation metrics.", "source": "marker_v2", "marker_block_id": "/page/14/Text/12"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0132", "section": "C.1. Sub-feature Category Ablation Experiment", "page_start": 15, "page_end": 15, "type": "Text", "text": "The four core feature categories are decomposed into 8 sub-features, as follows:", "source": "marker_v2", "marker_block_id": "/page/14/Text/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0133", "section": "C.1. Sub-feature Category Ablation Experiment", "page_start": 15, "page_end": 15, "type": "ListGroup", "text": "Magnitude Distribution Features: Abs Mean, Std Core Contribution Features: 10p Ratio, Sparsity Position Offset Features: Row Ecc, Col Ecc Row-Dimension Consistency Features: Row Mean Max, Row Mean Std", "source": "marker_v2", "marker_block_id": "/page/14/ListGroup/372"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0134", "section": "C.1. Sub-feature Category Ablation Experiment", "page_start": 15, "page_end": 15, "type": "Text", "text": "Ablation is performed by removing one sub-feature at a time (retaining the other 7), and the results are shown in Table 8.", "source": "marker_v2", "marker_block_id": "/page/14/Text/19"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0135", "section": "C.1. Sub-feature Category Ablation Experiment", "page_start": 15, "page_end": 15, "type": "TableGroup", "text": "Table 8. Ablation Experiment Results of Sub-features (AUC Scores). Dataset Sub-feature (Ablation Variant) -Abs Mean -Std -10p Ratio -Sparsity -Row Ecc -Col Ecc -Row Max -Row Std WikiMIA 0.95/0.71 0.95/0.72 0.95/0.70 0.94/0.67 0.95/0.70 0.93/0.62 0.95/0.73 0.95/0.72 0.96/0.84 ArxivTection 0.96/0.82 0.96/0.81 0.96/0.83 0.96/0.82 0.96/0.83 0.95/0.78 0.96/0.83 0.96/0.83 0.97/0.85", "source": "marker_v2", "marker_block_id": "/page/14/TableGroup/370"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0136", "section": "C.1. Sub-feature Category Ablation Experiment", "page_start": 15, "page_end": 15, "type": "Text", "text": "The sub-feature ablation results verify that all sub-features contribute to detection performance, with their combination achieving optimal AUC and TPR scores across both datasets. Among these sub-features, Col Ecc (a Position Offset Feature) is the most critical: its removal leads to the sharpest performance decline (AUC drops to 0.93 on WikiMIA and 0.95 on ArxivTection, with TPR falling to 0.62 and 0.78 respectively). In contrast, removing Abs Mean, Std, 10p Ratio, Row Ecc, Row Max, or Row Std induces only mild performance degradation, with AUC remaining above 0.95 on both datasets, indicating their relatively moderate importance; Sparsity also shows a slight impact on WikiMIA, with its ablation resulting in an AUC of 0.94. Overall, the fine-grained sub-feature design is rational, as each component provides complementary discriminative information for pre-training data detection.", "source": "marker_v2", "marker_block_id": "/page/14/Text/22"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0137", "section": "C.2. Sub-module Ablation Experiment", "page_start": 15, "page_end": 15, "type": "Text", "text": "The ATT and FFN modules are decomposed into 7 sub-modules based on Transformer architecture details:", "source": "marker_v2", "marker_block_id": "/page/14/Text/24"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0138", "section": "C.2. Sub-module Ablation Experiment", "page_start": 15, "page_end": 15, "type": "ListGroup", "text": "ATT-related sub-modules: Q-Proj, K-Proj, V-Proj, Out-Proj FFN-related sub-modules: Gate-Proj, Up-Proj, Down-Proj", "source": "marker_v2", "marker_block_id": "/page/14/ListGroup/373"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0139", "section": "C.2. Sub-module Ablation Experiment", "page_start": 15, "page_end": 15, "type": "Text", "text": "Ablation is performed by removing one sub-module's features at a time, and the results are shown in Table 9.", "source": "marker_v2", "marker_block_id": "/page/14/Text/27"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0140", "section": "C.2. Sub-module Ablation Experiment", "page_start": 15, "page_end": 15, "type": "TableGroup", "text": "Table 9. Ablation Experiment Results of Sub-modules (AUC / TPR@5% FPR Scores). Dataset Sub-module (Ablation Variant) -Q-Proj -K-Proj -V-Proj -Out-Proj -Gate-Proj -Up-Proj -Down-Proj WikiMIA 0.95/0.72 0.95/0.71 0.94/0.69 0.94/0.67 0.95/0.69 0.94/0.65 0.94/0.61 0.96/0.84 ArxivTection 0.96/0.80 0.96/0.82 0.95/0.79 0.96/0.80 0.96/0.82 0.95/0.78 0.96/0.82 0.97/0.85", "source": "marker_v2", "marker_block_id": "/page/14/TableGroup/371"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0141", "section": "C.2. Sub-module Ablation Experiment", "page_start": 15, "page_end": 15, "type": "Text", "text": "The sub-module ablation results demonstrate that all sub-modules provide complementary gradient information, as singlesub-module ablation consistently leads to performance degradation while integrating all sub-modules' features achieves", "source": "marker_v2", "marker_block_id": "/page/14/Text/30"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0142", "section": "C.2. Sub-module Ablation Experiment", "page_start": 16, "page_end": 16, "type": "FigureGroup", "text": "Figure 9. Impact Analysis of Training Set Size on WikiMIA. The abscissa denotes the training-validation set ratio, the ordinate represents the scores of two metrics, yellow indicates the AUROC score, and blue indicates the TPR@5% FPR.", "source": "marker_v2", "marker_block_id": "/page/15/FigureGroup/236"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0143", "section": "C.2. Sub-module Ablation Experiment", "page_start": 16, "page_end": 16, "type": "Text", "text": "the optimal AUC and TPR@5% FPR scores across both datasets. Though the performance differences between individual ablation variants are mild, ATT-related sub-modules show slightly stronger discriminative power than FFN-related ones, with K-Proj performing prominently among ATT sub-modules; in contrast, among FFN sub-modules, Down-Proj and Gate-Proj contribute more to detection performance than Up-Proj, as retaining the former two yields slightly higher AUC and TPR scores. The performance gap between single-sub-module variants and the full model further confirms the necessity of multi-sub-module feature fusion, which enables the capture of comprehensive gradient patterns across the Transformer architecture. It can be seen from this that our method also achieves excellent performance with smaller LoRA adaptation parameters and lower computational complexity.", "source": "marker_v2", "marker_block_id": "/page/15/Text/3"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0144", "section": "C.3. Low-Data Scenarios", "page_start": 16, "page_end": 16, "type": "Text", "text": "To evaluate the data efficiency of our method in scenarios with limited training data, we adjust the training-testing split ratio of the WikiMIA dataset to five settings: 1:9, 2:8, 3:7 and 4:6, while keeping the total sample size fixed. Figure Y shows AUC and TPR@5% FPR scores across different split ratios.", "source": "marker_v2", "marker_block_id": "/page/15/Text/5"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0145", "section": "C.3. Low-Data Scenarios", "page_start": 16, "page_end": 16, "type": "Text", "text": "Figure 9 show our method's performance improves steadily with increasing training set size. Notably, it achieves an AUC of 0.9 even with only 10% of data, accompanied by a TPR@5% FPR of 0.48, confirming that it can also achieve excellent performance with a small amount of data.", "source": "marker_v2", "marker_block_id": "/page/15/Text/6"}

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+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0000", "section": "Abstract", "page_start": 1, "page_end": 1, "type": "Text", "text": "Pre-training data detection for LLMs is essential for addressing copyright concerns and mitigating benchmark contamination. Existing methods mainly focus on the likelihood-based statistical features or heuristic signals before and after finetuning, but the former are susceptible to word frequency bias in corpora, and the latter strongly depend on the similarity of fine-tuning data. From an optimization perspective, we observe that during training, samples transition from unfamiliar to familiar in a manner reflected by systematic differences in gradient behavior. Familiar samples exhibit smaller update magnitudes, distinct update locations in model components, and more sharply activated neurons. Based on this insight, we propose GDS, a method that identifies pre-training data by probing Gradient Deviation Scores of target samples. Specifically, we first represent each sample using gradient profiles that capture the magnitude, location, and concentration of parameter updates across FFN and Attention modules, revealing consistent distinctions between member and non-member data. These features are then fed into a lightweight classifier to perform binary membership inference. Experiments on five public datasets show that GDS achieves state-ofthe-art performance with significantly improved cross-dataset transferability over strong baselines. Further interpretability analyse show gradient feature distribution differences, enabling practical and scalable pre-training data detection.", "source": "marker_v2", "marker_block_id": "/page/0/Text/4"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0001", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "Large language models (LLMs) performance scales with the size and quality of pre-training data (Kaplan et al., 2020) .", "source": "marker_v2", "marker_block_id": "/page/0/Text/6"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0002", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "FigureGroup", "text": "Figure 1. Heat maps of gradient matrices from the unfamiliar stage (epochs 0–1, panels a, c) to the familiar stage (epochs 6–7, panels b, d). Panels a and b display the update magnitude of the FFN module in layer 30, while panels c and d illustrate the update positions, with white for sparse and blue for core updates.", "source": "marker_v2", "marker_block_id": "/page/0/FigureGroup/453"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0003", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "As pre-training corpora expand to trillions of tokens and become increasingly proprietary and non-transparent, they raise significant concerns, such as unauthorized copyright, biased or harmful content, and contamination of evaluation benchmarks (Balloccu et al., 2024; Grynbaum & Mac, 2023) . These challenges motivate a specialized task of membership inference attacks, named pre-training data detection: determining whether a given text sample was included in a model's pre-training corpus (Carlini et al., 2021) .", "source": "marker_v2", "marker_block_id": "/page/0/Text/11"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0004", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "Recent studies (Carlini et al., 2021; Li; Shi et al., 2024; Zhang et al., 2025) primarily use likelihood-based statistical features to detect pre-training samples. For example, the Min-K method (Shi et al., 2024; Zhang et al., 2025) examines the k% of tokens with the lowest predicted probabilities, assuming non-member texts contain more low-likelihood tokens. However, these approaches are susceptible to word frequency bias in pre-training corpora, specifically for rare words or short texts scenarios. To improve detection accuracy, other researchers (Zhang et al.; Choi et al.) propose to analyze heuristic signals before and after fine-tuning, leveraging the fact that fine-tuning impacts member and non-member samples differently. For example, KDS (Choi et al.) shows that non-member datasets exhibit much larger embedding changes, while FSD (Zhang et al.) finds that their loss reductions are also significantly greater. Neverthe-", "source": "marker_v2", "marker_block_id": "/page/0/Text/12"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0005", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "less, these methods rely on the strong assumption that finetuning data closely match the target samples' distribution, requiring additional training on similar non-member data and thereby limiting cross-dataset generalization. Therefore, how to achieve highly generalizable pre-training data detection remains an open problem.", "source": "marker_v2", "marker_block_id": "/page/1/Text/1"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0006", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "Pretraining can be viewed as a gradual shift from unfamiliarity to familiarity with data. Optimization theory (Ruder, 2016; Frankle et al.; Wang et al., 2024) suggests that training drives parameters toward data-specific structure, reflected in consistent update patterns across magnitude, location, and concentration. As shown in Figure 1 and Section 3, we observe the following trends:", "source": "marker_v2", "marker_block_id": "/page/1/Text/2"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0007", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "ListGroup", "text": "1. Decay of update magnitude. Figure 1( a,b) shows that parameter updates are strongly attenuated as data grows familiar, consistent with loss-convergence theory (Bottou, 2010; Ruder, 2016) . 2. Gradually stabilizing of update locations. Figure 1( c,d) shows that parameter updates evolve from broad activation regions to a stable core set of neurons, consistent with the sparse activation behavior of LLMs (Liu et al., 2024) . 3. Increasing update sparsity. Figure 1( a,b) and Figures 2( b,c) show that during training, an increasing fraction of updates concentrates in the top 10% of neurons, consistent with Hessian spectrum reshaping during loss convergence (Gur-Ari et al., 2018) . Familiar data yields sparse, concentrated updates, whereas unfamiliar data leads to more distributed updates.", "source": "marker_v2", "marker_block_id": "/page/1/ListGroup/529"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0008", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "These observations reflect the evolutionary dynamics of neural network training, highlighting phase differences in parameter updates induced by identical samples. Together, they offer both theoretical motivation and empirical support for our detection method based on gradient deviation scores.", "source": "marker_v2", "marker_block_id": "/page/1/Text/6"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0009", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "Based on this insight, we propose GDS, a novel pretraining data detection method that infers pre-training data by probing Gradient Deviation Scores of target samples without fine-tuning. GDS exploits gradient differences between member and non-member samples to train a lightweight classifier with strong generalization. Specifically, within the LoRA framework, we collect per-sample gradients across layers during backpropagation, encoding them as eightdimensional features that capture the magnitude, location, and concentration of updates in attention and FFN modules. Compared to non-members, member samples show smaller matrix-level and row-wise update magnitudes, lower FFN but higher attention eccentricity, greater variability in matrixlevel and row-wise updates, a higher share of top gradients, and fewer sparse neurons. Then, we extract discriminative", "source": "marker_v2", "marker_block_id": "/page/1/Text/7"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0010", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "statistics from the signals to build fixed-dimensional feature vectors, which are fed to a lightweight MLP for binary membership classification.", "source": "marker_v2", "marker_block_id": "/page/1/Text/8"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0011", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "Extensive experiments on five benchmark datasets show that GDS is effective and generalizable, improving AUC by 6.5% and achieving a 67.3% TPR@5%FPR, substantially outperforming strong baselines. Further interpretability analyses reveal distributional differences in gradient features between member and non-member samples, offering intuitive evidence of training data imprints on the model and validating our methodology. 1 Our contributions are as follows:", "source": "marker_v2", "marker_block_id": "/page/1/Text/9"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0012", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "ListGroup", "text": "From a training optimization perspective, we analyze how LLMs evolve from unfamiliarity to familiarity with data and propose using stage-wise parameter update dynamics to identify pretraining data, offering a novel direction to solve this task. We propose gradient deviation features capturing magnitude, location, and concentration, and introduce a gradient deviation score–based method for pretraining data detection without fine-tuning. Extensive experiments across diverse datasets and backbone models validate the effectiveness and generalization of GDS, while interpretability analyses reveal clear gradient differences between member and nonmember samples, supporting its validity.", "source": "marker_v2", "marker_block_id": "/page/1/ListGroup/530"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0013", "section": "2. Related Work", "page_start": 2, "page_end": 2, "type": "Text", "text": "Likelihood-Based Scoring Methods. Early works distinguish member and non-member samples by capturing static statistical metrics in token-level likelihood distributions. Global-likelihood–based methods, such as PPL (Li) , Zlib (Carlini et al., 2021) , and Lowercase (Carlini et al., 2021) , perform discrimination by exploiting global probability features, compression entropy, and case-conversion ratios. However, global likelihood is highly sensitive to wordfrequency effects, leading to unstable performance. Mink% (Shi et al., 2024) and Min-k%++ (Zhang et al., 2025) mitigate global dependence by focusing on low-probability outlier tokens or target–candidate probability comparisons, with k and text length jointly determining the analyzed token subset. However, the fixed choice of k lacks adaptivity, causing severe score fluctuations in short texts with lowfrequency words. Although PC-PDD (Zhang et al., 2024) approximates the word-frequency distribution of pretraining corpora using public datasets, these references lack fidelity due to limited domain coverage.", "source": "marker_v2", "marker_block_id": "/page/1/Text/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0014", "section": "2. Related Work", "page_start": 2, "page_end": 2, "type": "Text", "text": "Fine-tuning Enhanced Methods. To address the instability of static statistical indicators, recent studies (Zhang et al.;", "source": "marker_v2", "marker_block_id": "/page/1/Text/15"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0015", "section": "2. Related Work", "page_start": 2, "page_end": 2, "type": "Footnote", "text": "1 Code in", "source": "marker_v2", "marker_block_id": "/page/1/Footnote/16"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0016", "section": "2. Related Work", "page_start": 3, "page_end": 3, "type": "FigureGroup", "text": "Figure 2. Dynamic curves of four parameter update characteristics defined in the Motivation section. i → j denotes the epoch interval. Ordinate shows values of predefined characteristics, with orange and blue representing Attention and FFN modules.", "source": "marker_v2", "marker_block_id": "/page/2/FigureGroup/764"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0017", "section": "2. Related Work", "page_start": 3, "page_end": 3, "type": "Text", "text": "Choi et al.) adopt lightweight fine-tuning to actively amplify asymmetric differences between member and non-member samples. KDS (Choi et al.) evaluates dataset contamination by comparing kernel similarity matrices of embeddings before and after fine-tuning, assuming non-member datasets undergo larger embedding changes than member datasets. However, it only estimates dataset-level contamination and cannot reliably detect contamination at the sample-level. Another representative method FSD (Zhang et al.) detects membership by comparing loss before and after fine-tuning, assuming non-member samples experience a larger loss reduction than member samples. Nevertheless, these methods assume that fine-tuning data closely matches the target distribution, requiring additional tuning on similar non-member data, which limits cross-dataset generalization.", "source": "marker_v2", "marker_block_id": "/page/2/Text/3"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0018", "section": "3. Motivation", "page_start": 3, "page_end": 3, "type": "Text", "text": "Inspired by optimization theory (Ruder, 2016; Bottou, 2010) , we examine how LLMs transition from unfamiliarity to familiarity with data, and how this cognitive shift relates to the dynamic evolution of model parameters during training. To evaluate it, we fine-tune LLaMA-7B with LoRA on the unseen split of BookMIA dataset and track LoRA parameter updates over 7 epochs. Stage-wise analysis in Figure 2 reveals the dynamic evolution of gradient features.", "source": "marker_v2", "marker_block_id": "/page/2/Text/5"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0019", "section": "3.1. Decay of Update Magnitude", "page_start": 3, "page_end": 3, "type": "Text", "text": "Model training aims to minimize the loss function L(θ), with update magnitude determined by the gradient norm ∥∇L(θ)∥. According to optimization convergence theory (Ruder, 2016) , as the parameters θ t approach the optimum θ ∗ , the gradient norm of the loss function vanishes, i.e.,limθ→ θ ∗ ∥∇L(θt)∥ = 0. This causes the parameter update magnitude to decrease synchronously. Therefore, we use ∆θ t as the core indicator of the average update magnitude across all trainable parameters at iteration t:", "source": "marker_v2", "marker_block_id": "/page/2/Text/7"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0020", "section": "3.1. Decay of Update Magnitude", "page_start": 3, "page_end": 3, "type": "Equation", "text": "\\Delta \\theta_{t} = \\frac{1}{N} \\sum_{i=1}^{N} |\\theta_{t,i} - \\theta_{t-1,i}|, \\qquad (1)", "source": "marker_v2", "marker_block_id": "/page/2/Equation/8"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0021", "section": "3.1. Decay of Update Magnitude", "page_start": 3, "page_end": 3, "type": "Text", "text": "where N denotes the total number of trainable parameters.", "source": "marker_v2", "marker_block_id": "/page/2/Text/9"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0022", "section": "3.1. Decay of Update Magnitude", "page_start": 3, "page_end": 3, "type": "Text", "text": "As training progresses, both the loss L(θt) and gradient norm ∥∇L(θt)∥ decrease, reducing the update magnitude ∆θ t and slowing its decay as parameters converge to the optimum θ ∗ . Eventually, L(θt) stabilizes near its minimum, parameter updates ∆θ t become negligible. As shown in Figure 2a, the mean update magnitude decreases monotonically with training, with the largest changes occurring in the first two epochs, consistent with loss convergence.", "source": "marker_v2", "marker_block_id": "/page/2/Text/10"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0023", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 3, "page_end": 3, "type": "Text", "text": "Existing studies (Liu et al., 2024; Tang et al., 2025) have shown that neural activations occur at different locations when processing member samples and non-member samples. Inspired by this, we adopt the parameter update eccentricity as the core indicator, which quantifies the deviation of the top-10% parameter update positions from the global parameter centroid. We first define the global centroid as:", "source": "marker_v2", "marker_block_id": "/page/2/Text/12"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0024", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 3, "page_end": 3, "type": "Equation", "text": "\\theta_c = \\frac{1}{N} \\sum_{i=1}^{N} \\theta_i, \\tag{2}", "source": "marker_v2", "marker_block_id": "/page/2/Equation/13"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0025", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 3, "page_end": 3, "type": "Text", "text": "where θ i is the coordinate of the i-th parameter.", "source": "marker_v2", "marker_block_id": "/page/2/Text/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0026", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 3, "page_end": 3, "type": "Text", "text": "The update eccentricity at iteration t is then defined as:", "source": "marker_v2", "marker_block_id": "/page/2/Text/15"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0027", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 3, "page_end": 3, "type": "Equation", "text": "E_{t} = \\frac{1}{\\operatorname{card}(U_{10,t})} \\sum_{\\theta_{i} \\in U_{10,t}} \\|\\theta_{i} - \\theta_{c}\\|_{2}, (3)", "source": "marker_v2", "marker_block_id": "/page/2/Equation/16"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0028", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 3, "page_end": 3, "type": "Text", "text": "where card(·) denotes the number of elements in a set, U10,t = {∥∆θt,i∥ 1 ∈ Top10%(∥∆θt∥1)}, ∥ · ∥ 1 denotes the ℓ 1 norm and ∥ · ∥ 2 denotes the ℓ 2 norm.", "source": "marker_v2", "marker_block_id": "/page/2/Text/17"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0029", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 3, "page_end": 3, "type": "Text", "text": "In the initial training stage, activation patterns are unstable, leading to scattered U10,t and thus random large values of Et. As training proceeds, the model identifies core parameters related to data features: θ t stabilizes to the optimal subset θ ∗ , and U10,t converges to the core parameter region, resulting in E t gradually stabilizing at a low level. Figure 2d shows that the eccentricity of parameter update evolves to a relatively stable value, consistent with the evolution of the", "source": "marker_v2", "marker_block_id": "/page/2/Text/18"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0030", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 4, "page_end": 4, "type": "FigureGroup", "text": "Figure 3. Overview of Gradient Deviation Scores method.", "source": "marker_v2", "marker_block_id": "/page/3/FigureGroup/643"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0031", "section": "3.2. Gradually Stabilizing of Update Locations", "page_start": 4, "page_end": 4, "type": "Text", "text": "neuron activation pattern, suggesting that training identifies the core parameters and stabilizes updates around them.", "source": "marker_v2", "marker_block_id": "/page/3/Text/4"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0032", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Text", "text": "The Hessian spectrum (Gur-Ari et al., 2018; Frankle et al.) is a core metric characterizing the loss function's curvature, directly determining the direction and efficiency of parameter updates. For the loss function L(θ), its Hessian matrix H(θ) = ∇2L(θ) describes the local curvature of the loss landscape, with eigenvalue decomposition:", "source": "marker_v2", "marker_block_id": "/page/3/Text/6"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0033", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Equation", "text": "\\mathcal{H}(\\theta) = U\\Lambda U^T,\\tag{4}", "source": "marker_v2", "marker_block_id": "/page/3/Equation/7"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0034", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Text", "text": "where U is the orthogonal eigenvector matrix (principal curvature directions), Λ = diag(λ1, . . . , λd) is the diagonal eigenvalue matrix (curvature magnitudes). During training, the Hessian spectrum changes from an almost uniform λ i ≈ c in the early stage to a late-stage structure with a few large eigenvalues and most near zero.", "source": "marker_v2", "marker_block_id": "/page/3/Text/8"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0035", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Text", "text": "This reshaping leads to concentrated updates, focusing on directions with large eigenvalues while leaving most others nearly unchanged. Consequently, update energy is confined to a small subset of parameters, motivating the selection of two joint indicators. S t measures the fraction of parameters with negligible updates (absolute value < 10 − 6 ) at iteration t, while T10,t measures the fraction of total update magnitude contributed by the top 10% largest updates.", "source": "marker_v2", "marker_block_id": "/page/3/Text/9"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0036", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Equation", "text": "S_t = \\frac{\\operatorname{card}\\left(i \\mid |\\Delta \\theta_{t,i}| < 10^{-6}\\right)}{N},\\tag{5}", "source": "marker_v2", "marker_block_id": "/page/3/Equation/10"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0037", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Equation", "text": "T_{10,t} = \\frac{\\sum_{|\\Delta\\theta_{t,i}| \\in U_{10,t}} |\\Delta\\theta_{t,i}|}{||\\Delta\\theta_t||_1}. (6)", "source": "marker_v2", "marker_block_id": "/page/3/Equation/11"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0038", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Text", "text": "As training progresses, parameter updates increasingly concentrate along core directions, with most parameters receiving negligible changes. Consequently, S t gradually", "source": "marker_v2", "marker_block_id": "/page/3/Text/12"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0039", "section": "3.3. Increasing Update Sparsity", "page_start": 4, "page_end": 4, "type": "Text", "text": "increases, while T10,t remains relatively large and stable(0.26–0.27), indicating that update energy is consistently dominated by a small subset of parameters. Figures 2b and 2c confirm this growing sparsity and stable Top 10% contribution, reflecting update energy aggregation driven by Hessian spectrum reshaping. Further details on the variation trends of the three metrics are provided in the appendix B.", "source": "marker_v2", "marker_block_id": "/page/3/Text/13"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0040", "section": "4.1. Task Definition", "page_start": 4, "page_end": 4, "type": "Text", "text": "Given a target text x and a target LLM f θ pre-trained on a corpus D, the goal of pre-training data detection task is to construct a detector h(x, fθ)to determine whether x belongs to D. This task can be formalized as a binary classification problem: h(x, fθ) → {0, 1} where \"1\" indicates x ∈ D as member and \"0\" indicates x /∈ D as non-member.", "source": "marker_v2", "marker_block_id": "/page/3/Text/16"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0041", "section": "4.1. Task Definition", "page_start": 4, "page_end": 4, "type": "Text", "text": "As illustrated in Figure 3, GDS comprises three stages: gradient matrix acquisition, feature vector extraction and light Multilayer Perceptron(MLP) training. For each training sample, we perform inference and backpropagation to obtain LoRA gradients across l layers and m sub-modules, yielding l × m gradient matrices G. From these matrices, we extract eight-dimensional features to form a gradient feature vector V l×m×8 , which is used to train a lightweight MLP classifier for binary membership prediction. During inference, the same feature extraction process is applied to a target sample x ∗ , and the resulting feature vector is fed into the trained MLP to produce the final classification result.", "source": "marker_v2", "marker_block_id": "/page/3/Text/17"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0042", "section": "4.2. Gradient Matrix Acquisition", "page_start": 4, "page_end": 4, "type": "Text", "text": "Given the target model f θ and training sample x, we first initialize f θ with LoRA, yielding l × m LoRA matrices L. We then feed a single sample x into f θ for forward", "source": "marker_v2", "marker_block_id": "/page/3/Text/19"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0043", "section": "4.2. Gradient Matrix Acquisition", "page_start": 5, "page_end": 5, "type": "Text", "text": "inference and backpropagation, obtaining LoRA gradient matrices \\mathbb{G} = \\nabla_{\\mathbb{L}} \\mathcal{L}_{\\text{CLM}}(f_{\\theta}(x)) , where \\mathcal{L}_{\\text{CLM}} denotes the causal language modeling loss of the pre-trained LLM. Since the LoRA_B matrices are fully initialized to zero, a single round of gradient propagation leads to zero gradients for the LoRA_A matrices. Thus, we only collect the gradient matrices of LoRA_B for subsequent processing.", "source": "marker_v2", "marker_block_id": "/page/4/Text/2"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0044", "section": "4.3. Feature Vector Extraction", "page_start": 5, "page_end": 5, "type": "Text", "text": "Given the gradient matrices \\mathbb{G} , we extract features based on the three parameter update trends introduced in Section 3.", "source": "marker_v2", "marker_block_id": "/page/4/Text/4"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0045", "section": "4.3.1. MAGNITUDE", "page_start": 5, "page_end": 5, "type": "Text", "text": "We propose two magnitude indicators to measure the overall scale of gradient updates in the LoRA parameter space.", "source": "marker_v2", "marker_block_id": "/page/4/Text/6"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0046", "section": "4.3.1. MAGNITUDE", "page_start": 5, "page_end": 5, "type": "Text", "text": "(1) Absolute Mean : The mean of the absolute values of all elements in the gradient matrix, which characterizes the overall parameter update strength:", "source": "marker_v2", "marker_block_id": "/page/4/Text/7"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0047", "section": "4.3.1. MAGNITUDE", "page_start": 5, "page_end": 5, "type": "Equation", "text": "Abs\\_Mean = \\frac{1}{r \\cdot h} \\sum_{i=1}^{r} \\sum_{j=1}^{h} |\\mathbb{G}_{i,j}|, (7)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/8"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0048", "section": "4.3.1. MAGNITUDE", "page_start": 5, "page_end": 5, "type": "Text", "text": "where \\mathbb{G}_{i,j} denotes the element in the i -th row and j -th column of the gradient matrix with r rows and h columns.", "source": "marker_v2", "marker_block_id": "/page/4/Text/9"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0049", "section": "4.3.1. MAGNITUDE", "page_start": 5, "page_end": 5, "type": "Text", "text": "(2) Max Row Mean: The mean of each row in the LoRA matrix and take the maximum value, which characterizes the most sample-responsive local optimal response dimension with the largest parameter update magnitude:", "source": "marker_v2", "marker_block_id": "/page/4/Text/10"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0050", "section": "4.3.1. MAGNITUDE", "page_start": 5, "page_end": 5, "type": "Equation", "text": "Row\\_Mean\\_Max = \\max_{1 \\le i \\le r} \\left( \\frac{1}{h} \\sum_{j=1}^{h} |\\mathbb{G}_{i,j}| \\right). (8)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/11"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0051", "section": "4.3.2. Position", "page_start": 5, "page_end": 5, "type": "Text", "text": "Screen the top 10% of gradient elements by absolute value from \\mathbb{G} and calculate their offset from this matrix center, capturing offset characteristics of core gradient positions for (1) Row Eccentricity and (2) Column Eccentricity, respectively:", "source": "marker_v2", "marker_block_id": "/page/4/Text/13"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0052", "section": "4.3.2. Position", "page_start": 5, "page_end": 5, "type": "Equation", "text": "Row\\_Ecc = \\frac{1}{\\operatorname{card}(S)} \\sum_{(i,j) \\in S} \\left| \\frac{2i - (r+1)}{r-1} \\right|, \\quad (9)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0053", "section": "4.3.2. Position", "page_start": 5, "page_end": 5, "type": "Equation", "text": "Col\\_Ecc = \\frac{1}{\\operatorname{card}(S)} \\sum_{(i,j) \\in S} \\left| \\frac{2j - (h+1)}{h-1} \\right|, \\quad (10)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/15"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0054", "section": "4.3.2. Position", "page_start": 5, "page_end": 5, "type": "Text", "text": "where S = \\{(i,j) \\mid |\\mathbb{G}_{i,j}| \\in \\text{Top10\\%}(|\\mathbb{G}|)\\} denotes the set of indices for the top 10% of elements in the gradient matrix \\mathbb{G} ranked by absolute gradient value. Top gradients near the center correspond to an eccentricity of 0, while those near the edge correspond to a score of 1.", "source": "marker_v2", "marker_block_id": "/page/4/Text/16"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0055", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Text", "text": "We propose four indicators to measure the concentration of gradient distributions.", "source": "marker_v2", "marker_block_id": "/page/4/Text/18"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0056", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Text", "text": "(1) Top-10% Ratio : The ratio of the sum of the top 10% largest gradient magnitudes to the total update magnitude of the gradient matrix, which quantifies the contribution ratio of core gradients:", "source": "marker_v2", "marker_block_id": "/page/4/Text/19"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0057", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Equation", "text": "10p\\_Ratio = \\frac{\\sum_{(i,j)\\in S} |\\mathbb{G}_{i,j}|}{\\|\\mathbb{G}\\|_1}, \\tag{11}", "source": "marker_v2", "marker_block_id": "/page/4/Equation/20"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0058", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Text", "text": "(2) Sparsity : The proportion of gradient elements with absolute values less than 10^{-6} , which quantifies the sparsity degree of gradient distributions:", "source": "marker_v2", "marker_block_id": "/page/4/Text/21"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0059", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Equation", "text": "Sparsity = \\frac{\\operatorname{card}\\left(\\left\\{\\left(i,j\\right) \\mid |\\mathbb{G}_{i,j}| < 10^{-6}\\right\\}\\right)}{r \\cdot h}. (12)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/22"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0060", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Text", "text": "(3) Standard Deviation : The standard deviation of the elements in the gradient matrix, which quantifies the dispersion degree of parameter updates:", "source": "marker_v2", "marker_block_id": "/page/4/Text/23"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0061", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Equation", "text": "Std = \\sqrt{\\frac{1}{r \\cdot h} \\sum_{i=1}^{r} \\sum_{j=1}^{h} (|\\mathbb{G}_{i,j}| - \\text{Abs\\_mean})^2}. (13)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/24"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0062", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Text", "text": "(4) Row Mean Standard Deviation: The mean of each row in the LoRA matrix and take the standard deviation, which quantifies the consistency of update strength across all rows:", "source": "marker_v2", "marker_block_id": "/page/4/Text/25"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0063", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Equation", "text": "Row\\_Mean\\_Std = \\sqrt{\\frac{1}{r} \\sum_{i=1}^{r} \\left(\\bar{\\mathbb{G}}_i - \\mu_{\\bar{\\mathbb{G}}}\\right)^2}, \\quad (14)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/26"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0064", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Text", "text": "where \\bar{\\mathbb{G}}_i = \\frac{1}{h} \\sum_{j=1}^h |\\mathbb{G}_{i,j}| denotes the i -th row's absolute mean, \\mu_{\\bar{\\mathbb{G}}} = \\frac{1}{r} \\sum_{i=1}^r \\bar{\\mathbb{G}}_i denotes t the mean of row means.", "source": "marker_v2", "marker_block_id": "/page/4/Text/27"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0065", "section": "4.3.3. CONCENTRATION", "page_start": 5, "page_end": 5, "type": "Text", "text": "We compute the aforementioned eight feature values from all gradient matrices to derive a feature vector \\mathbb{V}^{l\\times m\\times 8} \\triangleq [Abs_Mean, Row_Mean_Max, 10p_Ratio, Sparsity, Std, Row_Mean_Std, Row_Ecc, Col_Ecc] per sample, which is then used for subsequent MLP training and inference.", "source": "marker_v2", "marker_block_id": "/page/4/Text/28"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0066", "section": "4.4. Light MLP Training", "page_start": 5, "page_end": 5, "type": "Text", "text": "Given the feature vectors \\mathbb{V}_i from all training samples vectors \\mathbb{V}_s , we feed them into a lightweight MLP for training. The target output corresponds to the binary label \\{0,1\\} for each sample, where 0 denotes non-member and 1 denotes member. The training loss is defined as follows:", "source": "marker_v2", "marker_block_id": "/page/4/Text/30"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0067", "section": "4.4. Light MLP Training", "page_start": 5, "page_end": 5, "type": "Equation", "text": "\\mathcal{L} = -\\frac{1}{N} \\sum_{i=1}^{N} \\left[ y_i \\log \\hat{y}_i + (1 - y_i) \\log(1 - \\hat{y}_i) \\right], \\quad (15)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/31"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0068", "section": "4.4. Light MLP Training", "page_start": 5, "page_end": 5, "type": "Text", "text": "where N denotes the number of training samples, y_i \\in \\{0,1\\} is the ground-truth label of the i-th sample, and \\hat{y}_i is the predicted probability output by the MLP.", "source": "marker_v2", "marker_block_id": "/page/4/Text/32"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0069", "section": "4.4. Light MLP Training", "page_start": 6, "page_end": 6, "type": "TableGroup", "text": "Table 1. Comparison(AUROC/TPR@5%FPR) on 4 Datasets across 5 target models. Target models are denoted as 2.7B/6B/6.7B/6.9B/7B, corresponding to Neo-2.7B/GPT-J-6b/OPT-6.7b/Pythia-6.9b/LLaMA-7B respectively. The best result is bold. WikiMIA ArXivTection Method 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B PPL 0.61/0.13 0.64/0.13 0.60/0.12 0.63/0.13 0.69/0.14 0.62/0.13 0.64/0.13 0.60/0.12 0.63/0.13 0.70/0.14 ZLib 0.58/0.10 0.60/0.11 0.58/0.10 0.59/0.10 0.71/0.22 0.58/0.10 0.60/0.11 0.58/0.09 0.59/0.11 0.71/0.22 Min-k 0.65/0.17 0.67/0.19 0.63/0.15 0.67/0.19 0.73/0.18 0.65/0.17 0.68/0.19 0.63/0.15 0.67/0.19 0.72/0.18 Min-k++ 0.67/0.15 0.69/0.19 0.65/0.11 0.70/0.18 0.82/0.22 0.67/0.15 0.69/0.19 0.65/0.10 0.70/0.17 0.83/0.22 FSD 0.92/0.77 0.95/0.78 0.90/0.63 0.90/0.66 0.92/0.41 0.91/0.65 0.96/0.79 0.89/0.63 0.95/0.66 0.94/0.81 Ours 0.90/0.60 0.93/0.66 0.94/0.67 0.92/0.63 0.96/0.84 0.94/0.73 0.97/0.86 0.94/0.75 0.95/0.83 0.97/0.85 BookTection BookMIA Method 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B PPL 0.69/0.15 0.74/0.25 0.64/0.13 0.73/0.25 0.71/0.25 0.29/0.02 0.22/0.13 0.23/0.01 0.59/0.19 0.56/0.21 ZLib 0.56/0.16 0.58/0.20 0.55/0.14 0.58/0.19 0.57/0.19 0.20/0.02 0.38/0.13 0.15/0.00 0.49/0.17 0.48/0.18 Min-k 0.71/0.18 0.75/0.27 0.67/0.15 0.74/0.26 0.71/0.25 0.45/0.05 0.60/0.20 0.40/0.03 0.62/0.20 0.60/0.21 Min-k++ 0.64/0.13 0.67/0.18 0.61/0.11 0.66/0.19 0.63/0.15 0.54/0.13 0.64/0.29 0.49/0.09 0.60/0.23 0.58/0.20 FSD 0.92/0.53 0.91/0.52 0.96/0.77 0.93/0.59 0.92/0.55 0.98/0.93 0.97/0.89 0.98/0.96 0.98/0.93 0.98/0.91 Ours 0.96/0.84 0.97/0.88 0.98/0.92 0.96/0.83 0.98/0.92 0.99/0.98 0.99/0.99 0.99/0.99 0.99/0.98 0.99/0.99 Table 2. Performance Comparison on Mimir datasets with 7 subsets across 5 target models using AUROC scores.", "source": "marker_v2", "marker_block_id": "/page/5/TableGroup/510"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0070", "section": "4.4. Light MLP Training", "page_start": 6, "page_end": 6, "type": "Table", "text": "Wikipedia Github Pile CC PubMed Central Method 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B PPL 0.56 0.57 0.56 0.56 0.56 0.78 0.79 0.78 0.90 0.83 0.56 0.57 0.56 0.56 0.52 0.78 0.79 0.78 0.78 0.72 ZLib 0.62 0.65 0.59 0.65 0.58 0.90 0.91 0.79 0.91 0.86 0.55 0.55 0.55 0.55 0.52 0.78 0.78 0.73 0.77 0.71 Min-k 0.66 0.68 0.65 0.68 0.63 0.88 0.89 0.76 0.90 0.83 0.56 0.57 0.56 0.56 0.52 0.81 0.80 0.74 0.79 0.72 Min-k++ 0.65 0.68 0.60 0.69 0.56 0.84 0.86 0.56 0.86 0.73 0.54 0.55 0.54 0.56 0.51 0.71 0.72 0.60 0.70 0.59 FSD 0.61 0.67 0.60 0.65 0.60 0.77 0.80 0.62 0.77 0.72 0.55 0.55 0.54 0.55 0.52 0.71 0.79 0.63 0.56 0.63 Ours 0.63 0.64 0.65 0.65 0.64 0.90 0.92 0.88 0.92 0.91 0.59 0.59 0.59 0.57 0.59 0.84 0.85 0.84 0.79 0.82 ArXiv DM Mathematics HackerNews Average Method 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B PPL 0.78 0.79 0.65 0.78 0.70 0.78 0.79 0.65 0.91 0.31 0.65 0.62 0.59 0.62 0.59 0.64 0.66 0.62 0.73 0.59 ZLib 0.77 0.78 0.68 0.77 0.71 0.82 0.81 0.80 0.81 0.23 0.68 0.60 0.58 0.60 0.58 0.65 0.67 0.63 0.72 0.58 Min-k 0.78 0.79 0.65 0.78 0.70 0.93 0.93 0.92 0.92 0.32 0.65 0.62 0.59 0.62 0.59 0.71 0.73 0.69 0.75 0.60 Min-k++ 0.60 0.64 0.53 0.70 0.57 0.77 0.79 0.67 0.75 0.22 0.53 0.57 0.51 0.60 0.53 0.60 0.63 0.56 0.67 0.53 FSD 0.72 0.78 0.55 0.70 0.52 0.58 0.85 0.60 0.74 0.53 0.61 0.60 0.57 0.56 0.51 0.61 0.66 0.59 0.62 0.55 Ours 0.78 0.79 0.78 0.78 0.77 0.95 0.95 0.94 0.95 0.95 0.58 0.60 0.60 0.57 0.58 0.73 0.75 0.74 0.76 0.70", "source": "marker_v2", "marker_block_id": "/page/5/Table/5"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0071", "section": "5.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "Datasets Following prior work, we evaluate on five prevalent datasets: WikiMIA, BookMIA (Shi et al., 2024) ,ArxivTection, BookTection (Duarte et al.) , and MIMIR (Duan et al.) , a widely recognized challenging benchmark for pretraining data detection.", "source": "marker_v2", "marker_block_id": "/page/5/Text/8"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0072", "section": "5.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "Target Models We evaluate five open-source LLMs with diverse architectures: Neo-2.7B (Black et al., 2021) , GPT-J-6B (Wang & Komatsuzaki, 2021) , OPT-6.7B (Zhang et al., 2022) , Pythia-6.9B (Biderman et al., 2023) , and LLaMA-7B (Touvron et al., 2023) from Hugging Face.", "source": "marker_v2", "marker_block_id": "/page/5/Text/9"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0073", "section": "5.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "Comparison Methods We select five representative stateof-the-art baselines. Four scoring function–based methods", "source": "marker_v2", "marker_block_id": "/page/5/Text/10"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0074", "section": "5.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "include PPL (Carlini et al., 2021) , ZLib (Carlini et al., 2021) , Min-k (Shi et al., 2024) , and Min-k++ (Zhang et al., 2025) . The fine-tuning–enhanced method includes FSD (Zhang et al.) . More details are shown in Appendix A.", "source": "marker_v2", "marker_block_id": "/page/5/Text/11"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0075", "section": "5.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "Evaluation Metrics Two metrics evaluate the binary pretraining data detection task: AUROC measures overall discriminative performance, and TPR@5%FPR captures practical effectiveness by assessing detection rate under a 5% false positive constraint.", "source": "marker_v2", "marker_block_id": "/page/5/Text/12"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0076", "section": "5.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "Implementation Details We use the PEFT library (Man grulkar et al., 2022) for LoRA-based (Hu et al., 2022) gradient feature extraction without parameter updates. The MLP is trained on 30% of the data, with the remaining 70% used for inference evaluation under FSD settings. More Details can be seen in Appendix A.6.", "source": "marker_v2", "marker_block_id": "/page/5/Text/13"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0077", "section": "5.1. Experimental Setup", "page_start": 7, "page_end": 7, "type": "FigureGroup", "text": "Figure 4. Distribution differences of eight gradient features between member(red) and non-member(blue) samples. Dashed lines indicate distribution means. The x-axis represents feature values, and the y-axis denotes probability density.", "source": "marker_v2", "marker_block_id": "/page/6/FigureGroup/466"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0078", "section": "5.1. Experimental Setup", "page_start": 7, "page_end": 7, "type": "TableGroup", "text": "Table 3. Ablation results using AUROC on WikiMIA and Arxiv-Tection. - denotes the removal of related features. Dataset -Magnitude -Concentration -Position WikiMIA 0.94 (↓0.02) 0.94 (↓0.02) 0.93 (↓0.03) ArxivTection 0.96 (↓0.01) 0.95 (↓0.02) 0.95 (↓0.02) Table 4. Ablation results using AUROC and TPR@5%FPR. ATT-Only refers to performance validation using only attention module.", "source": "marker_v2", "marker_block_id": "/page/6/TableGroup/467"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0079", "section": "5.1. Experimental Setup", "page_start": 7, "page_end": 7, "type": "Table", "text": "Dataset ATT-Only FFN-Only Origin WikiMIA 0.94 / 0.68 0.93 / 0.64 0.96 / 0.84 ArxivTection 0.95 / 0.76 0.93 / 0.72 0.97 / 0.85", "source": "marker_v2", "marker_block_id": "/page/6/Table/6"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0080", "section": "5.2. Main Results", "page_start": 7, "page_end": 7, "type": "Text", "text": "Table 1 shows detection performance on WikiMIA, Arxiv-Tection, BookTection, and BookMIA. Specifically, when tested on WikiMIA with LLaMA-7B, GDS achieves an AUC score of 0.96, which is an improvement of 0.04 compared to the best baseline FSD and significantly higher than score-function-based methods such as Min-k++. GDS outperforms the best baseline in most settings, with especially large gains in TPR@5%FPR on BookTection and Book-MIA. Notably, with LLaMA-7B, BookTection performance improves by nearly 67.3%.", "source": "marker_v2", "marker_block_id": "/page/6/Text/8"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0081", "section": "5.2. Main Results", "page_start": 7, "page_end": 7, "type": "Text", "text": "Table 2 reports results on seven MIMIR subsets. Although all methods degrade due to similar data distributions, GDS achieves the best average improvements +2.8%, +2.7%, +7.2%, +1.3%, +16.6% across different models, and shows clear advantages on PubMed Central, DM Mathematics, and GitHub. Using the LLaMA model, the three subsets achieve AUC scores of 0.82, 0.95, and 0.91. Our method shows the most stable performance across models, with AUC variations mostly within 0.04, demonstrating strong generalization across different models.", "source": "marker_v2", "marker_block_id": "/page/6/Text/9"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0082", "section": "5.3. Ablation Study", "page_start": 7, "page_end": 7, "type": "Text", "text": "We perform two ablation studies: (1) removing each gradient feature category individually, and (2) using features from only the Attention or FFN module. Table 3 shows that all feature categories contribute to performance, with Position Offset and Magnitude being the most important. Concentration features have smaller effects, and the full combination performs best, highlighting the complementary nature of multi-dimensional features (see Appendix C for sub-feature ablations). Table 4 shows that Attention features are more discriminative than FFN features. Both single-module variants underperform the full model, indicating that Attention and FFN capture complementary gradient patterns and must be combined for optimal performance.", "source": "marker_v2", "marker_block_id": "/page/6/Text/11"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0083", "section": "5.4.1. FEATURE DISTRIBUTION", "page_start": 7, "page_end": 7, "type": "Text", "text": "To explain the classifier's effectiveness, we quantify feature distributions across all layers and sub-modules for member and non-member samples. Figure 4 shows the eight features with the largest discrepancies. Member samples exhibit smaller Abs Mean and Row Mean Max, indicating lower gradient magnitudes due to higher data familiarity, along with higher Sparsity, smaller Std and Row Mean Std, reflecting more concentrated and stable gradients. They also maintain a consistently higher 10p Ratio, occupying the core of gradient propagation. For locations Row Ecc and Col Ecc, member samples cluster at lower values, while non-members shift higher, suggesting that member-related parameters lie more centrally in weight matrices.", "source": "marker_v2", "marker_block_id": "/page/6/Text/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0084", "section": "5.4.1. FEATURE DISTRIBUTION", "page_start": 7, "page_end": 7, "type": "Text", "text": "We collect sub-features with the largest distribution differences between the two sample types and analyze their overall distribution patterns. Figure 5 show that discriminative sub-features are predominantly concentrated in low layers, while middle and high layers contribute far less. Among sub-modules, attention-related modules are the main sources", "source": "marker_v2", "marker_block_id": "/page/6/Text/15"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0085", "section": "5.4.1. FEATURE DISTRIBUTION", "page_start": 8, "page_end": 8, "type": "TableGroup", "text": "Table 5. Performance Comparison between LoRA and Full-Parameter Update using AUROC on WikiMIA and ArxivTection. Dataset Metric LLaMA-7B GPT-J-6B OPT-6.7B Pythia-6.9B Neo-2.7B LoRA Full LoRA Full LoRA Full LoRA Full LoRA Full WikiMIA AUC 0.96 0.96 0.93 0.90 0.94 0.92 0.92 0.89 0.90 0.88 TPR@5% FPR 0.84 0.79 0.66 0.58 0.67 0.56 0.63 0.50 0.60 0.51 ArxivTection AUC 0.97 0.96 0.97 0.96 0.94 0.93 0.95 0.94 0.94 0.94 TPR@5% FPR 0.85 0.84 0.86 0.79 0.75 0.67 0.83 0.73 0.73 0.75", "source": "marker_v2", "marker_block_id": "/page/7/TableGroup/516"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0086", "section": "5.4.1. FEATURE DISTRIBUTION", "page_start": 8, "page_end": 8, "type": "FigureGroup", "text": "Figure 5. Distribution Difference Statistics of Discriminative Features. The y-axis shows the statistical count.", "source": "marker_v2", "marker_block_id": "/page/7/FigureGroup/517"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0087", "section": "5.4.1. FEATURE DISTRIBUTION", "page_start": 8, "page_end": 8, "type": "Text", "text": "of discriminative features, with obvious differences in contribution across modules. In terms of gradient features, grad sparsity exhibits the strongest discriminative power, significantly outperforming other indicators.", "source": "marker_v2", "marker_block_id": "/page/7/Text/6"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0088", "section": "5.4.2. FULL PARAMETER TRAINING", "page_start": 8, "page_end": 8, "type": "Text", "text": "In LoRA training, only FFN and MLP modules are updated, while LayerNorm, despite containing meaningful training dynamics, is excluded. To account for this, we evaluate our method under full-parameter training on two small-scale datasets, BookMIA and ArxivTection, for computational feasibility. As shown in Table 5, although full-parameter updates cause a slight performance drop compared to LoRA, our method still outperforms most baselines. We attribute this gap to reduced gradient magnitudes in full training, which weaken discriminative signals between sample types.", "source": "marker_v2", "marker_block_id": "/page/7/Text/8"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0089", "section": "5.4.3. WIKIMIA MODIFICATION", "page_start": 8, "page_end": 8, "type": "Text", "text": "Dataset partitioning can introduce distribution shifts or dataset-specific artifacts. For example, WikiMIA is split by publication time, with all non-member samples labeled as 2023. To ensure our method does not exploit such artifacts, we remove all timestamp tokens and reevaluate all methods. As shown in Table 6, although token removal degrades performance, our method suffers a much smaller drop than the strongest baseline, FSD, and still achieves SOTA results.", "source": "marker_v2", "marker_block_id": "/page/7/Text/10"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0090", "section": "5.4.3. WIKIMIA MODIFICATION", "page_start": 8, "page_end": 8, "type": "TableGroup", "text": "Table 6. Comparison of Temporal Feature Perturbation via AU-ROC. Deletion denotes the removal of all year timestamps. Method Origin Deletion PPL 0.69 0.62 Min-k 0.73 0.63 Min-k++ 0.82 0.59 FSD 0.92 0.76 Ours 0.96 0.84 Table 7. Cross-Dataset Generalization Performance using AU-ROC. Wiki(arXiv) indicates training on ArxivTection with test on WikiMIA, while Mix indicates mixed datasets.", "source": "marker_v2", "marker_block_id": "/page/7/TableGroup/518"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0091", "section": "5.4.3. WIKIMIA MODIFICATION", "page_start": 8, "page_end": 8, "type": "Table", "text": "Method Wiki (arXiv) arXiv (Wiki) Mix FSD 0.52 0.58 0.92 Ours 0.66 0.68 0.95", "source": "marker_v2", "marker_block_id": "/page/7/Table/14"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0092", "section": "5.4.4. TRANSFERABILITY", "page_start": 8, "page_end": 8, "type": "Text", "text": "Although our method shares the same feature extraction framework, it requires dataset-specific classifiers. To examine whether a unified classifier is feasible, we train classifiers on WikiMIA and ArXiv separately and evaluate crossdataset generalization, as well as train a unified classifier on mixed data. Table 7 shows that cross-dataset transfer leads to notable performance degradation due to dataset shifts (e.g., distribution, difficulty, and pre-training differences), which cause classifiers to overfit dataset-specific gradient features. In contrast, the unified classifier performs well on mixed data, indicating that our method can capture universal feature discrepancies arising from model familiarity.", "source": "marker_v2", "marker_block_id": "/page/7/Text/16"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0093", "section": "6. Conclusion", "page_start": 8, "page_end": 8, "type": "Text", "text": "We revisit pre-training data detection from an optimization and training-dynamics perspective and introduce GDS, a fine-tuning–free method for inferring pre-training membership. By analyzing how models transition from unfamiliarity to familiarity, we show that member and non-member samples exhibit stable, interpretable differences in gradient magnitude, location, and concentration across datasets and architectures. Experiments show that GDS is effective and generalizable, outperforming strong baselines. Future work can focus on developing more generalizable detectors by contrastive learning or deeper feature extraction.", "source": "marker_v2", "marker_block_id": "/page/7/Text/18"}
+{"paper_id": "9346049b-7104-494c-9378-955a2d7393ed", "chunk_id": "9346049b-7104-494c-9378-955a2d7393ed:0094", "section": "Limitations", "page_start": 9, "page_end": 9, "type": "Text", "text": "This work investigates pre-training data detection, a form of membership inference that determines whether a given sample was included in a LLM's pre-training corpus. While our proposed GDS method improves detection accuracy and generalization without fine-tuning, it also raises important ethical concerns. Pre-training data detection methods could be misused to probe proprietary or confidential training corpora, potentially revealing sensitive information about data sources or collection practices. Although GDS does not reconstruct or expose training samples directly, it contributes to capabilities that may be exploited if applied irresponsibly. Our primary motivation is to support transparency, accountability, and safety. As pre-training datasets become increasingly large and opaque, tools like GDS can help researchers, auditors, and regulators verify data usage claims, identify potential copyright violations, and detect benchmark contamination. In this sense, GDS is intended as a diagnostic and auditing mechanism rather than a data extraction attack. We release code and models to promote reproducibility while encouraging responsible deployment. Overall, we hope this work advances trustworthy and transparent large-scale model development while highlighting the need for careful governance of pre-training data.", "source": "marker_v2", "marker_block_id": "/page/8/Text/2"}

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@@ -0,0 +1,284 @@
+[p. 1 | section: Abstract | type: Text]
+Pre-training data detection for LLMs is essential for addressing copyright concerns and mitigating benchmark contamination. Existing methods mainly focus on the likelihood-based statistical features or heuristic signals before and after finetuning, but the former are susceptible to word frequency bias in corpora, and the latter strongly depend on the similarity of fine-tuning data. From an optimization perspective, we observe that during training, samples transition from unfamiliar to familiar in a manner reflected by systematic differences in gradient behavior. Familiar samples exhibit smaller update magnitudes, distinct update locations in model components, and more sharply activated neurons. Based on this insight, we propose GDS, a method that identifies pre-training data by probing Gradient Deviation Scores of target samples. Specifically, we first represent each sample using gradient profiles that capture the magnitude, location, and concentration of parameter updates across FFN and Attention modules, revealing consistent distinctions between member and non-member data. These features are then fed into a lightweight classifier to perform binary membership inference. Experiments on five public datasets show that GDS achieves state-ofthe-art performance with significantly improved cross-dataset transferability over strong baselines. Further interpretability analyse show gradient feature distribution differences, enabling practical and scalable pre-training data detection.
+
+[p. 1 | section: 1. Introduction | type: Text]
+Large language models (LLMs) performance scales with the size and quality of pre-training data (Kaplan et al., 2020) .
+
+[p. 1 | section: 1. Introduction | type: FigureGroup]
+Figure 1. Heat maps of gradient matrices from the unfamiliar stage (epochs 0–1, panels a, c) to the familiar stage (epochs 6–7, panels b, d). Panels a and b display the update magnitude of the FFN module in layer 30, while panels c and d illustrate the update positions, with white for sparse and blue for core updates.
+
+[p. 1 | section: 1. Introduction | type: Text]
+As pre-training corpora expand to trillions of tokens and become increasingly proprietary and non-transparent, they raise significant concerns, such as unauthorized copyright, biased or harmful content, and contamination of evaluation benchmarks (Balloccu et al., 2024; Grynbaum & Mac, 2023) . These challenges motivate a specialized task of membership inference attacks, named pre-training data detection: determining whether a given text sample was included in a model's pre-training corpus (Carlini et al., 2021) .
+
+[p. 1 | section: 1. Introduction | type: Text]
+Recent studies (Carlini et al., 2021; Li; Shi et al., 2024; Zhang et al., 2025) primarily use likelihood-based statistical features to detect pre-training samples. For example, the Min-K method (Shi et al., 2024; Zhang et al., 2025) examines the k% of tokens with the lowest predicted probabilities, assuming non-member texts contain more low-likelihood tokens. However, these approaches are susceptible to word frequency bias in pre-training corpora, specifically for rare words or short texts scenarios. To improve detection accuracy, other researchers (Zhang et al.; Choi et al.) propose to analyze heuristic signals before and after fine-tuning, leveraging the fact that fine-tuning impacts member and non-member samples differently. For example, KDS (Choi et al.) shows that non-member datasets exhibit much larger embedding changes, while FSD (Zhang et al.) finds that their loss reductions are also significantly greater. Neverthe-
+
+[p. 2 | section: 1. Introduction | type: Text]
+less, these methods rely on the strong assumption that finetuning data closely match the target samples' distribution, requiring additional training on similar non-member data and thereby limiting cross-dataset generalization. Therefore, how to achieve highly generalizable pre-training data detection remains an open problem.
+
+[p. 2 | section: 1. Introduction | type: Text]
+Pretraining can be viewed as a gradual shift from unfamiliarity to familiarity with data. Optimization theory (Ruder, 2016; Frankle et al.; Wang et al., 2024) suggests that training drives parameters toward data-specific structure, reflected in consistent update patterns across magnitude, location, and concentration. As shown in Figure 1 and Section 3, we observe the following trends:
+
+[p. 2 | section: 1. Introduction | type: ListGroup]
+1. Decay of update magnitude. Figure 1( a,b) shows that parameter updates are strongly attenuated as data grows familiar, consistent with loss-convergence theory (Bottou, 2010; Ruder, 2016) . 2. Gradually stabilizing of update locations. Figure 1( c,d) shows that parameter updates evolve from broad activation regions to a stable core set of neurons, consistent with the sparse activation behavior of LLMs (Liu et al., 2024) . 3. Increasing update sparsity. Figure 1( a,b) and Figures 2( b,c) show that during training, an increasing fraction of updates concentrates in the top 10% of neurons, consistent with Hessian spectrum reshaping during loss convergence (Gur-Ari et al., 2018) . Familiar data yields sparse, concentrated updates, whereas unfamiliar data leads to more distributed updates.
+
+[p. 2 | section: 1. Introduction | type: Text]
+These observations reflect the evolutionary dynamics of neural network training, highlighting phase differences in parameter updates induced by identical samples. Together, they offer both theoretical motivation and empirical support for our detection method based on gradient deviation scores.
+
+[p. 2 | section: 1. Introduction | type: Text]
+Based on this insight, we propose GDS, a novel pretraining data detection method that infers pre-training data by probing Gradient Deviation Scores of target samples without fine-tuning. GDS exploits gradient differences between member and non-member samples to train a lightweight classifier with strong generalization. Specifically, within the LoRA framework, we collect per-sample gradients across layers during backpropagation, encoding them as eightdimensional features that capture the magnitude, location, and concentration of updates in attention and FFN modules. Compared to non-members, member samples show smaller matrix-level and row-wise update magnitudes, lower FFN but higher attention eccentricity, greater variability in matrixlevel and row-wise updates, a higher share of top gradients, and fewer sparse neurons. Then, we extract discriminative
+
+[p. 2 | section: 1. Introduction | type: Text]
+statistics from the signals to build fixed-dimensional feature vectors, which are fed to a lightweight MLP for binary membership classification.
+
+[p. 2 | section: 1. Introduction | type: Text]
+Extensive experiments on five benchmark datasets show that GDS is effective and generalizable, improving AUC by 6.5% and achieving a 67.3% TPR@5%FPR, substantially outperforming strong baselines. Further interpretability analyses reveal distributional differences in gradient features between member and non-member samples, offering intuitive evidence of training data imprints on the model and validating our methodology. 1 Our contributions are as follows:
+
+[p. 2 | section: 1. Introduction | type: ListGroup]
+From a training optimization perspective, we analyze how LLMs evolve from unfamiliarity to familiarity with data and propose using stage-wise parameter update dynamics to identify pretraining data, offering a novel direction to solve this task. We propose gradient deviation features capturing magnitude, location, and concentration, and introduce a gradient deviation score–based method for pretraining data detection without fine-tuning. Extensive experiments across diverse datasets and backbone models validate the effectiveness and generalization of GDS, while interpretability analyses reveal clear gradient differences between member and nonmember samples, supporting its validity.
+
+[p. 2 | section: 2. Related Work | type: Text]
+Likelihood-Based Scoring Methods. Early works distinguish member and non-member samples by capturing static statistical metrics in token-level likelihood distributions. Global-likelihood–based methods, such as PPL (Li) , Zlib (Carlini et al., 2021) , and Lowercase (Carlini et al., 2021) , perform discrimination by exploiting global probability features, compression entropy, and case-conversion ratios. However, global likelihood is highly sensitive to wordfrequency effects, leading to unstable performance. Mink% (Shi et al., 2024) and Min-k%++ (Zhang et al., 2025) mitigate global dependence by focusing on low-probability outlier tokens or target–candidate probability comparisons, with k and text length jointly determining the analyzed token subset. However, the fixed choice of k lacks adaptivity, causing severe score fluctuations in short texts with lowfrequency words. Although PC-PDD (Zhang et al., 2024) approximates the word-frequency distribution of pretraining corpora using public datasets, these references lack fidelity due to limited domain coverage.
+
+[p. 2 | section: 2. Related Work | type: Text]
+Fine-tuning Enhanced Methods. To address the instability of static statistical indicators, recent studies (Zhang et al.;
+
+[p. 2 | section: 2. Related Work | type: Footnote]
+1 Code in
+
+[p. 3 | section: 2. Related Work | type: FigureGroup]
+Figure 2. Dynamic curves of four parameter update characteristics defined in the Motivation section. i → j denotes the epoch interval. Ordinate shows values of predefined characteristics, with orange and blue representing Attention and FFN modules.
+
+[p. 3 | section: 2. Related Work | type: Text]
+Choi et al.) adopt lightweight fine-tuning to actively amplify asymmetric differences between member and non-member samples. KDS (Choi et al.) evaluates dataset contamination by comparing kernel similarity matrices of embeddings before and after fine-tuning, assuming non-member datasets undergo larger embedding changes than member datasets. However, it only estimates dataset-level contamination and cannot reliably detect contamination at the sample-level. Another representative method FSD (Zhang et al.) detects membership by comparing loss before and after fine-tuning, assuming non-member samples experience a larger loss reduction than member samples. Nevertheless, these methods assume that fine-tuning data closely matches the target distribution, requiring additional tuning on similar non-member data, which limits cross-dataset generalization.
+
+[p. 3 | section: 3. Motivation | type: Text]
+Inspired by optimization theory (Ruder, 2016; Bottou, 2010) , we examine how LLMs transition from unfamiliarity to familiarity with data, and how this cognitive shift relates to the dynamic evolution of model parameters during training. To evaluate it, we fine-tune LLaMA-7B with LoRA on the unseen split of BookMIA dataset and track LoRA parameter updates over 7 epochs. Stage-wise analysis in Figure 2 reveals the dynamic evolution of gradient features.
+
+[p. 3 | section: 3.1. Decay of Update Magnitude | type: Text]
+Model training aims to minimize the loss function L(θ), with update magnitude determined by the gradient norm ∥∇L(θ)∥. According to optimization convergence theory (Ruder, 2016) , as the parameters θ t approach the optimum θ ∗ , the gradient norm of the loss function vanishes, i.e.,limθ→ θ ∗ ∥∇L(θt)∥ = 0. This causes the parameter update magnitude to decrease synchronously. Therefore, we use ∆θ t as the core indicator of the average update magnitude across all trainable parameters at iteration t:
+
+[p. 3 | section: 3.1. Decay of Update Magnitude | type: Equation]
+\Delta \theta_{t} = \frac{1}{N} \sum_{i=1}^{N} |\theta_{t,i} - \theta_{t-1,i}|, \qquad (1)
+
+[p. 3 | section: 3.1. Decay of Update Magnitude | type: Text]
+where N denotes the total number of trainable parameters.
+
+[p. 3 | section: 3.1. Decay of Update Magnitude | type: Text]
+As training progresses, both the loss L(θt) and gradient norm ∥∇L(θt)∥ decrease, reducing the update magnitude ∆θ t and slowing its decay as parameters converge to the optimum θ ∗ . Eventually, L(θt) stabilizes near its minimum, parameter updates ∆θ t become negligible. As shown in Figure 2a, the mean update magnitude decreases monotonically with training, with the largest changes occurring in the first two epochs, consistent with loss convergence.
+
+[p. 3 | section: 3.2. Gradually Stabilizing of Update Locations | type: Text]
+Existing studies (Liu et al., 2024; Tang et al., 2025) have shown that neural activations occur at different locations when processing member samples and non-member samples. Inspired by this, we adopt the parameter update eccentricity as the core indicator, which quantifies the deviation of the top-10% parameter update positions from the global parameter centroid. We first define the global centroid as:
+
+[p. 3 | section: 3.2. Gradually Stabilizing of Update Locations | type: Equation]
+\theta_c = \frac{1}{N} \sum_{i=1}^{N} \theta_i, \tag{2}
+
+[p. 3 | section: 3.2. Gradually Stabilizing of Update Locations | type: Text]
+where θ i is the coordinate of the i-th parameter.
+
+[p. 3 | section: 3.2. Gradually Stabilizing of Update Locations | type: Text]
+The update eccentricity at iteration t is then defined as:
+
+[p. 3 | section: 3.2. Gradually Stabilizing of Update Locations | type: Equation]
+E_{t} = \frac{1}{\operatorname{card}(U_{10,t})} \sum_{\theta_{i} \in U_{10,t}} \|\theta_{i} - \theta_{c}\|_{2}, (3)
+
+[p. 3 | section: 3.2. Gradually Stabilizing of Update Locations | type: Text]
+where card(·) denotes the number of elements in a set, U10,t = {∥∆θt,i∥ 1 ∈ Top10%(∥∆θt∥1)}, ∥ · ∥ 1 denotes the ℓ 1 norm and ∥ · ∥ 2 denotes the ℓ 2 norm.
+
+[p. 3 | section: 3.2. Gradually Stabilizing of Update Locations | type: Text]
+In the initial training stage, activation patterns are unstable, leading to scattered U10,t and thus random large values of Et. As training proceeds, the model identifies core parameters related to data features: θ t stabilizes to the optimal subset θ ∗ , and U10,t converges to the core parameter region, resulting in E t gradually stabilizing at a low level. Figure 2d shows that the eccentricity of parameter update evolves to a relatively stable value, consistent with the evolution of the
+
+[p. 4 | section: 3.2. Gradually Stabilizing of Update Locations | type: FigureGroup]
+Figure 3. Overview of Gradient Deviation Scores method.
+
+[p. 4 | section: 3.2. Gradually Stabilizing of Update Locations | type: Text]
+neuron activation pattern, suggesting that training identifies the core parameters and stabilizes updates around them.
+
+[p. 4 | section: 3.3. Increasing Update Sparsity | type: Text]
+The Hessian spectrum (Gur-Ari et al., 2018; Frankle et al.) is a core metric characterizing the loss function's curvature, directly determining the direction and efficiency of parameter updates. For the loss function L(θ), its Hessian matrix H(θ) = ∇2L(θ) describes the local curvature of the loss landscape, with eigenvalue decomposition:
+
+[p. 4 | section: 3.3. Increasing Update Sparsity | type: Equation]
+\mathcal{H}(\theta) = U\Lambda U^T,\tag{4}
+
+[p. 4 | section: 3.3. Increasing Update Sparsity | type: Text]
+where U is the orthogonal eigenvector matrix (principal curvature directions), Λ = diag(λ1, . . . , λd) is the diagonal eigenvalue matrix (curvature magnitudes). During training, the Hessian spectrum changes from an almost uniform λ i ≈ c in the early stage to a late-stage structure with a few large eigenvalues and most near zero.
+
+[p. 4 | section: 3.3. Increasing Update Sparsity | type: Text]
+This reshaping leads to concentrated updates, focusing on directions with large eigenvalues while leaving most others nearly unchanged. Consequently, update energy is confined to a small subset of parameters, motivating the selection of two joint indicators. S t measures the fraction of parameters with negligible updates (absolute value < 10 − 6 ) at iteration t, while T10,t measures the fraction of total update magnitude contributed by the top 10% largest updates.
+
+[p. 4 | section: 3.3. Increasing Update Sparsity | type: Equation]
+S_t = \frac{\operatorname{card}\left(i \mid |\Delta \theta_{t,i}| < 10^{-6}\right)}{N},\tag{5}
+
+[p. 4 | section: 3.3. Increasing Update Sparsity | type: Equation]
+T_{10,t} = \frac{\sum_{|\Delta\theta_{t,i}| \in U_{10,t}} |\Delta\theta_{t,i}|}{||\Delta\theta_t||_1}. (6)
+
+[p. 4 | section: 3.3. Increasing Update Sparsity | type: Text]
+As training progresses, parameter updates increasingly concentrate along core directions, with most parameters receiving negligible changes. Consequently, S t gradually
+
+[p. 4 | section: 3.3. Increasing Update Sparsity | type: Text]
+increases, while T10,t remains relatively large and stable(0.26–0.27), indicating that update energy is consistently dominated by a small subset of parameters. Figures 2b and 2c confirm this growing sparsity and stable Top 10% contribution, reflecting update energy aggregation driven by Hessian spectrum reshaping. Further details on the variation trends of the three metrics are provided in the appendix B.
+
+[p. 4 | section: 4.1. Task Definition | type: Text]
+Given a target text x and a target LLM f θ pre-trained on a corpus D, the goal of pre-training data detection task is to construct a detector h(x, fθ)to determine whether x belongs to D. This task can be formalized as a binary classification problem: h(x, fθ) → {0, 1} where "1" indicates x ∈ D as member and "0" indicates x /∈ D as non-member.
+
+[p. 4 | section: 4.1. Task Definition | type: Text]
+As illustrated in Figure 3, GDS comprises three stages: gradient matrix acquisition, feature vector extraction and light Multilayer Perceptron(MLP) training. For each training sample, we perform inference and backpropagation to obtain LoRA gradients across l layers and m sub-modules, yielding l × m gradient matrices G. From these matrices, we extract eight-dimensional features to form a gradient feature vector V l×m×8 , which is used to train a lightweight MLP classifier for binary membership prediction. During inference, the same feature extraction process is applied to a target sample x ∗ , and the resulting feature vector is fed into the trained MLP to produce the final classification result.
+
+[p. 4 | section: 4.2. Gradient Matrix Acquisition | type: Text]
+Given the target model f θ and training sample x, we first initialize f θ with LoRA, yielding l × m LoRA matrices L. We then feed a single sample x into f θ for forward
+
+[p. 5 | section: 4.2. Gradient Matrix Acquisition | type: Text]
+inference and backpropagation, obtaining LoRA gradient matrices \mathbb{G} = \nabla_{\mathbb{L}} \mathcal{L}_{\text{CLM}}(f_{\theta}(x)) , where \mathcal{L}_{\text{CLM}} denotes the causal language modeling loss of the pre-trained LLM. Since the LoRA_B matrices are fully initialized to zero, a single round of gradient propagation leads to zero gradients for the LoRA_A matrices. Thus, we only collect the gradient matrices of LoRA_B for subsequent processing.
+
+[p. 5 | section: 4.3. Feature Vector Extraction | type: Text]
+Given the gradient matrices \mathbb{G} , we extract features based on the three parameter update trends introduced in Section 3.
+
+[p. 5 | section: 4.3.1. MAGNITUDE | type: Text]
+We propose two magnitude indicators to measure the overall scale of gradient updates in the LoRA parameter space.
+
+[p. 5 | section: 4.3.1. MAGNITUDE | type: Text]
+(1) Absolute Mean : The mean of the absolute values of all elements in the gradient matrix, which characterizes the overall parameter update strength:
+
+[p. 5 | section: 4.3.1. MAGNITUDE | type: Equation]
+Abs\_Mean = \frac{1}{r \cdot h} \sum_{i=1}^{r} \sum_{j=1}^{h} |\mathbb{G}_{i,j}|, (7)
+
+[p. 5 | section: 4.3.1. MAGNITUDE | type: Text]
+where \mathbb{G}_{i,j} denotes the element in the i -th row and j -th column of the gradient matrix with r rows and h columns.
+
+[p. 5 | section: 4.3.1. MAGNITUDE | type: Text]
+(2) Max Row Mean: The mean of each row in the LoRA matrix and take the maximum value, which characterizes the most sample-responsive local optimal response dimension with the largest parameter update magnitude:
+
+[p. 5 | section: 4.3.1. MAGNITUDE | type: Equation]
+Row\_Mean\_Max = \max_{1 \le i \le r} \left( \frac{1}{h} \sum_{j=1}^{h} |\mathbb{G}_{i,j}| \right). (8)
+
+[p. 5 | section: 4.3.2. Position | type: Text]
+Screen the top 10% of gradient elements by absolute value from \mathbb{G} and calculate their offset from this matrix center, capturing offset characteristics of core gradient positions for (1) Row Eccentricity and (2) Column Eccentricity, respectively:
+
+[p. 5 | section: 4.3.2. Position | type: Equation]
+Row\_Ecc = \frac{1}{\operatorname{card}(S)} \sum_{(i,j) \in S} \left| \frac{2i - (r+1)}{r-1} \right|, \quad (9)
+
+[p. 5 | section: 4.3.2. Position | type: Equation]
+Col\_Ecc = \frac{1}{\operatorname{card}(S)} \sum_{(i,j) \in S} \left| \frac{2j - (h+1)}{h-1} \right|, \quad (10)
+
+[p. 5 | section: 4.3.2. Position | type: Text]
+where S = \{(i,j) \mid |\mathbb{G}_{i,j}| \in \text{Top10\%}(|\mathbb{G}|)\} denotes the set of indices for the top 10% of elements in the gradient matrix \mathbb{G} ranked by absolute gradient value. Top gradients near the center correspond to an eccentricity of 0, while those near the edge correspond to a score of 1.
+
+[p. 5 | section: 4.3.3. CONCENTRATION | type: Text]
+We propose four indicators to measure the concentration of gradient distributions.
+
+[p. 5 | section: 4.3.3. CONCENTRATION | type: Text]
+(1) Top-10% Ratio : The ratio of the sum of the top 10% largest gradient magnitudes to the total update magnitude of the gradient matrix, which quantifies the contribution ratio of core gradients:
+
+[p. 5 | section: 4.3.3. CONCENTRATION | type: Equation]
+10p\_Ratio = \frac{\sum_{(i,j)\in S} |\mathbb{G}_{i,j}|}{\|\mathbb{G}\|_1}, \tag{11}
+
+[p. 5 | section: 4.3.3. CONCENTRATION | type: Text]
+(2) Sparsity : The proportion of gradient elements with absolute values less than 10^{-6} , which quantifies the sparsity degree of gradient distributions:
+
+[p. 5 | section: 4.3.3. CONCENTRATION | type: Equation]
+Sparsity = \frac{\operatorname{card}\left(\left\{\left(i,j\right) \mid |\mathbb{G}_{i,j}| < 10^{-6}\right\}\right)}{r \cdot h}. (12)
+
+[p. 5 | section: 4.3.3. CONCENTRATION | type: Text]
+(3) Standard Deviation : The standard deviation of the elements in the gradient matrix, which quantifies the dispersion degree of parameter updates:
+
+[p. 5 | section: 4.3.3. CONCENTRATION | type: Equation]
+Std = \sqrt{\frac{1}{r \cdot h} \sum_{i=1}^{r} \sum_{j=1}^{h} (|\mathbb{G}_{i,j}| - \text{Abs\_mean})^2}. (13)
+
+[p. 5 | section: 4.3.3. CONCENTRATION | type: Text]
+(4) Row Mean Standard Deviation: The mean of each row in the LoRA matrix and take the standard deviation, which quantifies the consistency of update strength across all rows:
+
+[p. 5 | section: 4.3.3. CONCENTRATION | type: Equation]
+Row\_Mean\_Std = \sqrt{\frac{1}{r} \sum_{i=1}^{r} \left(\bar{\mathbb{G}}_i - \mu_{\bar{\mathbb{G}}}\right)^2}, \quad (14)
+
+[p. 5 | section: 4.3.3. CONCENTRATION | type: Text]
+where \bar{\mathbb{G}}_i = \frac{1}{h} \sum_{j=1}^h |\mathbb{G}_{i,j}| denotes the i -th row's absolute mean, \mu_{\bar{\mathbb{G}}} = \frac{1}{r} \sum_{i=1}^r \bar{\mathbb{G}}_i denotes t the mean of row means.
+
+[p. 5 | section: 4.3.3. CONCENTRATION | type: Text]
+We compute the aforementioned eight feature values from all gradient matrices to derive a feature vector \mathbb{V}^{l\times m\times 8} \triangleq [Abs_Mean, Row_Mean_Max, 10p_Ratio, Sparsity, Std, Row_Mean_Std, Row_Ecc, Col_Ecc] per sample, which is then used for subsequent MLP training and inference.
+
+[p. 5 | section: 4.4. Light MLP Training | type: Text]
+Given the feature vectors \mathbb{V}_i from all training samples vectors \mathbb{V}_s , we feed them into a lightweight MLP for training. The target output corresponds to the binary label \{0,1\} for each sample, where 0 denotes non-member and 1 denotes member. The training loss is defined as follows:
+
+[p. 5 | section: 4.4. Light MLP Training | type: Equation]
+\mathcal{L} = -\frac{1}{N} \sum_{i=1}^{N} \left[ y_i \log \hat{y}_i + (1 - y_i) \log(1 - \hat{y}_i) \right], \quad (15)
+
+[p. 5 | section: 4.4. Light MLP Training | type: Text]
+where N denotes the number of training samples, y_i \in \{0,1\} is the ground-truth label of the i-th sample, and \hat{y}_i is the predicted probability output by the MLP.
+
+[p. 6 | section: 4.4. Light MLP Training | type: TableGroup]
+Table 1. Comparison(AUROC/TPR@5%FPR) on 4 Datasets across 5 target models. Target models are denoted as 2.7B/6B/6.7B/6.9B/7B, corresponding to Neo-2.7B/GPT-J-6b/OPT-6.7b/Pythia-6.9b/LLaMA-7B respectively. The best result is bold. WikiMIA ArXivTection Method 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B PPL 0.61/0.13 0.64/0.13 0.60/0.12 0.63/0.13 0.69/0.14 0.62/0.13 0.64/0.13 0.60/0.12 0.63/0.13 0.70/0.14 ZLib 0.58/0.10 0.60/0.11 0.58/0.10 0.59/0.10 0.71/0.22 0.58/0.10 0.60/0.11 0.58/0.09 0.59/0.11 0.71/0.22 Min-k 0.65/0.17 0.67/0.19 0.63/0.15 0.67/0.19 0.73/0.18 0.65/0.17 0.68/0.19 0.63/0.15 0.67/0.19 0.72/0.18 Min-k++ 0.67/0.15 0.69/0.19 0.65/0.11 0.70/0.18 0.82/0.22 0.67/0.15 0.69/0.19 0.65/0.10 0.70/0.17 0.83/0.22 FSD 0.92/0.77 0.95/0.78 0.90/0.63 0.90/0.66 0.92/0.41 0.91/0.65 0.96/0.79 0.89/0.63 0.95/0.66 0.94/0.81 Ours 0.90/0.60 0.93/0.66 0.94/0.67 0.92/0.63 0.96/0.84 0.94/0.73 0.97/0.86 0.94/0.75 0.95/0.83 0.97/0.85 BookTection BookMIA Method 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B PPL 0.69/0.15 0.74/0.25 0.64/0.13 0.73/0.25 0.71/0.25 0.29/0.02 0.22/0.13 0.23/0.01 0.59/0.19 0.56/0.21 ZLib 0.56/0.16 0.58/0.20 0.55/0.14 0.58/0.19 0.57/0.19 0.20/0.02 0.38/0.13 0.15/0.00 0.49/0.17 0.48/0.18 Min-k 0.71/0.18 0.75/0.27 0.67/0.15 0.74/0.26 0.71/0.25 0.45/0.05 0.60/0.20 0.40/0.03 0.62/0.20 0.60/0.21 Min-k++ 0.64/0.13 0.67/0.18 0.61/0.11 0.66/0.19 0.63/0.15 0.54/0.13 0.64/0.29 0.49/0.09 0.60/0.23 0.58/0.20 FSD 0.92/0.53 0.91/0.52 0.96/0.77 0.93/0.59 0.92/0.55 0.98/0.93 0.97/0.89 0.98/0.96 0.98/0.93 0.98/0.91 Ours 0.96/0.84 0.97/0.88 0.98/0.92 0.96/0.83 0.98/0.92 0.99/0.98 0.99/0.99 0.99/0.99 0.99/0.98 0.99/0.99 Table 2. Performance Comparison on Mimir datasets with 7 subsets across 5 target models using AUROC scores.
+
+[p. 6 | section: 4.4. Light MLP Training | type: Table]
+Wikipedia Github Pile CC PubMed Central Method 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B PPL 0.56 0.57 0.56 0.56 0.56 0.78 0.79 0.78 0.90 0.83 0.56 0.57 0.56 0.56 0.52 0.78 0.79 0.78 0.78 0.72 ZLib 0.62 0.65 0.59 0.65 0.58 0.90 0.91 0.79 0.91 0.86 0.55 0.55 0.55 0.55 0.52 0.78 0.78 0.73 0.77 0.71 Min-k 0.66 0.68 0.65 0.68 0.63 0.88 0.89 0.76 0.90 0.83 0.56 0.57 0.56 0.56 0.52 0.81 0.80 0.74 0.79 0.72 Min-k++ 0.65 0.68 0.60 0.69 0.56 0.84 0.86 0.56 0.86 0.73 0.54 0.55 0.54 0.56 0.51 0.71 0.72 0.60 0.70 0.59 FSD 0.61 0.67 0.60 0.65 0.60 0.77 0.80 0.62 0.77 0.72 0.55 0.55 0.54 0.55 0.52 0.71 0.79 0.63 0.56 0.63 Ours 0.63 0.64 0.65 0.65 0.64 0.90 0.92 0.88 0.92 0.91 0.59 0.59 0.59 0.57 0.59 0.84 0.85 0.84 0.79 0.82 ArXiv DM Mathematics HackerNews Average Method 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B 2.7B 6B 6.7B 6.9B 7B PPL 0.78 0.79 0.65 0.78 0.70 0.78 0.79 0.65 0.91 0.31 0.65 0.62 0.59 0.62 0.59 0.64 0.66 0.62 0.73 0.59 ZLib 0.77 0.78 0.68 0.77 0.71 0.82 0.81 0.80 0.81 0.23 0.68 0.60 0.58 0.60 0.58 0.65 0.67 0.63 0.72 0.58 Min-k 0.78 0.79 0.65 0.78 0.70 0.93 0.93 0.92 0.92 0.32 0.65 0.62 0.59 0.62 0.59 0.71 0.73 0.69 0.75 0.60 Min-k++ 0.60 0.64 0.53 0.70 0.57 0.77 0.79 0.67 0.75 0.22 0.53 0.57 0.51 0.60 0.53 0.60 0.63 0.56 0.67 0.53 FSD 0.72 0.78 0.55 0.70 0.52 0.58 0.85 0.60 0.74 0.53 0.61 0.60 0.57 0.56 0.51 0.61 0.66 0.59 0.62 0.55 Ours 0.78 0.79 0.78 0.78 0.77 0.95 0.95 0.94 0.95 0.95 0.58 0.60 0.60 0.57 0.58 0.73 0.75 0.74 0.76 0.70
+
+[p. 6 | section: 5.1. Experimental Setup | type: Text]
+Datasets Following prior work, we evaluate on five prevalent datasets: WikiMIA, BookMIA (Shi et al., 2024) ,ArxivTection, BookTection (Duarte et al.) , and MIMIR (Duan et al.) , a widely recognized challenging benchmark for pretraining data detection.
+
+[p. 6 | section: 5.1. Experimental Setup | type: Text]
+Target Models We evaluate five open-source LLMs with diverse architectures: Neo-2.7B (Black et al., 2021) , GPT-J-6B (Wang & Komatsuzaki, 2021) , OPT-6.7B (Zhang et al., 2022) , Pythia-6.9B (Biderman et al., 2023) , and LLaMA-7B (Touvron et al., 2023) from Hugging Face.
+
+[p. 6 | section: 5.1. Experimental Setup | type: Text]
+Comparison Methods We select five representative stateof-the-art baselines. Four scoring function–based methods
+
+[p. 6 | section: 5.1. Experimental Setup | type: Text]
+include PPL (Carlini et al., 2021) , ZLib (Carlini et al., 2021) , Min-k (Shi et al., 2024) , and Min-k++ (Zhang et al., 2025) . The fine-tuning–enhanced method includes FSD (Zhang et al.) . More details are shown in Appendix A.
+
+[p. 6 | section: 5.1. Experimental Setup | type: Text]
+Evaluation Metrics Two metrics evaluate the binary pretraining data detection task: AUROC measures overall discriminative performance, and TPR@5%FPR captures practical effectiveness by assessing detection rate under a 5% false positive constraint.
+
+[p. 6 | section: 5.1. Experimental Setup | type: Text]
+Implementation Details We use the PEFT library (Man grulkar et al., 2022) for LoRA-based (Hu et al., 2022) gradient feature extraction without parameter updates. The MLP is trained on 30% of the data, with the remaining 70% used for inference evaluation under FSD settings. More Details can be seen in Appendix A.6.
+
+[p. 7 | section: 5.1. Experimental Setup | type: FigureGroup]
+Figure 4. Distribution differences of eight gradient features between member(red) and non-member(blue) samples. Dashed lines indicate distribution means. The x-axis represents feature values, and the y-axis denotes probability density.
+
+[p. 7 | section: 5.1. Experimental Setup | type: TableGroup]
+Table 3. Ablation results using AUROC on WikiMIA and Arxiv-Tection. - denotes the removal of related features. Dataset -Magnitude -Concentration -Position WikiMIA 0.94 (↓0.02) 0.94 (↓0.02) 0.93 (↓0.03) ArxivTection 0.96 (↓0.01) 0.95 (↓0.02) 0.95 (↓0.02) Table 4. Ablation results using AUROC and TPR@5%FPR. ATT-Only refers to performance validation using only attention module.
+
+[p. 7 | section: 5.1. Experimental Setup | type: Table]
+Dataset ATT-Only FFN-Only Origin WikiMIA 0.94 / 0.68 0.93 / 0.64 0.96 / 0.84 ArxivTection 0.95 / 0.76 0.93 / 0.72 0.97 / 0.85
+
+[p. 7 | section: 5.2. Main Results | type: Text]
+Table 1 shows detection performance on WikiMIA, Arxiv-Tection, BookTection, and BookMIA. Specifically, when tested on WikiMIA with LLaMA-7B, GDS achieves an AUC score of 0.96, which is an improvement of 0.04 compared to the best baseline FSD and significantly higher than score-function-based methods such as Min-k++. GDS outperforms the best baseline in most settings, with especially large gains in TPR@5%FPR on BookTection and Book-MIA. Notably, with LLaMA-7B, BookTection performance improves by nearly 67.3%.
+
+[p. 7 | section: 5.2. Main Results | type: Text]
+Table 2 reports results on seven MIMIR subsets. Although all methods degrade due to similar data distributions, GDS achieves the best average improvements +2.8%, +2.7%, +7.2%, +1.3%, +16.6% across different models, and shows clear advantages on PubMed Central, DM Mathematics, and GitHub. Using the LLaMA model, the three subsets achieve AUC scores of 0.82, 0.95, and 0.91. Our method shows the most stable performance across models, with AUC variations mostly within 0.04, demonstrating strong generalization across different models.
+
+[p. 7 | section: 5.3. Ablation Study | type: Text]
+We perform two ablation studies: (1) removing each gradient feature category individually, and (2) using features from only the Attention or FFN module. Table 3 shows that all feature categories contribute to performance, with Position Offset and Magnitude being the most important. Concentration features have smaller effects, and the full combination performs best, highlighting the complementary nature of multi-dimensional features (see Appendix C for sub-feature ablations). Table 4 shows that Attention features are more discriminative than FFN features. Both single-module variants underperform the full model, indicating that Attention and FFN capture complementary gradient patterns and must be combined for optimal performance.
+
+[p. 7 | section: 5.4.1. FEATURE DISTRIBUTION | type: Text]
+To explain the classifier's effectiveness, we quantify feature distributions across all layers and sub-modules for member and non-member samples. Figure 4 shows the eight features with the largest discrepancies. Member samples exhibit smaller Abs Mean and Row Mean Max, indicating lower gradient magnitudes due to higher data familiarity, along with higher Sparsity, smaller Std and Row Mean Std, reflecting more concentrated and stable gradients. They also maintain a consistently higher 10p Ratio, occupying the core of gradient propagation. For locations Row Ecc and Col Ecc, member samples cluster at lower values, while non-members shift higher, suggesting that member-related parameters lie more centrally in weight matrices.
+
+[p. 7 | section: 5.4.1. FEATURE DISTRIBUTION | type: Text]
+We collect sub-features with the largest distribution differences between the two sample types and analyze their overall distribution patterns. Figure 5 show that discriminative sub-features are predominantly concentrated in low layers, while middle and high layers contribute far less. Among sub-modules, attention-related modules are the main sources
+
+[p. 8 | section: 5.4.1. FEATURE DISTRIBUTION | type: TableGroup]
+Table 5. Performance Comparison between LoRA and Full-Parameter Update using AUROC on WikiMIA and ArxivTection. Dataset Metric LLaMA-7B GPT-J-6B OPT-6.7B Pythia-6.9B Neo-2.7B LoRA Full LoRA Full LoRA Full LoRA Full LoRA Full WikiMIA AUC 0.96 0.96 0.93 0.90 0.94 0.92 0.92 0.89 0.90 0.88 TPR@5% FPR 0.84 0.79 0.66 0.58 0.67 0.56 0.63 0.50 0.60 0.51 ArxivTection AUC 0.97 0.96 0.97 0.96 0.94 0.93 0.95 0.94 0.94 0.94 TPR@5% FPR 0.85 0.84 0.86 0.79 0.75 0.67 0.83 0.73 0.73 0.75
+
+[p. 8 | section: 5.4.1. FEATURE DISTRIBUTION | type: FigureGroup]
+Figure 5. Distribution Difference Statistics of Discriminative Features. The y-axis shows the statistical count.
+
+[p. 8 | section: 5.4.1. FEATURE DISTRIBUTION | type: Text]
+of discriminative features, with obvious differences in contribution across modules. In terms of gradient features, grad sparsity exhibits the strongest discriminative power, significantly outperforming other indicators.
+
+[p. 8 | section: 5.4.2. FULL PARAMETER TRAINING | type: Text]
+In LoRA training, only FFN and MLP modules are updated, while LayerNorm, despite containing meaningful training dynamics, is excluded. To account for this, we evaluate our method under full-parameter training on two small-scale datasets, BookMIA and ArxivTection, for computational feasibility. As shown in Table 5, although full-parameter updates cause a slight performance drop compared to LoRA, our method still outperforms most baselines. We attribute this gap to reduced gradient magnitudes in full training, which weaken discriminative signals between sample types.
+
+[p. 8 | section: 5.4.3. WIKIMIA MODIFICATION | type: Text]
+Dataset partitioning can introduce distribution shifts or dataset-specific artifacts. For example, WikiMIA is split by publication time, with all non-member samples labeled as 2023. To ensure our method does not exploit such artifacts, we remove all timestamp tokens and reevaluate all methods. As shown in Table 6, although token removal degrades performance, our method suffers a much smaller drop than the strongest baseline, FSD, and still achieves SOTA results.
+
+[p. 8 | section: 5.4.3. WIKIMIA MODIFICATION | type: TableGroup]
+Table 6. Comparison of Temporal Feature Perturbation via AU-ROC. Deletion denotes the removal of all year timestamps. Method Origin Deletion PPL 0.69 0.62 Min-k 0.73 0.63 Min-k++ 0.82 0.59 FSD 0.92 0.76 Ours 0.96 0.84 Table 7. Cross-Dataset Generalization Performance using AU-ROC. Wiki(arXiv) indicates training on ArxivTection with test on WikiMIA, while Mix indicates mixed datasets.
+
+[p. 8 | section: 5.4.3. WIKIMIA MODIFICATION | type: Table]
+Method Wiki (arXiv) arXiv (Wiki) Mix FSD 0.52 0.58 0.92 Ours 0.66 0.68 0.95
+
+[p. 8 | section: 5.4.4. TRANSFERABILITY | type: Text]
+Although our method shares the same feature extraction framework, it requires dataset-specific classifiers. To examine whether a unified classifier is feasible, we train classifiers on WikiMIA and ArXiv separately and evaluate crossdataset generalization, as well as train a unified classifier on mixed data. Table 7 shows that cross-dataset transfer leads to notable performance degradation due to dataset shifts (e.g., distribution, difficulty, and pre-training differences), which cause classifiers to overfit dataset-specific gradient features. In contrast, the unified classifier performs well on mixed data, indicating that our method can capture universal feature discrepancies arising from model familiarity.
+
+[p. 8 | section: 6. Conclusion | type: Text]
+We revisit pre-training data detection from an optimization and training-dynamics perspective and introduce GDS, a fine-tuning–free method for inferring pre-training membership. By analyzing how models transition from unfamiliarity to familiarity, we show that member and non-member samples exhibit stable, interpretable differences in gradient magnitude, location, and concentration across datasets and architectures. Experiments show that GDS is effective and generalizable, outperforming strong baselines. Future work can focus on developing more generalizable detectors by contrastive learning or deeper feature extraction.
+
+[p. 9 | section: Limitations | type: Text]
+This work investigates pre-training data detection, a form of membership inference that determines whether a given sample was included in a LLM's pre-training corpus. While our proposed GDS method improves detection accuracy and generalization without fine-tuning, it also raises important ethical concerns. Pre-training data detection methods could be misused to probe proprietary or confidential training corpora, potentially revealing sensitive information about data sources or collection practices. Although GDS does not reconstruct or expose training samples directly, it contributes to capabilities that may be exploited if applied irresponsibly. Our primary motivation is to support transparency, accountability, and safety. As pre-training datasets become increasingly large and opaque, tools like GDS can help researchers, auditors, and regulators verify data usage claims, identify potential copyright violations, and detect benchmark contamination. In this sense, GDS is intended as a diagnostic and auditing mechanism rather than a data extraction attack. We release code and models to promote reproducibility while encouraging responsible deployment. Overall, we hope this work advances trustworthy and transparent large-scale model development while highlighting the need for careful governance of pre-training data.

icml26/9346049b-7104-494c-9378-955a2d7393ed/paper.md

@@ -0,0 +1,649 @@
+
+
+{0}------------------------------------------------
+
+# From Unfamiliar to Familiar: Detecting Pre-training Data via Gradient Deviations in Large Language Models
+
+### Anonymous Authors<sup>1</sup>
+
+# Abstract
+
+Pre-training data detection for LLMs is essential for addressing copyright concerns and mitigating benchmark contamination. Existing methods mainly focus on the likelihood-based statistical features or heuristic signals before and after finetuning, but the former are susceptible to word frequency bias in corpora, and the latter strongly depend on the similarity of fine-tuning data. From an optimization perspective, we observe that during training, samples transition from unfamiliar to familiar in a manner reflected by systematic differences in gradient behavior. Familiar samples exhibit smaller update magnitudes, distinct update locations in model components, and more sharply activated neurons. Based on this insight, we propose GDS, a method that identifies pre-training data by probing Gradient Deviation Scores of target samples. Specifically, we first represent each sample using gradient profiles that capture the magnitude, location, and concentration of parameter updates across FFN and Attention modules, revealing consistent distinctions between member and non-member data. These features are then fed into a lightweight classifier to perform binary membership inference. Experiments on five public datasets show that GDS achieves state-ofthe-art performance with significantly improved cross-dataset transferability over strong baselines. Further interpretability analyse show gradient feature distribution differences, enabling practical and scalable pre-training data detection.
+
+# 1. Introduction
+
+Large language models (LLMs) performance scales with the size and quality of pre-training data [\(Kaplan et al.,](#page-8-0) [2020\)](#page-8-0).
+
+Preliminary work. Under review by the International Conference on Machine Learning (ICML). Do not distribute.
+
+<span id="page-0-0"></span>![](_page_0_Figure_9.jpeg)
+
+*Figure 1.* Heat maps of gradient matrices from the unfamiliar stage (epochs 0–1, panels a, c) to the familiar stage (epochs 6–7, panels b, d). Panels a and b display the update magnitude of the FFN module in layer 30, while panels c and d illustrate the update positions, with white for sparse and blue for core updates.
+
+As pre-training corpora expand to trillions of tokens and become increasingly proprietary and non-transparent, they raise significant concerns, such as unauthorized copyright, biased or harmful content, and contamination of evaluation benchmarks [\(Balloccu et al.,](#page-8-1) [2024;](#page-8-1) [Grynbaum & Mac,](#page-8-2) [2023\)](#page-8-2). These challenges motivate a specialized task of membership inference attacks, named pre-training data detection: determining whether a given text sample was included in a model's pre-training corpus [\(Carlini et al.,](#page-8-3) [2021\)](#page-8-3).
+
+Recent studies [\(Carlini et al.,](#page-8-3) [2021;](#page-8-3) [Li;](#page-8-4) [Shi et al.,](#page-9-0) [2024;](#page-9-0) [Zhang et al.,](#page-9-1) [2025\)](#page-9-1) primarily use likelihood-based statistical features to detect pre-training samples. For example, the Min-K method [\(Shi et al.,](#page-9-0) [2024;](#page-9-0) [Zhang et al.,](#page-9-1) [2025\)](#page-9-1) examines the k% of tokens with the lowest predicted probabilities, assuming non-member texts contain more low-likelihood tokens. However, these approaches are susceptible to word frequency bias in pre-training corpora, specifically for rare words or short texts scenarios. To improve detection accuracy, other researchers [\(Zhang et al.;](#page-9-2) [Choi et al.\)](#page-8-5) propose to analyze heuristic signals before and after fine-tuning, leveraging the fact that fine-tuning impacts member and non-member samples differently. For example, KDS [\(Choi](#page-8-5) [et al.\)](#page-8-5) shows that non-member datasets exhibit much larger embedding changes, while FSD [\(Zhang et al.\)](#page-9-2) finds that their loss reductions are also significantly greater. Neverthe-
+
+<sup>1</sup>Anonymous Institution, Anonymous City, Anonymous Region, Anonymous Country. Correspondence to: Anonymous Author <anon.email@domain.com>.
+
+{1}------------------------------------------------
+
+less, these methods rely on the strong assumption that finetuning data closely match the target samples' distribution, requiring additional training on similar non-member data and thereby limiting cross-dataset generalization. Therefore, how to achieve highly generalizable pre-training data detection remains an open problem.
+
+104
+
+106
+
+108 109 Pretraining can be viewed as a gradual shift from unfamiliarity to familiarity with data. Optimization theory [\(Ruder,](#page-8-6) [2016;](#page-8-6) [Frankle et al.;](#page-8-7) [Wang et al.,](#page-9-3) [2024\)](#page-9-3) suggests that training drives parameters toward data-specific structure, reflected in consistent update patterns across magnitude, location, and concentration. As shown in Figure [1](#page-0-0) and Section [3,](#page-2-0) we observe the following trends:
+
+- 1. Decay of update magnitude. Figure [1\(](#page-0-0)a,b) shows that parameter updates are strongly attenuated as data grows familiar, consistent with loss-convergence theory [\(Bottou,](#page-8-8) [2010;](#page-8-8) [Ruder,](#page-8-6) [2016\)](#page-8-6).
+- 2. Gradually stabilizing of update locations. Figure [1\(](#page-0-0)c,d) shows that parameter updates evolve from broad activation regions to a stable core set of neurons, consistent with the sparse activation behavior of LLMs [\(Liu et al.,](#page-8-9) [2024\)](#page-8-9).
+- 3. Increasing update sparsity. Figure [1\(](#page-0-0)a,b) and Figures [2\(](#page-2-1)b,c) show that during training, an increasing fraction of updates concentrates in the top 10% of neurons, consistent with Hessian spectrum reshaping during loss convergence [\(Gur-Ari et al.,](#page-8-10) [2018\)](#page-8-10). Familiar data yields sparse, concentrated updates, whereas unfamiliar data leads to more distributed updates.
+
+These observations reflect the evolutionary dynamics of neural network training, highlighting phase differences in parameter updates induced by identical samples. Together, they offer both theoretical motivation and empirical support for our detection method based on gradient deviation scores.
+
+Based on this insight, we propose GDS, a novel pretraining data detection method that infers pre-training data by probing Gradient Deviation Scores of target samples without fine-tuning. GDS exploits gradient differences between member and non-member samples to train a lightweight classifier with strong generalization. Specifically, within the LoRA framework, we collect per-sample gradients across layers during backpropagation, encoding them as eightdimensional features that capture the magnitude, location, and concentration of updates in attention and FFN modules. Compared to non-members, member samples show smaller matrix-level and row-wise update magnitudes, lower FFN but higher attention eccentricity, greater variability in matrixlevel and row-wise updates, a higher share of top gradients, and fewer sparse neurons. Then, we extract discriminative
+
+statistics from the signals to build fixed-dimensional feature vectors, which are fed to a lightweight MLP for binary membership classification.
+
+Extensive experiments on five benchmark datasets show that GDS is effective and generalizable, improving AUC by 6.5% and achieving a 67.3% TPR@5%FPR, substantially outperforming strong baselines. Further interpretability analyses reveal distributional differences in gradient features between member and non-member samples, offering intuitive evidence of training data imprints on the model and validating our methodology. [1](#page-1-0) Our contributions are as follows:
+
+- From a training optimization perspective, we analyze how LLMs evolve from unfamiliarity to familiarity with data and propose using stage-wise parameter update dynamics to identify pretraining data, offering a novel direction to solve this task.
+- We propose gradient deviation features capturing magnitude, location, and concentration, and introduce a gradient deviation score–based method for pretraining data detection without fine-tuning.
+- Extensive experiments across diverse datasets and backbone models validate the effectiveness and generalization of GDS, while interpretability analyses reveal clear gradient differences between member and nonmember samples, supporting its validity.
+
+# 2. Related Work
+
+Likelihood-Based Scoring Methods. Early works distinguish member and non-member samples by capturing static statistical metrics in token-level likelihood distributions. Global-likelihood–based methods, such as PPL [\(Li\)](#page-8-4), Zlib [\(Carlini et al.,](#page-8-3) [2021\)](#page-8-3), and Lowercase [\(Carlini et al.,](#page-8-3) [2021\)](#page-8-3), perform discrimination by exploiting global probability features, compression entropy, and case-conversion ratios. However, global likelihood is highly sensitive to wordfrequency effects, leading to unstable performance. Mink% [\(Shi et al.,](#page-9-0) [2024\)](#page-9-0) and Min-k%++ [\(Zhang et al.,](#page-9-1) [2025\)](#page-9-1) mitigate global dependence by focusing on low-probability outlier tokens or target–candidate probability comparisons, with k and text length jointly determining the analyzed token subset. However, the fixed choice of k lacks adaptivity, causing severe score fluctuations in short texts with lowfrequency words. Although PC-PDD [\(Zhang et al.,](#page-9-4) [2024\)](#page-9-4) approximates the word-frequency distribution of pretraining corpora using public datasets, these references lack fidelity due to limited domain coverage.
+
+Fine-tuning Enhanced Methods. To address the instability of static statistical indicators, recent studies [\(Zhang et al.;](#page-9-2)
+
+<span id="page-1-0"></span><sup>1</sup>Code in https://github.com/kiky-space/icml-pdd
+
+{2}------------------------------------------------
+
+<span id="page-2-1"></span>![](_page_2_Figure_1.jpeg)
+
+*Figure 2.* Dynamic curves of four parameter update characteristics defined in the Motivation section. i → j denotes the epoch interval. Ordinate shows values of predefined characteristics, with orange and blue representing Attention and FFN modules.
+
+[Choi et al.\)](#page-8-5) adopt lightweight fine-tuning to actively amplify asymmetric differences between member and non-member samples. KDS [\(Choi et al.\)](#page-8-5) evaluates dataset contamination by comparing kernel similarity matrices of embeddings before and after fine-tuning, assuming non-member datasets undergo larger embedding changes than member datasets. However, it only estimates dataset-level contamination and cannot reliably detect contamination at the sample-level. Another representative method FSD [\(Zhang et al.\)](#page-9-2) detects membership by comparing loss before and after fine-tuning, assuming non-member samples experience a larger loss reduction than member samples. Nevertheless, these methods assume that fine-tuning data closely matches the target distribution, requiring additional tuning on similar non-member data, which limits cross-dataset generalization.
+
+# <span id="page-2-0"></span>3. Motivation
+
+153 154
+
+Inspired by optimization theory [\(Ruder,](#page-8-6) [2016;](#page-8-6) [Bottou,](#page-8-8) [2010\)](#page-8-8), we examine how LLMs transition from unfamiliarity to familiarity with data, and how this cognitive shift relates to the dynamic evolution of model parameters during training. To evaluate it, we fine-tune LLaMA-7B with LoRA on the unseen split of BookMIA dataset and track LoRA parameter updates over 7 epochs. Stage-wise analysis in Figure [2](#page-2-1) reveals the dynamic evolution of gradient features.
+
+#### 3.1. Decay of Update Magnitude
+
+Model training aims to minimize the loss function L(θ), with update magnitude determined by the gradient norm ∥∇L(θ)∥. According to optimization convergence theory [\(Ruder,](#page-8-6) [2016\)](#page-8-6), as the parameters θ<sup>t</sup> approach the optimum θ ∗ , the gradient norm of the loss function vanishes, i.e.,limθ→<sup>θ</sup> <sup>∗</sup> ∥∇L(θt)∥ = 0. This causes the parameter update magnitude to decrease synchronously. Therefore, we use ∆θ<sup>t</sup> as the core indicator of the average update magnitude across all trainable parameters at iteration t:
+
+$$\Delta \theta_{t} = \frac{1}{N} \sum_{i=1}^{N} |\theta_{t,i} - \theta_{t-1,i}|, \qquad (1)$$
+
+where N denotes the total number of trainable parameters.
+
+As training progresses, both the loss L(θt) and gradient norm ∥∇L(θt)∥ decrease, reducing the update magnitude ∆θ<sup>t</sup> and slowing its decay as parameters converge to the optimum θ ∗ . Eventually, L(θt) stabilizes near its minimum, parameter updates ∆θ<sup>t</sup> become negligible. As shown in Figure [2a,](#page-2-1) the mean update magnitude decreases monotonically with training, with the largest changes occurring in the first two epochs, consistent with loss convergence.
+
+### 3.2. Gradually Stabilizing of Update Locations
+
+Existing studies [\(Liu et al.,](#page-8-9) [2024;](#page-8-9) [Tang et al.,](#page-9-5) [2025\)](#page-9-5) have shown that neural activations occur at different locations when processing member samples and non-member samples. Inspired by this, we adopt the parameter update eccentricity as the core indicator, which quantifies the deviation of the top-10% parameter update positions from the global parameter centroid. We first define the global centroid as:
+
+$$\theta_c = \frac{1}{N} \sum_{i=1}^{N} \theta_i, \tag{2}$$
+
+where θ<sup>i</sup> is the coordinate of the i-th parameter.
+
+The update eccentricity at iteration t is then defined as:
+
+$$E_{t} = \frac{1}{\operatorname{card}(U_{10,t})} \sum_{\theta_{i} \in U_{10,t}} \|\theta_{i} - \theta_{c}\|_{2},$$
+ (3)
+
+where card(·) denotes the number of elements in a set, U10,t = {∥∆θt,i∥<sup>1</sup> ∈ Top10%(∥∆θt∥1)}, ∥ · ∥<sup>1</sup> denotes the ℓ<sup>1</sup> norm and ∥ · ∥<sup>2</sup> denotes the ℓ<sup>2</sup> norm.
+
+In the initial training stage, activation patterns are unstable, leading to scattered U10,t and thus random large values of Et. As training proceeds, the model identifies core parameters related to data features: θ<sup>t</sup> stabilizes to the optimal subset θ ∗ , and U10,t converges to the core parameter region, resulting in E<sup>t</sup> gradually stabilizing at a low level. Figure [2d](#page-2-1) shows that the eccentricity of parameter update evolves to a relatively stable value, consistent with the evolution of the
+
+{3}------------------------------------------------
+
+216
+
+218 219
+
+<span id="page-3-0"></span>![](_page_3_Figure_2.jpeg)
+
+*Figure 3.* Overview of Gradient Deviation Scores method.
+
+neuron activation pattern, suggesting that training identifies the core parameters and stabilizes updates around them.
+
+#### 3.3. Increasing Update Sparsity
+
+The Hessian spectrum [\(Gur-Ari et al.,](#page-8-10) [2018;](#page-8-10) [Frankle et al.\)](#page-8-7) is a core metric characterizing the loss function's curvature, directly determining the direction and efficiency of parameter updates. For the loss function L(θ), its Hessian matrix H(θ) = ∇2L(θ) describes the local curvature of the loss landscape, with eigenvalue decomposition:
+
+$$\mathcal{H}(\theta) = U\Lambda U^T,\tag{4}$$
+
+where U is the orthogonal eigenvector matrix (principal curvature directions), Λ = diag(λ1, . . . , λd) is the diagonal eigenvalue matrix (curvature magnitudes). During training, the Hessian spectrum changes from an almost uniform λ<sup>i</sup> ≈ c in the early stage to a late-stage structure with a few large eigenvalues and most near zero.
+
+This reshaping leads to concentrated updates, focusing on directions with large eigenvalues while leaving most others nearly unchanged. Consequently, update energy is confined to a small subset of parameters, motivating the selection of two joint indicators. S<sup>t</sup> measures the fraction of parameters with negligible updates (absolute value < 10<sup>−</sup><sup>6</sup> ) at iteration t, while T10,t measures the fraction of total update magnitude contributed by the top 10% largest updates.
+
+$$S_t = \frac{\operatorname{card}\left(i \mid |\Delta \theta_{t,i}| < 10^{-6}\right)}{N},\tag{5}$$
+
+$$T_{10,t} = \frac{\sum_{|\Delta\theta_{t,i}| \in U_{10,t}} |\Delta\theta_{t,i}|}{||\Delta\theta_t||_1}.$$
+ (6)
+
+As training progresses, parameter updates increasingly concentrate along core directions, with most parameters receiving negligible changes. Consequently, S<sup>t</sup> gradually
+
+increases, while T10,t remains relatively large and stable(0.26–0.27), indicating that update energy is consistently dominated by a small subset of parameters. Figures [2b](#page-2-1) and [2c](#page-2-1) confirm this growing sparsity and stable Top 10% contribution, reflecting update energy aggregation driven by Hessian spectrum reshaping. Further details on the variation trends of the three metrics are provided in the appendix [B.](#page-12-0)
+
+# 4. Method
+
+### 4.1. Task Definition
+
+Given a target text x and a target LLM f<sup>θ</sup> pre-trained on a corpus D, the goal of pre-training data detection task is to construct a detector h(x, fθ)to determine whether x belongs to D. This task can be formalized as a binary classification problem: h(x, fθ) → {0, 1} where "1" indicates x ∈ D as member and "0" indicates x /∈ D as non-member.
+
+As illustrated in Figure [3,](#page-3-0) GDS comprises three stages: gradient matrix acquisition, feature vector extraction and light Multilayer Perceptron(MLP) training. For each training sample, we perform inference and backpropagation to obtain LoRA gradients across l layers and m sub-modules, yielding l × m gradient matrices G. From these matrices, we extract eight-dimensional features to form a gradient feature vector V l×m×8 , which is used to train a lightweight MLP classifier for binary membership prediction. During inference, the same feature extraction process is applied to a target sample x ∗ , and the resulting feature vector is fed into the trained MLP to produce the final classification result.
+
+#### 4.2. Gradient Matrix Acquisition
+
+Given the target model f<sup>θ</sup> and training sample x, we first initialize f<sup>θ</sup> with LoRA, yielding l × m LoRA matrices L. We then feed a single sample x into f<sup>θ</sup> for forward
+
+{4}------------------------------------------------
+
+inference and backpropagation, obtaining LoRA gradient matrices  $\mathbb{G} = \nabla_{\mathbb{L}} \mathcal{L}_{\text{CLM}}(f_{\theta}(x))$ , where  $\mathcal{L}_{\text{CLM}}$  denotes the causal language modeling loss of the pre-trained LLM. Since the LoRA\_B matrices are fully initialized to zero, a single round of gradient propagation leads to zero gradients for the LoRA\_A matrices. Thus, we only collect the gradient matrices of LoRA\_B for subsequent processing.
+
+#### 4.3. Feature Vector Extraction
+
+Given the gradient matrices  $\mathbb{G}$ , we extract features based on the three parameter update trends introduced in Section 3.
+
+#### 4.3.1. MAGNITUDE
+
+We propose two magnitude indicators to measure the overall scale of gradient updates in the LoRA parameter space.
+
+(1) **Absolute Mean**: The mean of the absolute values of all elements in the gradient matrix, which characterizes the overall parameter update strength:
+
+$$Abs\_Mean = \frac{1}{r \cdot h} \sum_{i=1}^{r} \sum_{j=1}^{h} |\mathbb{G}_{i,j}|,$$
+ (7)
+
+where  $\mathbb{G}_{i,j}$  denotes the element in the *i*-th row and *j*-th column of the gradient matrix with r rows and h columns.
+
+(2) Max Row Mean: The mean of each row in the LoRA matrix and take the maximum value, which characterizes the most sample-responsive local optimal response dimension with the largest parameter update magnitude:
+
+$$Row\_Mean\_Max = \max_{1 \le i \le r} \left( \frac{1}{h} \sum_{j=1}^{h} |\mathbb{G}_{i,j}| \right).$$
+ (8)
+
+#### 4.3.2. Position
+
+Screen the top 10% of gradient elements by absolute value from  $\mathbb{G}$  and calculate their offset from this matrix center, capturing offset characteristics of core gradient positions for (1) Row Eccentricity and (2) Column Eccentricity, respectively:
+
+$$Row\_Ecc = \frac{1}{\operatorname{card}(S)} \sum_{(i,j) \in S} \left| \frac{2i - (r+1)}{r-1} \right|, \quad (9)$$
+
+$$Col\_Ecc = \frac{1}{\operatorname{card}(S)} \sum_{(i,j) \in S} \left| \frac{2j - (h+1)}{h-1} \right|, \quad (10)$$
+
+where  $S = \{(i,j) \mid |\mathbb{G}_{i,j}| \in \text{Top10\%}(|\mathbb{G}|)\}$  denotes the set of indices for the top 10% of elements in the gradient matrix  $\mathbb{G}$  ranked by absolute gradient value. Top gradients near the center correspond to an eccentricity of 0, while those near the edge correspond to a score of 1.
+
+#### 4.3.3. CONCENTRATION
+
+We propose four indicators to measure the concentration of gradient distributions.
+
+(1) **Top-10% Ratio**: The ratio of the sum of the top 10% largest gradient magnitudes to the total update magnitude of the gradient matrix, which quantifies the contribution ratio of core gradients:
+
+$$10p\_Ratio = \frac{\sum_{(i,j)\in S} |\mathbb{G}_{i,j}|}{\|\mathbb{G}\|_1}, \tag{11}$$
+
+(2) **Sparsity**: The proportion of gradient elements with absolute values less than  $10^{-6}$ , which quantifies the sparsity degree of gradient distributions:
+
+$$Sparsity = \frac{\operatorname{card}\left(\left\{\left(i,j\right) \mid |\mathbb{G}_{i,j}| < 10^{-6}\right\}\right)}{r \cdot h}.$$
+ (12)
+
+(3) **Standard Deviation**: The standard deviation of the elements in the gradient matrix, which quantifies the dispersion degree of parameter updates:
+
+$$Std = \sqrt{\frac{1}{r \cdot h} \sum_{i=1}^{r} \sum_{j=1}^{h} (|\mathbb{G}_{i,j}| - \text{Abs\_mean})^2}.$$
+ (13)
+
+(4) Row Mean Standard Deviation: The mean of each row in the LoRA matrix and take the standard deviation, which quantifies the consistency of update strength across all rows:
+
+$$Row\_Mean\_Std = \sqrt{\frac{1}{r} \sum_{i=1}^{r} \left(\bar{\mathbb{G}}_i - \mu_{\bar{\mathbb{G}}}\right)^2}, \quad (14)$$
+
+where  $\bar{\mathbb{G}}_i = \frac{1}{h} \sum_{j=1}^h |\mathbb{G}_{i,j}|$  denotes the *i*-th row's absolute mean,  $\mu_{\bar{\mathbb{G}}} = \frac{1}{r} \sum_{i=1}^r \bar{\mathbb{G}}_i$  denotes t the mean of row means.
+
+We compute the aforementioned eight feature values from all gradient matrices to derive a feature vector  $\mathbb{V}^{l\times m\times 8}$   $\triangleq$  [Abs\_Mean, Row\_Mean\_Max, 10p\_Ratio, Sparsity, Std, Row\_Mean\_Std, Row\_Ecc, Col\_Ecc] per sample, which is then used for subsequent MLP training and inference.
+
+#### 4.4. Light MLP Training
+
+Given the feature vectors  $\mathbb{V}_i$  from all training samples vectors  $\mathbb{V}_s$ , we feed them into a lightweight MLP for training. The target output corresponds to the binary label  $\{0,1\}$  for each sample, where 0 denotes non-member and 1 denotes member. The training loss is defined as follows:
+
+$$\mathcal{L} = -\frac{1}{N} \sum_{i=1}^{N} \left[ y_i \log \hat{y}_i + (1 - y_i) \log(1 - \hat{y}_i) \right], \quad (15)$$
+
+where N denotes the number of training samples,  $y_i \in \{0,1\}$  is the ground-truth label of the i-th sample, and  $\hat{y}_i$  is the predicted probability output by the MLP.
+
+{5}------------------------------------------------
+
+294
+
+296
+
+313 314
+
+316
+
+324
+
+326
+
+328 329
+
+<span id="page-5-0"></span>*Table 1.* Comparison(AUROC/TPR@5%FPR) on 4 Datasets across 5 target models. Target models are denoted as 2.7B/6B/6.7B/6.9B/7B, corresponding to Neo-2.7B/GPT-J-6b/OPT-6.7b/Pythia-6.9b/LLaMA-7B respectively. The best result is bold.
+
+|        |                   |           | WikiMIA     |           |           |           |           | ArXivTection |           |           |  |
+|--------|-------------------|-----------|-------------|-----------|-----------|-----------|-----------|--------------|-----------|-----------|--|
+| Method | 2.7B              | 6B        | 6.7B        | 6.9B      | 7B        | 2.7B      | 6B        | 6.7B         | 6.9B      | 7B        |  |
+| PPL    | 0.61/0.13         | 0.64/0.13 | 0.60/0.12   | 0.63/0.13 | 0.69/0.14 | 0.62/0.13 | 0.64/0.13 | 0.60/0.12    | 0.63/0.13 | 0.70/0.14 |  |
+| ZLib   | 0.58/0.10         | 0.60/0.11 | 0.58/0.10   | 0.59/0.10 | 0.71/0.22 | 0.58/0.10 | 0.60/0.11 | 0.58/0.09    | 0.59/0.11 | 0.71/0.22 |  |
+| Min-k  | 0.65/0.17         | 0.67/0.19 | 0.63/0.15   | 0.67/0.19 | 0.73/0.18 | 0.65/0.17 | 0.68/0.19 | 0.63/0.15    | 0.67/0.19 | 0.72/0.18 |  |
+|        | Min-k++ 0.67/0.15 | 0.69/0.19 | 0.65/0.11   | 0.70/0.18 | 0.82/0.22 | 0.67/0.15 | 0.69/0.19 | 0.65/0.10    | 0.70/0.17 | 0.83/0.22 |  |
+| FSD    | 0.92/0.77         | 0.95/0.78 | 0.90/0.63   | 0.90/0.66 | 0.92/0.41 | 0.91/0.65 | 0.96/0.79 | 0.89/0.63    | 0.95/0.66 | 0.94/0.81 |  |
+| Ours   | 0.90/0.60         | 0.93/0.66 | 0.94/0.67   | 0.92/0.63 | 0.96/0.84 | 0.94/0.73 | 0.97/0.86 | 0.94/0.75    | 0.95/0.83 | 0.97/0.85 |  |
+|        |                   |           | BookTection |           |           | BookMIA   |           |              |           |           |  |
+| Method | 2.7B              | 6B        | 6.7B        | 6.9B      | 7B        | 2.7B      | 6B        | 6.7B         | 6.9B      | 7B        |  |
+| PPL    | 0.69/0.15         | 0.74/0.25 | 0.64/0.13   | 0.73/0.25 | 0.71/0.25 | 0.29/0.02 | 0.22/0.13 | 0.23/0.01    | 0.59/0.19 | 0.56/0.21 |  |
+| ZLib   | 0.56/0.16         | 0.58/0.20 | 0.55/0.14   | 0.58/0.19 | 0.57/0.19 | 0.20/0.02 | 0.38/0.13 | 0.15/0.00    | 0.49/0.17 | 0.48/0.18 |  |
+| Min-k  | 0.71/0.18         | 0.75/0.27 | 0.67/0.15   | 0.74/0.26 | 0.71/0.25 | 0.45/0.05 | 0.60/0.20 | 0.40/0.03    | 0.62/0.20 | 0.60/0.21 |  |
+|        | Min-k++ 0.64/0.13 | 0.67/0.18 | 0.61/0.11   | 0.66/0.19 | 0.63/0.15 | 0.54/0.13 | 0.64/0.29 | 0.49/0.09    | 0.60/0.23 | 0.58/0.20 |  |
+| FSD    | 0.92/0.53         | 0.91/0.52 | 0.96/0.77   | 0.93/0.59 | 0.92/0.55 | 0.98/0.93 | 0.97/0.89 | 0.98/0.96    | 0.98/0.93 | 0.98/0.91 |  |
+| Ours   | 0.96/0.84         | 0.97/0.88 | 0.98/0.92   | 0.96/0.83 | 0.98/0.92 | 0.99/0.98 | 0.99/0.99 | 0.99/0.99    | 0.99/0.98 | 0.99/0.99 |  |
+
+*Table 2.* Performance Comparison on Mimir datasets with 7 subsets across 5 target models using AUROC scores.
+
+<span id="page-5-1"></span>
+
+|                                                                                                             |    | Wikipedia                                                                                           |           |         |    | Github |                |         |    | Pile CC    |           |         |    | PubMed Central |           |    |
+|-------------------------------------------------------------------------------------------------------------|----|-----------------------------------------------------------------------------------------------------|-----------|---------|----|--------|----------------|---------|----|------------|-----------|---------|----|----------------|-----------|----|
+| Method 2.7B                                                                                                 | 6B |                                                                                                     | 6.7B 6.9B | 7B 2.7B | 6B |        | 6.7B 6.9B      | 7B 2.7B | 6B |            | 6.7B 6.9B | 7B 2.7B | 6B |                | 6.7B 6.9B | 7B |
+| PPL                                                                                                         |    | 0.56 0.57 0.56 0.56 0.56 0.78 0.79 0.78 0.90 0.83 0.56 0.57 0.56 0.56 0.52 0.78 0.79 0.78 0.78 0.72 |           |         |    |        |                |         |    |            |           |         |    |                |           |    |
+| ZLib                                                                                                        |    | 0.62 0.65 0.59 0.65 0.58 0.90 0.91 0.79 0.91 0.86 0.55 0.55 0.55 0.55 0.52 0.78 0.78 0.73 0.77 0.71 |           |         |    |        |                |         |    |            |           |         |    |                |           |    |
+| Min-k                                                                                                       |    | 0.66 0.68 0.65 0.68 0.63 0.88 0.89 0.76 0.90 0.83 0.56 0.57 0.56 0.56 0.52 0.81 0.80 0.74 0.79 0.72 |           |         |    |        |                |         |    |            |           |         |    |                |           |    |
+| Min-k++ 0.65 0.68 0.60 0.69 0.56 0.84 0.86 0.56 0.86 0.73 0.54 0.55 0.54 0.56 0.51 0.71 0.72 0.60 0.70 0.59 |    |                                                                                                     |           |         |    |        |                |         |    |            |           |         |    |                |           |    |
+| FSD                                                                                                         |    | 0.61 0.67 0.60 0.65 0.60 0.77 0.80 0.62 0.77 0.72 0.55 0.55 0.54 0.55 0.52 0.71 0.79 0.63 0.56 0.63 |           |         |    |        |                |         |    |            |           |         |    |                |           |    |
+| Ours                                                                                                        |    | 0.63 0.64 0.65 0.65 0.64 0.90 0.92 0.88 0.92 0.91 0.59 0.59 0.59 0.57 0.59 0.84 0.85 0.84 0.79 0.82 |           |         |    |        |                |         |    |            |           |         |    |                |           |    |
+|                                                                                                             |    | ArXiv                                                                                               |           |         |    |        | DM Mathematics |         |    | HackerNews |           |         |    | Average        |           |    |
+| Method 2.7B                                                                                                 | 6B |                                                                                                     | 6.7B 6.9B | 7B 2.7B | 6B |        | 6.7B 6.9B      | 7B 2.7B | 6B |            | 6.7B 6.9B | 7B 2.7B | 6B |                | 6.7B 6.9B | 7B |
+| PPL                                                                                                         |    | 0.78 0.79 0.65 0.78 0.70 0.78 0.79 0.65 0.91 0.31 0.65 0.62 0.59 0.62 0.59 0.64 0.66 0.62 0.73 0.59 |           |         |    |        |                |         |    |            |           |         |    |                |           |    |
+| ZLib                                                                                                        |    | 0.77 0.78 0.68 0.77 0.71 0.82 0.81 0.80 0.81 0.23 0.68 0.60 0.58 0.60 0.58 0.65 0.67 0.63 0.72 0.58 |           |         |    |        |                |         |    |            |           |         |    |                |           |    |
+| Min-k                                                                                                       |    | 0.78 0.79 0.65 0.78 0.70 0.93 0.93 0.92 0.92 0.32 0.65 0.62 0.59 0.62 0.59 0.71 0.73 0.69 0.75 0.60 |           |         |    |        |                |         |    |            |           |         |    |                |           |    |
+| Min-k++ 0.60 0.64 0.53 0.70 0.57 0.77 0.79 0.67 0.75 0.22 0.53 0.57 0.51 0.60 0.53 0.60 0.63 0.56 0.67 0.53 |    |                                                                                                     |           |         |    |        |                |         |    |            |           |         |    |                |           |    |
+| FSD                                                                                                         |    | 0.72 0.78 0.55 0.70 0.52 0.58 0.85 0.60 0.74 0.53 0.61 0.60 0.57 0.56 0.51 0.61 0.66 0.59 0.62 0.55 |           |         |    |        |                |         |    |            |           |         |    |                |           |    |
+| Ours                                                                                                        |    | 0.78 0.79 0.78 0.78 0.77 0.95 0.95 0.94 0.95 0.95 0.58 0.60 0.60 0.57 0.58 0.73 0.75 0.74 0.76 0.70 |           |         |    |        |                |         |    |            |           |         |    |                |           |    |
+
+# 5. Experiments
+
+#### 5.1. Experimental Setup
+
+Datasets Following prior work, we evaluate on five prevalent datasets: WikiMIA, BookMIA [\(Shi et al.,](#page-9-0) [2024\)](#page-9-0),ArxivTection, BookTection [\(Duarte et al.\)](#page-8-11), and MIMIR [\(Duan](#page-8-12) [et al.\)](#page-8-12), a widely recognized challenging benchmark for pretraining data detection.
+
+Target Models We evaluate five open-source LLMs with diverse architectures: Neo-2.7B [\(Black et al.,](#page-8-13) [2021\)](#page-8-13), GPT-J-6B [\(Wang & Komatsuzaki,](#page-9-6) [2021\)](#page-9-6), OPT-6.7B [\(Zhang et al.,](#page-9-7) [2022\)](#page-9-7), Pythia-6.9B [\(Biderman et al.,](#page-8-14) [2023\)](#page-8-14), and LLaMA-7B [\(Touvron et al.,](#page-9-8) [2023\)](#page-9-8) from Hugging Face.
+
+Comparison Methods We select five representative stateof-the-art baselines. Four scoring function–based methods
+
+include PPL [\(Carlini et al.,](#page-8-3) [2021\)](#page-8-3), ZLib [\(Carlini et al.,](#page-8-3) [2021\)](#page-8-3), Min-k [\(Shi et al.,](#page-9-0) [2024\)](#page-9-0), and Min-k++ [\(Zhang et al.,](#page-9-1) [2025\)](#page-9-1). The fine-tuning–enhanced method includes FSD [\(Zhang](#page-9-2) [et al.\)](#page-9-2). More details are shown in Appendix [A.](#page-10-0)
+
+Evaluation Metrics Two metrics evaluate the binary pretraining data detection task: AUROC measures overall discriminative performance, and TPR@5%FPR captures practical effectiveness by assessing detection rate under a 5% false positive constraint.
+
+Implementation Details We use the PEFT library [\(Man](#page-8-15)[grulkar et al.,](#page-8-15) [2022\)](#page-8-15) for LoRA-based [\(Hu et al.,](#page-8-16) [2022\)](#page-8-16) gradient feature extraction without parameter updates. The MLP is trained on 30% of the data, with the remaining 70% used for inference evaluation under FSD settings. More Details can be seen in Appendix [A.6.](#page-11-0)
+
+{6}------------------------------------------------
+
+<span id="page-6-2"></span>![](_page_6_Figure_1.jpeg)
+
+*Figure 4.* Distribution differences of eight gradient features between member(red) and non-member(blue) samples. Dashed lines indicate distribution means. The x-axis represents feature values, and the y-axis denotes probability density.
+
+<span id="page-6-0"></span>*Table 3.* Ablation results using AUROC on WikiMIA and Arxiv-Tection. - denotes the removal of related features.
+
+| Dataset      | -Magnitude   | -Concentration | -Position    |
+|--------------|--------------|----------------|--------------|
+| WikiMIA      | 0.94 (↓0.02) | 0.94 (↓0.02)   | 0.93 (↓0.03) |
+| ArxivTection | 0.96 (↓0.01) | 0.95 (↓0.02)   | 0.95 (↓0.02) |
+
+<span id="page-6-1"></span>*Table 4.* Ablation results using AUROC and TPR@5%FPR. ATT-Only refers to performance validation using only attention module.
+
+| Dataset      | ATT-Only    | FFN-Only    | Origin      |
+|--------------|-------------|-------------|-------------|
+| WikiMIA      | 0.94 / 0.68 | 0.93 / 0.64 | 0.96 / 0.84 |
+| ArxivTection | 0.95 / 0.76 | 0.93 / 0.72 | 0.97 / 0.85 |
+
+# 5.2. Main Results
+
+330
+
+334
+
+336
+
+354
+
+356
+
+374
+
+376
+
+Table [1](#page-5-0) shows detection performance on WikiMIA, Arxiv-Tection, BookTection, and BookMIA. Specifically, when tested on WikiMIA with LLaMA-7B, GDS achieves an AUC score of 0.96, which is an improvement of 0.04 compared to the best baseline FSD and significantly higher than score-function-based methods such as Min-k++. GDS outperforms the best baseline in most settings, with especially large gains in TPR@5%FPR on BookTection and Book-MIA. Notably, with LLaMA-7B, BookTection performance improves by nearly 67.3%.
+
+Table [2](#page-5-1) reports results on seven MIMIR subsets. Although all methods degrade due to similar data distributions, GDS achieves the best average improvements +2.8%, +2.7%, +7.2%, +1.3%, +16.6% across different models, and shows clear advantages on PubMed Central, DM Mathematics, and GitHub. Using the LLaMA model, the three subsets achieve AUC scores of 0.82, 0.95, and 0.91. Our method shows the most stable performance across models, with AUC variations mostly within 0.04, demonstrating strong generalization across different models.
+
+#### 5.3. Ablation Study
+
+We perform two ablation studies: (1) removing each gradient feature category individually, and (2) using features from only the Attention or FFN module. Table [3](#page-6-0) shows that all feature categories contribute to performance, with Position Offset and Magnitude being the most important. Concentration features have smaller effects, and the full combination performs best, highlighting the complementary nature of multi-dimensional features (see Appendix [C](#page-14-0) for sub-feature ablations). Table [4](#page-6-1) shows that Attention features are more discriminative than FFN features. Both single-module variants underperform the full model, indicating that Attention and FFN capture complementary gradient patterns and must be combined for optimal performance.
+
+#### 5.4. Analysis
+
+# 5.4.1. FEATURE DISTRIBUTION
+
+To explain the classifier's effectiveness, we quantify feature distributions across all layers and sub-modules for member and non-member samples. Figure [4](#page-6-2) shows the eight features with the largest discrepancies. Member samples exhibit smaller Abs Mean and Row Mean Max, indicating lower gradient magnitudes due to higher data familiarity, along with higher Sparsity, smaller Std and Row Mean Std, reflecting more concentrated and stable gradients. They also maintain a consistently higher 10p Ratio, occupying the core of gradient propagation. For locations Row Ecc and Col Ecc, member samples cluster at lower values, while non-members shift higher, suggesting that member-related parameters lie more centrally in weight matrices.
+
+We collect sub-features with the largest distribution differences between the two sample types and analyze their overall distribution patterns. Figure [5](#page-7-0) show that discriminative sub-features are predominantly concentrated in low layers, while middle and high layers contribute far less. Among sub-modules, attention-related modules are the main sources
+
+{7}------------------------------------------------
+
+<span id="page-7-1"></span>*Table 5.* Performance Comparison between LoRA and Full-Parameter Update using AUROC on WikiMIA and ArxivTection.
+
+| Dataset      | Metric     | LLaMA-7B |      | GPT-J-6B |      | OPT-6.7B |      | Pythia-6.9B |      | Neo-2.7B |      |
+|--------------|------------|----------|------|----------|------|----------|------|-------------|------|----------|------|
+|              |            | LoRA     | Full | LoRA     | Full | LoRA     | Full | LoRA        | Full | LoRA     | Full |
+| WikiMIA      | AUC        | 0.96     | 0.96 | 0.93     | 0.90 | 0.94     | 0.92 | 0.92        | 0.89 | 0.90     | 0.88 |
+|              | TPR@5% FPR | 0.84     | 0.79 | 0.66     | 0.58 | 0.67     | 0.56 | 0.63        | 0.50 | 0.60     | 0.51 |
+| ArxivTection | AUC        | 0.97     | 0.96 | 0.97     | 0.96 | 0.94     | 0.93 | 0.95        | 0.94 | 0.94     | 0.94 |
+|              | TPR@5% FPR | 0.85     | 0.84 | 0.86     | 0.79 | 0.75     | 0.67 | 0.83        | 0.73 | 0.73     | 0.75 |
+
+<span id="page-7-0"></span>![](_page_7_Figure_4.jpeg)
+
+*Figure 5.* Distribution Difference Statistics of Discriminative Features. The y-axis shows the statistical count.
+
+of discriminative features, with obvious differences in contribution across modules. In terms of gradient features, grad sparsity exhibits the strongest discriminative power, significantly outperforming other indicators.
+
+# 5.4.2. FULL PARAMETER TRAINING
+
+In LoRA training, only FFN and MLP modules are updated, while LayerNorm, despite containing meaningful training dynamics, is excluded. To account for this, we evaluate our method under full-parameter training on two small-scale datasets, BookMIA and ArxivTection, for computational feasibility. As shown in Table [5,](#page-7-1) although full-parameter updates cause a slight performance drop compared to LoRA, our method still outperforms most baselines. We attribute this gap to reduced gradient magnitudes in full training, which weaken discriminative signals between sample types.
+
+#### 5.4.3. WIKIMIA MODIFICATION
+
+Dataset partitioning can introduce distribution shifts or dataset-specific artifacts. For example, WikiMIA is split by publication time, with all non-member samples labeled as 2023. To ensure our method does not exploit such artifacts, we remove all timestamp tokens and reevaluate all methods. As shown in Table [6,](#page-7-2) although token removal degrades performance, our method suffers a much smaller drop than the strongest baseline, FSD, and still achieves SOTA results.
+
+<span id="page-7-2"></span>*Table 6.* Comparison of Temporal Feature Perturbation via AU-ROC. Deletion denotes the removal of all year timestamps.
+
+| Method  | Origin | Deletion |
+|---------|--------|----------|
+| PPL     | 0.69   | 0.62     |
+| Min-k   | 0.73   | 0.63     |
+| Min-k++ | 0.82   | 0.59     |
+| FSD     | 0.92   | 0.76     |
+| Ours    | 0.96   | 0.84     |
+
+<span id="page-7-3"></span>*Table 7.* Cross-Dataset Generalization Performance using AU-ROC. Wiki(arXiv) indicates training on ArxivTection with test on WikiMIA, while Mix indicates mixed datasets.
+
+| Method | Wiki (arXiv) | arXiv (Wiki) | Mix  |
+|--------|--------------|--------------|------|
+| FSD    | 0.52         | 0.58         | 0.92 |
+| Ours   | 0.66         | 0.68         | 0.95 |
+
+### 5.4.4. TRANSFERABILITY
+
+Although our method shares the same feature extraction framework, it requires dataset-specific classifiers. To examine whether a unified classifier is feasible, we train classifiers on WikiMIA and ArXiv separately and evaluate crossdataset generalization, as well as train a unified classifier on mixed data. Table [7](#page-7-3) shows that cross-dataset transfer leads to notable performance degradation due to dataset shifts (e.g., distribution, difficulty, and pre-training differences), which cause classifiers to overfit dataset-specific gradient features. In contrast, the unified classifier performs well on mixed data, indicating that our method can capture universal feature discrepancies arising from model familiarity.
+
+# 6. Conclusion
+
+We revisit pre-training data detection from an optimization and training-dynamics perspective and introduce GDS, a fine-tuning–free method for inferring pre-training membership. By analyzing how models transition from unfamiliarity to familiarity, we show that member and non-member samples exhibit stable, interpretable differences in gradient magnitude, location, and concentration across datasets and architectures. Experiments show that GDS is effective and generalizable, outperforming strong baselines. Future work can focus on developing more generalizable detectors by contrastive learning or deeper feature extraction.
+
+{8}------------------------------------------------
+
+# Limitations
+
+This work investigates pre-training data detection, a form of membership inference that determines whether a given sample was included in a LLM's pre-training corpus. While our proposed GDS method improves detection accuracy and generalization without fine-tuning, it also raises important ethical concerns. Pre-training data detection methods could be misused to probe proprietary or confidential training corpora, potentially revealing sensitive information about data sources or collection practices. Although GDS does not reconstruct or expose training samples directly, it contributes to capabilities that may be exploited if applied irresponsibly. Our primary motivation is to support transparency, accountability, and safety. As pre-training datasets become increasingly large and opaque, tools like GDS can help researchers, auditors, and regulators verify data usage claims, identify potential copyright violations, and detect benchmark contamination. In this sense, GDS is intended as a diagnostic and auditing mechanism rather than a data extraction attack. We release code and models to promote reproducibility while encouraging responsible deployment. Overall, we hope this work advances trustworthy and transparent large-scale model development while highlighting the need for careful governance of pre-training data.
+
+# References
+
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+- <span id="page-8-14"></span>Biderman, S., Schoelkopf, H., Anthony, Q. G., Bradley, H., O'Brien, K., Hallahan, E., Khan, M. A., Purohit, S., Prashanth, U. S., Raff, E., et al. Pythia: A suite for analyzing large language models across training and scaling. In *International Conference on Machine Learning*, pp. 2397–2430. PMLR, 2023.
+- <span id="page-8-13"></span>Black, S., Leo, G., Wang, P., Leahy, C., and Biderman, S. Gpt-neo: Large scale autoregressive language modeling with mesh-tensorflow. *Zenodo*, 2021.
+- <span id="page-8-8"></span>Bottou, L. Large-scale machine learning with stochastic gradient descent. In *Proceedings of COMPSTAT'2010: 19th International Conference on Computational StatisticsParis France, August 22-27, 2010 Keynote, Invited and Contributed Papers*, pp. 177–186. Springer, 2010.
+- <span id="page-8-3"></span>Carlini, N., Tramer, F., Wallace, E., Jagielski, M., Herbert-Voss, A., Lee, K., Roberts, A., Brown, T., Song, D., Erlingsson, U., et al. Extracting training data from large
+
+- language models. In *30th USENIX security symposium (USENIX Security 21)*, pp. 2633–2650, 2021.
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+- <span id="page-8-11"></span>Duarte, A. V., Zhao, X., Oliveira, A. L., and Li, L. Decop: Detecting copyrighted content in language models training data. In *Forty-first International Conference on Machine Learning*.
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+- <span id="page-8-10"></span>Gur-Ari, G., Roberts, D. A., and Dyer, E. Gradient descent happens in a tiny subspace. *arXiv preprint arXiv:1812.04754*, 2018.
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+- <span id="page-8-0"></span>Kaplan, J., McCandlish, S., Henighan, T., Brown, T. B., Chess, B., Child, R., Gray, S., Radford, A., Wu, J., and Amodei, D. Scaling laws for neural language models. *arXiv preprint arXiv:2001.08361*, 2020.
+- <span id="page-8-4"></span>Li, Y. Estimating contamination via perplexity: Quantifying memorisation in language model evaluation. In *The Future of Machine Learning Data Practices and Repositories at ICLR 2025*.
+- <span id="page-8-9"></span>Liu, Z., Zhu, T., Tan, C., Liu, B., Lu, H., and Chen, W. Probing language models for pre-training data detection. In *Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)*, pp. 1576–1587, 2024.
+- <span id="page-8-15"></span>Mangrulkar, S., Gugger, S., Debut, L., Belkada, Y., Paul, S., and Bossan, B. Peft: State-of-the-art parameter-efficient fine-tuning methods. 2022.
+- <span id="page-8-6"></span>Ruder, S. An overview of gradient descent optimization algorithms. *arXiv preprint arXiv:1609.04747*, 2016.
+
+{9}------------------------------------------------
+
+<span id="page-9-0"></span>Shi, W., Ajith, A., Xia, M., Huang, Y., Liu, D., Blevins, T., Chen, D., and Zettlemoyer, L. Detecting pretraining data from large language models. In *12th International Conference on Learning Representations, ICLR 2024*, 2024.
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+534
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+- <span id="page-9-5"></span>Tang, H., Zhu, Z., and Yang, Y. Identifying pre-training data in llms: A neuron activation-based detection framework. In *Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing*, pp. 18738– 18751, 2025.
+- <span id="page-9-8"></span>Touvron, H., Lavril, T., Izacard, G., Martinet, X., Lachaux, M.-A., Lacroix, T., Roziere, B., Goyal, N., Hambro, E., ` Azhar, F., et al. Llama: Open and efficient foundation language models. *arXiv preprint arXiv:2302.13971*, 2023.
+- <span id="page-9-6"></span>Wang, B. and Komatsuzaki, A. Gpt-j-6b: A 6 billion parameter autoregressive language model, 2021.
+- Wang, H., Ma, S., Wang, R., and Wei, F. Q-sparse: All large language models can be fully sparsely-activated. *arXiv preprint arXiv:2407.10969*, 2024.
+- Zhang, H., Zhang, S., Jing, B., and Wei, H. Fine-tuning can help detect pretraining data from large language models. In *The Thirteenth International Conference on Learning Representations*.
+- <span id="page-9-1"></span>Zhang, J., Sun, J., Yeats, E., Ouyang, Y., Kuo, M., Zhang, J., Yang, H. F., and Li, H. Min-k%++: Improved baseline for pre-training data detection from large language models. In *The Thirteenth International Conference on Learning Representations*, 2025.
+- Zhang, S., Roller, S., Goyal, N., Artetxe, M., Chen, M., Chen, S., Dewan, C., Diab, M., Li, X., Lin, X. V., et al. Opt: Open pre-trained transformer language models. *arXiv preprint arXiv:2205.01068*, 2022.
+- <span id="page-9-4"></span>Zhang, W., Zhang, R., Guo, J., Rijke, M., Fan, Y., and Cheng, X. Pretraining data detection for large language models: A divergence-based calibration method. In *Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing*, pp. 5263–5274, 2024.
+
+{10}------------------------------------------------
+
+# <span id="page-10-0"></span>A. Details of Baseline
+
+Shared Notations: We first define the universal notations used across all baseline methods for consistency:
+
+- x: Input text sample for membership inference detection.
+- {x1, x2, . . . , x<sup>N</sup> }: Token sequence of input text sample x, where N denotes the total number of tokens in the text.
+- x<t: Prefix token sequence of the t-th token xt, i.e., x<t = {x1, . . . , xt−1}.
+- θ: Trainable parameters of the pre-trained language model.
+- p(· | ·; θ): Conditional probability distribution parameterized by the model parameters θ.
+- k%: Percentage threshold for selecting low-probability outlier tokens (used in Min-k% and Min-k%++).
+
+#### A.1. PPL
+
+550
+
+554
+
+556
+
+574
+
+576
+
+594
+
+596
+
+Perplexity (PPL) is a classic global likelihood-based metric that measures the model's uncertainty in predicting a given text, with lower PPL indicating higher text familiarity (more likely to be a member sample). First, the text is tokenized into a sequence of tokens {x1, x2, . . . , x<sup>N</sup> }. Then, the log-likelihood of each token is calculated conditional on the preceding tokens, and the final PPL is derived by normalizing the sum of log-likelihoods by the token sequence length and performing an exponential transformation.
+
+$$PPL = \exp\left(-\frac{1}{N} \sum_{i=1}^{N} \log p(x_i|x_1, ..., x_{x-1}; \theta)\right)$$
+ (16)
+
+#### A.2. Zlib
+
+Zlib is a compression-based global likelihood-related method that leverages compression entropy to distinguish member and non-member samples, which calibrates the loss using the input's Zlib entropy. For an input text sample x and a pre-trained model M, the Zlib score is defined as the ratio of the loss related to the text and model to the Zlib compression entropy of the input text:
+
+Zlib Score = 
+$$\frac{L(x, M)}{\text{zlib}(x)}$$
+ (17)
+
+where L(x, M) denotes the loss value associated with the input text x under the model M and zlib(x) represents the Zlib compression entropy of the input text x, which is derived from the length of the text after Zlib compression.
+
+#### A.3. Min-k%
+
+Min-k% is a local likelihood-based method that mitigates global word frequency interference by focusing on low-probability outlier tokens. For an input text token sequence x = {x1, x2, . . . , x<sup>N</sup> } (where N denotes the total number of tokens), it first calculates the conditional log-likelihood of each token x<sup>i</sup> given its preceding context:
+
+$$\log p(x_i \mid x_1, x_2, \dots, x_{i-1}; \theta)$$
+
+Subsequently, it sorts all token conditional probabilities in ascending order, selects the bottom k% tokens (i.e., the k% tokens with the smallest conditional probabilities) to form the low-probability set Tmin(k%) = Min-K%(x). The final Min-k% score is defined as the average conditional log-likelihood of tokens in Tmin(k%):
+
+Min-k% Score(x) = 
+$$\frac{1}{|T_{\min(k\%)}|} \sum_{x_i \in T_{\min(k\%)}} \log p(x_i \mid x_1, \dots, x_{i-1}; \theta)$$
+ (18)
+
+where |Tmin(k%)| = ⌊k% × N⌋ denotes the cardinality of the low-probability token set (rounded down to the nearest integer). During detection, a threshold is set on Min-k% Score(x): text with a score below the threshold is classified as a member sample (since member samples tend to contain more low-probability outlier tokens), and vice versa.
+
+{11}------------------------------------------------
+
+#### A.4. Min-k%++
+
+Min-k%++ is an optimized variant of Min-k% that enhances detection robustness by integrating vocabulary-level probability statistics, addressing the text-length dependency and short-text fluctuation issues of the original method. For an input text token sequence  $x = \{x_1, x_2, \dots, x_N\}$ , it first computes the normalized conditional log-likelihood for each token  $x_t$  (given prefix  $x_{< t} = \{x_1, \dots, x_{t-1}\}$ ) by normalizing with the vocabulary-wide log-probability statistics of the prefix  $x_{< t}$ .
+
+#### **Core Token-Level Score Calculation**
+
+For each token  $x_t$ , the token-level Min-k%++ score is defined as:
+
+$$Min-k\% + +_{token}(x_{< t}, x_t) = \frac{\log p(x_t \mid x_{< t}; \theta) - \mu_{x_{< t}}}{\sigma_{x_{< t}}}$$
+(19)
+
+where  $\mu_{x_{< t}} = \mathbb{E}_{z \sim p(\cdot \mid x_{< t}; \theta)} [\log p(z \mid x_{< t}; \theta)]$ : Expectation of the next-token log-likelihood over the model's vocabulary, given prefix  $x_{< t}$ ;  $\sigma_{x_{< t}} = \sqrt{\mathbb{E}_{z \sim p(\cdot \mid x_{< t}; \theta)} \left[ (\log p(z \mid x_{< t}; \theta) - \mu_{x_{< t}})^2 \right]}$ : Standard deviation of the next-token log-likelihood over the vocabulary, given prefix  $x_{< t}$ .
+
+Both  $\mu_{x_{< t}}$  and  $\sigma_{x_{< t}}$  can be computed analytically using the model's output logits (since  $p(\cdot \mid x_{< t}; \theta)$  follows a categorical distribution), requiring no additional computational overhead beyond standard LLM inference.
+
+#### **Final Sequence-Level Score Calculation**
+
+Similar to Min-k%, Min-k%++ selects the bottom k% tokens with the smallest Min-k%++<sub>token</sub> scores to form the low-probability set  $T_{\min(k\%)}^+$ . The final sequence-level score is the average of the token-level scores in this set:
+
+$$Min-k\% ++ Score(x) = \frac{1}{|T_{\min(k\%)}^+|} \sum_{(x_{< t}, x_t) \in T_{\min(k\%)}^+} Min-k\% ++_{token}(x_{< t}, x_t)$$
+ (20)
+
+where  $|T_{\min(k\%)}^+| = \lfloor k\% \times N \rfloor$  denotes the cardinality of the low-probability token set. During detection, a threshold is applied: text with a lower Min-k%++ score is more likely to be a member sample, as the normalized score better distinguishes low-probability outlier tokens of member samples from non-member ones.
+
+#### A.5. FSD
+
+Fine-tuned Score Deviation (FSD) is a fine-tuning enhanced method that leverages score discrepancies between pre-trained and fine-tuned models for member sample detection. Its core workflow includes two key steps: first, constructing a domain-matched non-member fine-tuning dataset (using post-model-release unseen data), then performing self-supervised next-token prediction fine-tuning on the pre-trained model. Finally, it calculates the score difference between the pre-trained and fine-tuned models to distinguish member and non-member samples. The self-supervised fine-tuning loss is defined as:
+
+$$\mathcal{L}_{\text{fine-tuning}}(x) = -\frac{1}{n} \sum_{i=1}^{n} \log f_{\theta}(x_i \mid x_1, \dots, x_{i-1})$$
+(21)
+
+The final FSD score is the deviation between the sample scores obtained from the pre-trained model  $f_{\theta}$  and the fine-tuned model  $f_{\theta'}$  (with parameters  $\theta'$ ):
+
+$$FSD(x; f_{\theta}, f_{\theta'}) = S(x; f_{\theta}) - S(x; f_{\theta'})$$
+(22)
+
+where  $S(\cdot)$  represents a base scoring function (e.g., Perplexity, Min-k%). A large FSD score indicates the sample is likely a non-member (fine-tuning reduces non-member perplexity significantly), while a small score suggests a member sample (fine-tuning has negligible impact on member perplexity). A validation-set optimized threshold  $\varepsilon$  is used for final classification.
+
+#### <span id="page-11-0"></span>A.6. Experimental Settings
+
+We use the PEFT library (Mangrulkar et al., 2022) for LoRA-based (Hu et al., 2022) gradient feature extraction without parameter updates. The base model is initialized from pre-trained checkpoints, and for LoRA configuration, we adopt
+
+{12}------------------------------------------------
+
+default settings with rank r = 16, LoRA scaling factor α = 32, and dropout set to 0 since we only focus on gradients from a single backpropagation step and no parameter updates are required. Target modules include all submodules of attention and FFN, including query, key, value, output, gate, up, and down projections. For different datasets, we select the tokenizer sequence length based on the overall length distribution: 256 for the WikiMIA dataset and 512 for all other datasets. When training the MLP classifier, the dataset is uniformly split into training and validation sets at a ratio of 3:7. The MLP classifier is configured with two hidden layers of dimensions 128 and 64, respectively, and uses the default Adam optimizer with a learning rate of 0.001. An early stopping strategy is implemented to avoid overfitting.
+
+# <span id="page-12-0"></span>B. Motivation Experiment Supplementary Details
+
+ To verify the parameter update law driven by the training process, we conduct LoRA fine-tuning with 8 epochs on LLaMA-7B using the unseen set of BookMIA dataset, counting LoRA matrix parameter updates per epoch to extract dynamic change curves of target features. Experiments are performed under three learning rates (1e − 5, 3e − 5, 5e − 5). We present the variation trends of the four feature categories across different modules and layers under each learning rate.
+
+We present the variation trends of the four feature categories across different modules and layers under each learning rate. Across all learning rates, ∆Θ<sup>t</sup> and S<sup>t</sup> exhibit clear epoch-wise patterns: ∆Θ<sup>t</sup> continuously decreases with training epochs, while S<sup>t</sup> gradually increases. For Et, distinct opposite trends are observed between the ATT and MLP modules—the update positions of the ATT module tend to be centralized, whereas those of the MLP module tend to be marginalized. Despite this divergence, E<sup>t</sup> values of both modules converge to the same stable range across the three learning rates. In contrast, T10,t shows a different dynamic: under large learning rates, it first increases and then decreases, yet remains stably around 0.27 throughout training. Notably, the inflection point of T10,t decline coincides with the stage when E<sup>t</sup> stabilizes. This aligns with our core hypothesis: during training, the model identifies core parameters correlated with the input data and performs concentrated updates on them; once this process is completed, the overall parameter update dynamics tend to stabilize. Regarding different hierarchical levels, only E<sup>t</sup> shows noticeable discrepancies, while all other features follow the same evolutionary laws.
+
+![](_page_12_Figure_5.jpeg)
+
+*Figure 6.* Feature Dynamic Changes During LoRA Fine-Tuning (Learning Rate 1e−5). Top row: Features in ATT/MLP modules; Bottom row: Features in low/middle/high layers.
+
+{13}------------------------------------------------
+
+![](_page_13_Figure_1.jpeg)
+
+*Figure 7.* Feature Dynamic Changes During LoRA Fine-Tuning (Learning Rate 3e − 5).
+
+![](_page_13_Figure_3.jpeg)
+
+*Figure 8.* Feature Dynamic Changes During LoRA Fine-Tuning (Learning Rate 5e − 5).
+
+{14}------------------------------------------------
+
+# 771 774
+
+# 776 778
+
+# 779 780 781 782 783 784 785
+
+# 787 788 789 790 791
+
+786
+
+# 794 796 798 799 800 801
+
+# 806 807 808 809 810 811 812
+
+813 814
+
+# <span id="page-14-0"></span>C. Ablation Experiments on Sub-features and Sub-modules
+
+To further explore the discriminative power of fine-grained components in our method, we conduct two additional ablation experiments: sub-feature category ablation (8 sub-features) and sub-module ablation (7 sub-modules). All experiments follow the same configuration as the main text (LLaMA-7B model, WikiMIA/ArxivTection datasets), with AUC and TPR@5% FPR as evaluation metrics.
+
+# C.1. Sub-feature Category Ablation Experiment
+
+The four core feature categories are decomposed into 8 sub-features, as follows:
+
+- Magnitude Distribution Features: Abs Mean, Std
+- Core Contribution Features: 10p Ratio, Sparsity
+- Position Offset Features: Row Ecc, Col Ecc
+- Row-Dimension Consistency Features: Row Mean Max, Row Mean Std
+
+<span id="page-14-1"></span>Ablation is performed by removing one sub-feature at a time (retaining the other 7), and the results are shown in Table [8.](#page-14-1)
+
+*Table 8.* Ablation Experiment Results of Sub-features (AUC Scores).
+
+| Dataset      | Sub-feature (Ablation Variant) |                                                                                 |           |           |           |           |           |           |           |  |  |
+|--------------|--------------------------------|---------------------------------------------------------------------------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|--|--|
+|              | -Abs Mean                      | -Std<br>-10p Ratio<br>-Sparsity<br>-Row Ecc<br>-Col Ecc<br>-Row Max<br>-Row Std |           |           |           |           |           |           |           |  |  |
+| WikiMIA      | 0.95/0.71                      | 0.95/0.72                                                                       | 0.95/0.70 | 0.94/0.67 | 0.95/0.70 | 0.93/0.62 | 0.95/0.73 | 0.95/0.72 | 0.96/0.84 |  |  |
+| ArxivTection | 0.96/0.82                      | 0.96/0.81                                                                       | 0.96/0.83 | 0.96/0.82 | 0.96/0.83 | 0.95/0.78 | 0.96/0.83 | 0.96/0.83 | 0.97/0.85 |  |  |
+
+The sub-feature ablation results verify that all sub-features contribute to detection performance, with their combination achieving optimal AUC and TPR scores across both datasets. Among these sub-features, Col Ecc (a Position Offset Feature) is the most critical: its removal leads to the sharpest performance decline (AUC drops to 0.93 on WikiMIA and 0.95 on ArxivTection, with TPR falling to 0.62 and 0.78 respectively). In contrast, removing Abs Mean, Std, 10p Ratio, Row Ecc, Row Max, or Row Std induces only mild performance degradation, with AUC remaining above 0.95 on both datasets, indicating their relatively moderate importance; Sparsity also shows a slight impact on WikiMIA, with its ablation resulting in an AUC of 0.94. Overall, the fine-grained sub-feature design is rational, as each component provides complementary discriminative information for pre-training data detection.
+
+#### C.2. Sub-module Ablation Experiment
+
+The ATT and FFN modules are decomposed into 7 sub-modules based on Transformer architecture details:
+
+- ATT-related sub-modules: Q-Proj, K-Proj, V-Proj, Out-Proj
+- FFN-related sub-modules: Gate-Proj, Up-Proj, Down-Proj
+
+<span id="page-14-2"></span>Ablation is performed by removing one sub-module's features at a time, and the results are shown in Table [9.](#page-14-2)
+
+*Table 9.* Ablation Experiment Results of Sub-modules (AUC / TPR@5% FPR Scores).
+
+| Dataset      | Sub-module (Ablation Variant) |           |                                                              |           |           |           |           |           |  |  |
+|--------------|-------------------------------|-----------|--------------------------------------------------------------|-----------|-----------|-----------|-----------|-----------|--|--|
+|              | -Q-Proj                       | -K-Proj   | -V-Proj<br>-Out-Proj<br>-Gate-Proj<br>-Up-Proj<br>-Down-Proj |           |           |           |           |           |  |  |
+| WikiMIA      | 0.95/0.72                     | 0.95/0.71 | 0.94/0.69                                                    | 0.94/0.67 | 0.95/0.69 | 0.94/0.65 | 0.94/0.61 | 0.96/0.84 |  |  |
+| ArxivTection | 0.96/0.80                     | 0.96/0.82 | 0.95/0.79                                                    | 0.96/0.80 | 0.96/0.82 | 0.95/0.78 | 0.96/0.82 | 0.97/0.85 |  |  |
+
+The sub-module ablation results demonstrate that all sub-modules provide complementary gradient information, as singlesub-module ablation consistently leads to performance degradation while integrating all sub-modules' features achieves
+
+{15}------------------------------------------------
+
+<span id="page-15-0"></span>![](_page_15_Figure_1.jpeg)
+
+*Figure 9.* Impact Analysis of Training Set Size on WikiMIA. The abscissa denotes the training-validation set ratio, the ordinate represents the scores of two metrics, yellow indicates the AUROC score, and blue indicates the TPR@5% FPR.
+
+the optimal AUC and TPR@5% FPR scores across both datasets. Though the performance differences between individual ablation variants are mild, ATT-related sub-modules show slightly stronger discriminative power than FFN-related ones, with K-Proj performing prominently among ATT sub-modules; in contrast, among FFN sub-modules, Down-Proj and Gate-Proj contribute more to detection performance than Up-Proj, as retaining the former two yields slightly higher AUC and TPR scores. The performance gap between single-sub-module variants and the full model further confirms the necessity of multi-sub-module feature fusion, which enables the capture of comprehensive gradient patterns across the Transformer architecture. It can be seen from this that our method also achieves excellent performance with smaller LoRA adaptation parameters and lower computational complexity.
+
+#### C.3. Low-Data Scenarios
+
+To evaluate the data efficiency of our method in scenarios with limited training data, we adjust the training-testing split ratio of the WikiMIA dataset to five settings: 1:9, 2:8, 3:7 and 4:6, while keeping the total sample size fixed. Figure Y shows AUC and TPR@5% FPR scores across different split ratios.
+
+Figure [9](#page-15-0) show our method's performance improves steadily with increasing training set size. Notably, it achieves an AUC of 0.9 even with only 10% of data, accompanied by a TPR@5% FPR of 0.48, confirming that it can also achieve excellent performance with a small amount of data.

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+[p. 9 | section: References | type: ListGroup]
+Balloccu, S., Schmidtova, P., Lango, M., and Du ´ sek, O. ˇ Leak, cheat, repeat: Data contamination and evaluation malpractices in closed-source llms. In Proceedings of the 18th Conference of the European Chapter of the Asso ciation for Computational Linguistics (Volume 1: Long Papers) , pp. 67–93, 2024. Biderman, S., Schoelkopf, H., Anthony, Q. G., Bradley, H., O'Brien, K., Hallahan, E., Khan, M. A., Purohit, S., Prashanth, U. S., Raff, E., et al. Pythia: A suite for analyzing large language models across training and scaling. In International Conference on Machine Learning , pp. 2397–2430. PMLR, 2023. Black, S., Leo, G., Wang, P., Leahy, C., and Biderman, S. Gpt-neo: Large scale autoregressive language modeling with mesh-tensorflow. Zenodo , 2021. Bottou, L. Large-scale machine learning with stochastic gradient descent. In Proceedings of COMPSTAT'2010: 19th International Conference on Computational Statis ticsParis France, August 22-27, 2010 Keynote, Invited and Contributed Papers , pp. 177–186. Springer, 2010. Carlini, N., Tramer, F., Wallace, E., Jagielski, M., Herbert-Voss, A., Lee, K., Roberts, A., Brown, T., Song, D., Erlingsson, U., et al. Extracting training data from large
+
+[p. 9 | section: References | type: ListGroup]
+language models. In 30th USENIX security symposium (USENIX Security 21) , pp. 2633–2650, 2021. Choi, H. K., Khanov, M., Wei, H., and Li, Y. How contaminated is your benchmark? measuring dataset leakage in large language models with kernel divergence. In Forty second International Conference on Machine Learning . Duan, M., Suri, A., Mireshghallah, N., Min, S., Shi, W., Zettlemoyer, L., Tsvetkov, Y., Choi, Y., Evans, D., and Hajishirzi, H. Do membership inference attacks work on large language models? In First Conference on Language Modeling . Duarte, A. V., Zhao, X., Oliveira, A. L., and Li, L. Decop: Detecting copyrighted content in language models training data. In Forty-first International Conference on Machine Learning . Frankle, J., Schwab, D. J., and Morcos, A. S. The early phase of neural network training. In International Con ference on Learning Representations . Grynbaum, M. M. and Mac, R. The times sues openai and microsoft over ai use of copyrighted work. The New York Times , 27(1), 2023. Gur-Ari, G., Roberts, D. A., and Dyer, E. Gradient descent happens in a tiny subspace. arXiv preprint arXiv:1812.04754 , 2018. Hu, E. J., Shen, Y., Wallis, P., Allen-Zhu, Z., Li, Y., Wang, S., Wang, L., Chen, W., et al. Lora: Low-rank adaptation of large language models. ICLR , 1(2):3, 2022. Kaplan, J., McCandlish, S., Henighan, T., Brown, T. B., Chess, B., Child, R., Gray, S., Radford, A., Wu, J., and Amodei, D. Scaling laws for neural language models. arXiv preprint arXiv:2001.08361 , 2020. Li, Y. Estimating contamination via perplexity: Quantifying memorisation in language model evaluation. In The Future of Machine Learning Data Practices and Reposi tories at ICLR 2025 . Liu, Z., Zhu, T., Tan, C., Liu, B., Lu, H., and Chen, W. Probing language models for pre-training data detection. In Proceedings of the 62nd Annual Meeting of the Asso ciation for Computational Linguistics (Volume 1: Long Papers) , pp. 1576–1587, 2024. Mangrulkar, S., Gugger, S., Debut, L., Belkada, Y., Paul, S., and Bossan, B. Peft: State-of-the-art parameter-efficient fine-tuning methods. 2022. Ruder, S. An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747 , 2016.
+
+[p. 10 | section: References | type: Text]
+Shi, W., Ajith, A., Xia, M., Huang, Y., Liu, D., Blevins, T., Chen, D., and Zettlemoyer, L. Detecting pretraining data from large language models. In 12th International Conference on Learning Representations, ICLR 2024 , 2024.
+
+[p. 10 | section: References | type: ListGroup]
+Tang, H., Zhu, Z., and Yang, Y. Identifying pre-training data in llms: A neuron activation-based detection framework. In Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing , pp. 18738– 18751, 2025. Touvron, H., Lavril, T., Izacard, G., Martinet, X., Lachaux, M.-A., Lacroix, T., Roziere, B., Goyal, N., Hambro, E., ` Azhar, F., et al. Llama: Open and efficient foundation language models. arXiv preprint arXiv:2302.13971 , 2023. Wang, B. and Komatsuzaki, A. Gpt-j-6b: A 6 billion parameter autoregressive language model, 2021. Wang, H., Ma, S., Wang, R., and Wei, F. Q-sparse: All large language models can be fully sparsely-activated. arXiv preprint arXiv:2407.10969 , 2024. Zhang, H., Zhang, S., Jing, B., and Wei, H. Fine-tuning can help detect pretraining data from large language models. In The Thirteenth International Conference on Learning Representations . Zhang, J., Sun, J., Yeats, E., Ouyang, Y., Kuo, M., Zhang, J., Yang, H. F., and Li, H. Min-k%++: Improved baseline for pre-training data detection from large language models. In The Thirteenth International Conference on Learning Representations , 2025. Zhang, S., Roller, S., Goyal, N., Artetxe, M., Chen, M., Chen, S., Dewan, C., Diab, M., Li, X., Lin, X. V., et al. Opt: Open pre-trained transformer language models. arXiv preprint arXiv:2205.01068 , 2022. Zhang, W., Zhang, R., Guo, J., Rijke, M., Fan, Y., and Cheng, X. Pretraining data detection for large language models: A divergence-based calibration method. In Pro ceedings of the 2024 Conference on Empirical Methods in Natural Language Processing , pp. 5263–5274, 2024.

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+{0}
+# Abstract
+Pre-training data detection for LLMs is essential for addressing copyright concerns and mitigating benchmark contamination. Existing methods mainly focus on the likelihood-based statistical features or heuristic signals before and after finetuning, but the former are susceptible to word frequency bias in corpora, and the latter strongly depend on the similarity of fine-tuning data. From an optimization perspective, we observe that during training, samples transition from unfamiliar to familiar in a manner reflected by systematic differences in gradient behavior. Familiar samples exhibit smaller update magnitudes, distinct update locations in model components, and more sharply activated neurons. Based on this insight, we propose GDS, a method that identifies pre-training data by probing Gradient Deviation Scores of target samples. Specifically, we first represent each sample using gradient profiles that capture the magnitude, location, and concentration of parameter updates across FFN and Attention modules, revealing consistent distinctions between member and non-member data. These features are then fed into a lightweight classifier to perform binary membership inference. Experiments on five public datasets show that GDS achieves state-ofthe-art performance with significantly improved cross-dataset transferability over strong baselines. Further interpretability analyse show gradient feature distribution differences, enabling practical and scalable pre-training data detection.
+# 1. Introduction
+Large language models (LLMs) performance scales with the size and quality of pre-training data [\(Kaplan et al.,](#page-8-0) [2020\)](#page-8-0).
+<span id="page-0-0"></span>![](_page_0_Figure_9.jpeg)
+*Figure 1.* Heat maps of gradient matrices from the unfamiliar stage (epochs 0–1, panels a, c) to the familiar stage (epochs 6–7, panels b, d). Panels a and b display the update magnitude of the FFN module in layer 30, while panels c and d illustrate the update positions, with white for sparse and blue for core updates.
+As pre-training corpora expand to trillions of tokens and become increasingly proprietary and non-transparent, they raise significant concerns, such as unauthorized copyright, biased or harmful content, and contamination of evaluation benchmarks [\(Balloccu et al.,](#page-8-1) [2024;](#page-8-1) [Grynbaum & Mac,](#page-8-2) [2023\)](#page-8-2). These challenges motivate a specialized task of membership inference attacks, named pre-training data detection: determining whether a given text sample was included in a model's pre-training corpus [\(Carlini et al.,](#page-8-3) [2021\)](#page-8-3).
+Recent studies [\(Carlini et al.,](#page-8-3) [2021;](#page-8-3) [Li;](#page-8-4) [Shi et al.,](#page-9-0) [2024;](#page-9-0) [Zhang et al.,](#page-9-1) [2025\)](#page-9-1) primarily use likelihood-based statistical features to detect pre-training samples. For example, the Min-K method [\(Shi et al.,](#page-9-0) [2024;](#page-9-0) [Zhang et al.,](#page-9-1) [2025\)](#page-9-1) examines the k% of tokens with the lowest predicted probabilities, assuming non-member texts contain more low-likelihood tokens. However, these approaches are susceptible to word frequency bias in pre-training corpora, specifically for rare words or short texts scenarios. To improve detection accuracy, other researchers [\(Zhang et al.;](#page-9-2) [Choi et al.\)](#page-8-5) propose to analyze heuristic signals before and after fine-tuning, leveraging the fact that fine-tuning impacts member and non-member samples differently. For example, KDS [\(Choi](#page-8-5) [et al.\)](#page-8-5) shows that non-member datasets exhibit much larger embedding changes, while FSD [\(Zhang et al.\)](#page-9-2) finds that their loss reductions are also significantly greater. Neverthe-
+{1}------------------------------------------------
+less, these methods rely on the strong assumption that finetuning data closely match the target samples' distribution, requiring additional training on similar non-member data and thereby limiting cross-dataset generalization. Therefore, how to achieve highly generalizable pre-training data detection remains an open problem.
+108 109 Pretraining can be viewed as a gradual shift from unfamiliarity to familiarity with data. Optimization theory [\(Ruder,](#page-8-6) [2016;](#page-8-6) [Frankle et al.;](#page-8-7) [Wang et al.,](#page-9-3) [2024\)](#page-9-3) suggests that training drives parameters toward data-specific structure, reflected in consistent update patterns across magnitude, location, and concentration. As shown in Figure [1](#page-0-0) and Section [3,](#page-2-0) we observe the following trends:
+- 1. Decay of update magnitude. Figure [1\(](#page-0-0)a,b) shows that parameter updates are strongly attenuated as data grows familiar, consistent with loss-convergence theory [\(Bottou,](#page-8-8) [2010;](#page-8-8) [Ruder,](#page-8-6) [2016\)](#page-8-6).
+- 2. Gradually stabilizing of update locations. Figure [1\(](#page-0-0)c,d) shows that parameter updates evolve from broad activation regions to a stable core set of neurons, consistent with the sparse activation behavior of LLMs [\(Liu et al.,](#page-8-9) [2024\)](#page-8-9).
+- 3. Increasing update sparsity. Figure [1\(](#page-0-0)a,b) and Figures [2\(](#page-2-1)b,c) show that during training, an increasing fraction of updates concentrates in the top 10% of neurons, consistent with Hessian spectrum reshaping during loss convergence [\(Gur-Ari et al.,](#page-8-10) [2018\)](#page-8-10). Familiar data yields sparse, concentrated updates, whereas unfamiliar data leads to more distributed updates.
+These observations reflect the evolutionary dynamics of neural network training, highlighting phase differences in parameter updates induced by identical samples. Together, they offer both theoretical motivation and empirical support for our detection method based on gradient deviation scores.
+Based on this insight, we propose GDS, a novel pretraining data detection method that infers pre-training data by probing Gradient Deviation Scores of target samples without fine-tuning. GDS exploits gradient differences between member and non-member samples to train a lightweight classifier with strong generalization. Specifically, within the LoRA framework, we collect per-sample gradients across layers during backpropagation, encoding them as eightdimensional features that capture the magnitude, location, and concentration of updates in attention and FFN modules. Compared to non-members, member samples show smaller matrix-level and row-wise update magnitudes, lower FFN but higher attention eccentricity, greater variability in matrixlevel and row-wise updates, a higher share of top gradients, and fewer sparse neurons. Then, we extract discriminative
+statistics from the signals to build fixed-dimensional feature vectors, which are fed to a lightweight MLP for binary membership classification.
+Extensive experiments on five benchmark datasets show that GDS is effective and generalizable, improving AUC by 6.5% and achieving a 67.3% TPR@5%FPR, substantially outperforming strong baselines. Further interpretability analyses reveal distributional differences in gradient features between member and non-member samples, offering intuitive evidence of training data imprints on the model and validating our methodology. [1](#page-1-0) Our contributions are as follows:
+- From a training optimization perspective, we analyze how LLMs evolve from unfamiliarity to familiarity with data and propose using stage-wise parameter update dynamics to identify pretraining data, offering a novel direction to solve this task.
+- We propose gradient deviation features capturing magnitude, location, and concentration, and introduce a gradient deviation score–based method for pretraining data detection without fine-tuning.
+- Extensive experiments across diverse datasets and backbone models validate the effectiveness and generalization of GDS, while interpretability analyses reveal clear gradient differences between member and nonmember samples, supporting its validity.
+# 2. Related Work
+Likelihood-Based Scoring Methods. Early works distinguish member and non-member samples by capturing static statistical metrics in token-level likelihood distributions. Global-likelihood–based methods, such as PPL [\(Li\)](#page-8-4), Zlib [\(Carlini et al.,](#page-8-3) [2021\)](#page-8-3), and Lowercase [\(Carlini et al.,](#page-8-3) [2021\)](#page-8-3), perform discrimination by exploiting global probability features, compression entropy, and case-conversion ratios. However, global likelihood is highly sensitive to wordfrequency effects, leading to unstable performance. Mink% [\(Shi et al.,](#page-9-0) [2024\)](#page-9-0) and Min-k%++ [\(Zhang et al.,](#page-9-1) [2025\)](#page-9-1) mitigate global dependence by focusing on low-probability outlier tokens or target–candidate probability comparisons, with k and text length jointly determining the analyzed token subset. However, the fixed choice of k lacks adaptivity, causing severe score fluctuations in short texts with lowfrequency words. Although PC-PDD [\(Zhang et al.,](#page-9-4) [2024\)](#page-9-4) approximates the word-frequency distribution of pretraining corpora using public datasets, these references lack fidelity due to limited domain coverage.
+Fine-tuning Enhanced Methods. To address the instability of static statistical indicators, recent studies [\(Zhang et al.;](#page-9-2)
+<span id="page-1-0"></span><sup>1</sup>Code in
+{2}------------------------------------------------
+<span id="page-2-1"></span>![](_page_2_Figure_1.jpeg)
+*Figure 2.* Dynamic curves of four parameter update characteristics defined in the Motivation section. i → j denotes the epoch interval. Ordinate shows values of predefined characteristics, with orange and blue representing Attention and FFN modules.
+[Choi et al.\)](#page-8-5) adopt lightweight fine-tuning to actively amplify asymmetric differences between member and non-member samples. KDS [\(Choi et al.\)](#page-8-5) evaluates dataset contamination by comparing kernel similarity matrices of embeddings before and after fine-tuning, assuming non-member datasets undergo larger embedding changes than member datasets. However, it only estimates dataset-level contamination and cannot reliably detect contamination at the sample-level. Another representative method FSD [\(Zhang et al.\)](#page-9-2) detects membership by comparing loss before and after fine-tuning, assuming non-member samples experience a larger loss reduction than member samples. Nevertheless, these methods assume that fine-tuning data closely matches the target distribution, requiring additional tuning on similar non-member data, which limits cross-dataset generalization.
+# <span id="page-2-0"></span>3. Motivation
+Inspired by optimization theory [\(Ruder,](#page-8-6) [2016;](#page-8-6) [Bottou,](#page-8-8) [2010\)](#page-8-8), we examine how LLMs transition from unfamiliarity to familiarity with data, and how this cognitive shift relates to the dynamic evolution of model parameters during training. To evaluate it, we fine-tune LLaMA-7B with LoRA on the unseen split of BookMIA dataset and track LoRA parameter updates over 7 epochs. Stage-wise analysis in Figure [2](#page-2-1) reveals the dynamic evolution of gradient features.
+#### 3.1. Decay of Update Magnitude
+Model training aims to minimize the loss function L(θ), with update magnitude determined by the gradient norm ∥∇L(θ)∥. According to optimization convergence theory [\(Ruder,](#page-8-6) [2016\)](#page-8-6), as the parameters θ<sup>t</sup> approach the optimum θ ∗ , the gradient norm of the loss function vanishes, i.e.,limθ→<sup>θ</sup> <sup>∗</sup> ∥∇L(θt)∥ = 0. This causes the parameter update magnitude to decrease synchronously. Therefore, we use ∆θ<sup>t</sup> as the core indicator of the average update magnitude across all trainable parameters at iteration t:
+$$\Delta \theta_{t} = \frac{1}{N} \sum_{i=1}^{N} |\theta_{t,i} - \theta_{t-1,i}|, \qquad (1)$$
+where N denotes the total number of trainable parameters.
+As training progresses, both the loss L(θt) and gradient norm ∥∇L(θt)∥ decrease, reducing the update magnitude ∆θ<sup>t</sup> and slowing its decay as parameters converge to the optimum θ ∗ . Eventually, L(θt) stabilizes near its minimum, parameter updates ∆θ<sup>t</sup> become negligible. As shown in Figure [2a,](#page-2-1) the mean update magnitude decreases monotonically with training, with the largest changes occurring in the first two epochs, consistent with loss convergence.
+### 3.2. Gradually Stabilizing of Update Locations
+Existing studies [\(Liu et al.,](#page-8-9) [2024;](#page-8-9) [Tang et al.,](#page-9-5) [2025\)](#page-9-5) have shown that neural activations occur at different locations when processing member samples and non-member samples. Inspired by this, we adopt the parameter update eccentricity as the core indicator, which quantifies the deviation of the top-10% parameter update positions from the global parameter centroid. We first define the global centroid as:
+$$\theta_c = \frac{1}{N} \sum_{i=1}^{N} \theta_i, \tag{2}$$
+where θ<sup>i</sup> is the coordinate of the i-th parameter.
+The update eccentricity at iteration t is then defined as:
+$$E_{t} = \frac{1}{\operatorname{card}(U_{10,t})} \sum_{\theta_{i} \in U_{10,t}} \|\theta_{i} - \theta_{c}\|_{2},$$
+(3)
+where card(·) denotes the number of elements in a set, U10,t = {∥∆θt,i∥<sup>1</sup> ∈ Top10%(∥∆θt∥1)}, ∥ · ∥<sup>1</sup> denotes the ℓ<sup>1</sup> norm and ∥ · ∥<sup>2</sup> denotes the ℓ<sup>2</sup> norm.
+In the initial training stage, activation patterns are unstable, leading to scattered U10,t and thus random large values of Et. As training proceeds, the model identifies core parameters related to data features: θ<sup>t</sup> stabilizes to the optimal subset θ ∗ , and U10,t converges to the core parameter region, resulting in E<sup>t</sup> gradually stabilizing at a low level. Figure [2d](#page-2-1) shows that the eccentricity of parameter update evolves to a relatively stable value, consistent with the evolution of the
+{3}------------------------------------------------
+<span id="page-3-0"></span>![](_page_3_Figure_2.jpeg)
+*Figure 3.* Overview of Gradient Deviation Scores method.
+neuron activation pattern, suggesting that training identifies the core parameters and stabilizes updates around them.
+#### 3.3. Increasing Update Sparsity
+The Hessian spectrum [\(Gur-Ari et al.,](#page-8-10) [2018;](#page-8-10) [Frankle et al.\)](#page-8-7) is a core metric characterizing the loss function's curvature, directly determining the direction and efficiency of parameter updates. For the loss function L(θ), its Hessian matrix H(θ) = ∇2L(θ) describes the local curvature of the loss landscape, with eigenvalue decomposition:
+$$\mathcal{H}(\theta) = U\Lambda U^T,\tag{4}$$
+where U is the orthogonal eigenvector matrix (principal curvature directions), Λ = diag(λ1, . . . , λd) is the diagonal eigenvalue matrix (curvature magnitudes). During training, the Hessian spectrum changes from an almost uniform λ<sup>i</sup> ≈ c in the early stage to a late-stage structure with a few large eigenvalues and most near zero.
+This reshaping leads to concentrated updates, focusing on directions with large eigenvalues while leaving most others nearly unchanged. Consequently, update energy is confined to a small subset of parameters, motivating the selection of two joint indicators. S<sup>t</sup> measures the fraction of parameters with negligible updates (absolute value < 10<sup>−</sup><sup>6</sup> ) at iteration t, while T10,t measures the fraction of total update magnitude contributed by the top 10% largest updates.
+$$S_t = \frac{\operatorname{card}\left(i \mid |\Delta \theta_{t,i}| < 10^{-6}\right)}{N},\tag{5}$$
+$$T_{10,t} = \frac{\sum_{|\Delta\theta_{t,i}| \in U_{10,t}} |\Delta\theta_{t,i}|}{||\Delta\theta_t||_1}.$$
+(6)
+As training progresses, parameter updates increasingly concentrate along core directions, with most parameters receiving negligible changes. Consequently, S<sup>t</sup> gradually
+increases, while T10,t remains relatively large and stable(0.26–0.27), indicating that update energy is consistently dominated by a small subset of parameters. Figures [2b](#page-2-1) and [2c](#page-2-1) confirm this growing sparsity and stable Top 10% contribution, reflecting update energy aggregation driven by Hessian spectrum reshaping. Further details on the variation trends of the three metrics are provided in the appendix [B.](#page-12-0)
+# 4. Method
+### 4.1. Task Definition
+Given a target text x and a target LLM f<sup>θ</sup> pre-trained on a corpus D, the goal of pre-training data detection task is to construct a detector h(x, fθ)to determine whether x belongs to D. This task can be formalized as a binary classification problem: h(x, fθ) → {0, 1} where "1" indicates x ∈ D as member and "0" indicates x /∈ D as non-member.
+As illustrated in Figure [3,](#page-3-0) GDS comprises three stages: gradient matrix acquisition, feature vector extraction and light Multilayer Perceptron(MLP) training. For each training sample, we perform inference and backpropagation to obtain LoRA gradients across l layers and m sub-modules, yielding l × m gradient matrices G. From these matrices, we extract eight-dimensional features to form a gradient feature vector V l×m×8 , which is used to train a lightweight MLP classifier for binary membership prediction. During inference, the same feature extraction process is applied to a target sample x ∗ , and the resulting feature vector is fed into the trained MLP to produce the final classification result.
+#### 4.2. Gradient Matrix Acquisition
+Given the target model f<sup>θ</sup> and training sample x, we first initialize f<sup>θ</sup> with LoRA, yielding l × m LoRA matrices L. We then feed a single sample x into f<sup>θ</sup> for forward
+{4}------------------------------------------------
+inference and backpropagation, obtaining LoRA gradient matrices $\mathbb{G} = \nabla_{\mathbb{L}} \mathcal{L}_{\text{CLM}}(f_{\theta}(x))$ , where $\mathcal{L}_{\text{CLM}}$ denotes the causal language modeling loss of the pre-trained LLM. Since the LoRA\_B matrices are fully initialized to zero, a single round of gradient propagation leads to zero gradients for the LoRA\_A matrices. Thus, we only collect the gradient matrices of LoRA\_B for subsequent processing.
+#### 4.3. Feature Vector Extraction
+Given the gradient matrices $\mathbb{G}$ , we extract features based on the three parameter update trends introduced in Section 3.
+#### 4.3.1. MAGNITUDE
+We propose two magnitude indicators to measure the overall scale of gradient updates in the LoRA parameter space.
+(1) **Absolute Mean**: The mean of the absolute values of all elements in the gradient matrix, which characterizes the overall parameter update strength:
+$$Abs\_Mean = \frac{1}{r \cdot h} \sum_{i=1}^{r} \sum_{j=1}^{h} |\mathbb{G}_{i,j}|,$$
+(7)
+where $\mathbb{G}_{i,j}$ denotes the element in the *i*-th row and *j*-th column of the gradient matrix with r rows and h columns.
+(2) Max Row Mean: The mean of each row in the LoRA matrix and take the maximum value, which characterizes the most sample-responsive local optimal response dimension with the largest parameter update magnitude:
+$$Row\_Mean\_Max = \max_{1 \le i \le r} \left( \frac{1}{h} \sum_{j=1}^{h} |\mathbb{G}_{i,j}| \right).$$
+(8)
+#### 4.3.2. Position
+Screen the top 10% of gradient elements by absolute value from $\mathbb{G}$ and calculate their offset from this matrix center, capturing offset characteristics of core gradient positions for (1) Row Eccentricity and (2) Column Eccentricity, respectively:
+$$Row\_Ecc = \frac{1}{\operatorname{card}(S)} \sum_{(i,j) \in S} \left| \frac{2i - (r+1)}{r-1} \right|, \quad (9)$$
+$$Col\_Ecc = \frac{1}{\operatorname{card}(S)} \sum_{(i,j) \in S} \left| \frac{2j - (h+1)}{h-1} \right|, \quad (10)$$
+where $S = \{(i,j) \mid |\mathbb{G}_{i,j}| \in \text{Top10\%}(|\mathbb{G}|)\}$ denotes the set of indices for the top 10% of elements in the gradient matrix $\mathbb{G}$ ranked by absolute gradient value. Top gradients near the center correspond to an eccentricity of 0, while those near the edge correspond to a score of 1.
+#### 4.3.3. CONCENTRATION
+We propose four indicators to measure the concentration of gradient distributions.
+(1) **Top-10% Ratio**: The ratio of the sum of the top 10% largest gradient magnitudes to the total update magnitude of the gradient matrix, which quantifies the contribution ratio of core gradients:
+$$10p\_Ratio = \frac{\sum_{(i,j)\in S} |\mathbb{G}_{i,j}|}{\|\mathbb{G}\|_1}, \tag{11}$$
+(2) **Sparsity**: The proportion of gradient elements with absolute values less than $10^{-6}$ , which quantifies the sparsity degree of gradient distributions:
+$$Sparsity = \frac{\operatorname{card}\left(\left\{\left(i,j\right) \mid |\mathbb{G}_{i,j}| < 10^{-6}\right\}\right)}{r \cdot h}.$$
+(12)
+(3) **Standard Deviation**: The standard deviation of the elements in the gradient matrix, which quantifies the dispersion degree of parameter updates:
+$$Std = \sqrt{\frac{1}{r \cdot h} \sum_{i=1}^{r} \sum_{j=1}^{h} (|\mathbb{G}_{i,j}| - \text{Abs\_mean})^2}.$$
+(13)
+(4) Row Mean Standard Deviation: The mean of each row in the LoRA matrix and take the standard deviation, which quantifies the consistency of update strength across all rows:
+$$Row\_Mean\_Std = \sqrt{\frac{1}{r} \sum_{i=1}^{r} \left(\bar{\mathbb{G}}_i - \mu_{\bar{\mathbb{G}}}\right)^2}, \quad (14)$$
+where $\bar{\mathbb{G}}_i = \frac{1}{h} \sum_{j=1}^h |\mathbb{G}_{i,j}|$ denotes the *i*-th row's absolute mean, $\mu_{\bar{\mathbb{G}}} = \frac{1}{r} \sum_{i=1}^r \bar{\mathbb{G}}_i$ denotes t the mean of row means.
+We compute the aforementioned eight feature values from all gradient matrices to derive a feature vector $\mathbb{V}^{l\times m\times 8}$ $\triangleq$ [Abs\_Mean, Row\_Mean\_Max, 10p\_Ratio, Sparsity, Std, Row\_Mean\_Std, Row\_Ecc, Col\_Ecc] per sample, which is then used for subsequent MLP training and inference.
+#### 4.4. Light MLP Training
+Given the feature vectors $\mathbb{V}_i$ from all training samples vectors $\mathbb{V}_s$ , we feed them into a lightweight MLP for training. The target output corresponds to the binary label $\{0,1\}$ for each sample, where 0 denotes non-member and 1 denotes member. The training loss is defined as follows:
+$$\mathcal{L} = -\frac{1}{N} \sum_{i=1}^{N} \left[ y_i \log \hat{y}_i + (1 - y_i) \log(1 - \hat{y}_i) \right], \quad (15)$$
+where N denotes the number of training samples, $y_i \in \{0,1\}$ is the ground-truth label of the i-th sample, and $\hat{y}_i$ is the predicted probability output by the MLP.
+{5}------------------------------------------------
+<span id="page-5-0"></span>*Table 1.* Comparison(AUROC/TPR@5%FPR) on 4 Datasets across 5 target models. Target models are denoted as 2.7B/6B/6.7B/6.9B/7B, corresponding to Neo-2.7B/GPT-J-6b/OPT-6.7b/Pythia-6.9b/LLaMA-7B respectively. The best result is bold.
+| | | | WikiMIA | | | | | ArXivTection | | | |
+|--------|-------------------|-----------|-------------|-----------|-----------|-----------|-----------|--------------|-----------|-----------|--|
+| Method | 2.7B | 6B | 6.7B | 6.9B | 7B | 2.7B | 6B | 6.7B | 6.9B | 7B | |
+| PPL | 0.61/0.13 | 0.64/0.13 | 0.60/0.12 | 0.63/0.13 | 0.69/0.14 | 0.62/0.13 | 0.64/0.13 | 0.60/0.12 | 0.63/0.13 | 0.70/0.14 | |
+| ZLib | 0.58/0.10 | 0.60/0.11 | 0.58/0.10 | 0.59/0.10 | 0.71/0.22 | 0.58/0.10 | 0.60/0.11 | 0.58/0.09 | 0.59/0.11 | 0.71/0.22 | |
+| Min-k | 0.65/0.17 | 0.67/0.19 | 0.63/0.15 | 0.67/0.19 | 0.73/0.18 | 0.65/0.17 | 0.68/0.19 | 0.63/0.15 | 0.67/0.19 | 0.72/0.18 | |
+| | Min-k++ 0.67/0.15 | 0.69/0.19 | 0.65/0.11 | 0.70/0.18 | 0.82/0.22 | 0.67/0.15 | 0.69/0.19 | 0.65/0.10 | 0.70/0.17 | 0.83/0.22 | |
+| FSD | 0.92/0.77 | 0.95/0.78 | 0.90/0.63 | 0.90/0.66 | 0.92/0.41 | 0.91/0.65 | 0.96/0.79 | 0.89/0.63 | 0.95/0.66 | 0.94/0.81 | |
+| Ours | 0.90/0.60 | 0.93/0.66 | 0.94/0.67 | 0.92/0.63 | 0.96/0.84 | 0.94/0.73 | 0.97/0.86 | 0.94/0.75 | 0.95/0.83 | 0.97/0.85 | |
+| | | | BookTection | | | BookMIA | | | | | |
+| Method | 2.7B | 6B | 6.7B | 6.9B | 7B | 2.7B | 6B | 6.7B | 6.9B | 7B | |
+| PPL | 0.69/0.15 | 0.74/0.25 | 0.64/0.13 | 0.73/0.25 | 0.71/0.25 | 0.29/0.02 | 0.22/0.13 | 0.23/0.01 | 0.59/0.19 | 0.56/0.21 | |
+| ZLib | 0.56/0.16 | 0.58/0.20 | 0.55/0.14 | 0.58/0.19 | 0.57/0.19 | 0.20/0.02 | 0.38/0.13 | 0.15/0.00 | 0.49/0.17 | 0.48/0.18 | |
+| Min-k | 0.71/0.18 | 0.75/0.27 | 0.67/0.15 | 0.74/0.26 | 0.71/0.25 | 0.45/0.05 | 0.60/0.20 | 0.40/0.03 | 0.62/0.20 | 0.60/0.21 | |
+| | Min-k++ 0.64/0.13 | 0.67/0.18 | 0.61/0.11 | 0.66/0.19 | 0.63/0.15 | 0.54/0.13 | 0.64/0.29 | 0.49/0.09 | 0.60/0.23 | 0.58/0.20 | |
+| FSD | 0.92/0.53 | 0.91/0.52 | 0.96/0.77 | 0.93/0.59 | 0.92/0.55 | 0.98/0.93 | 0.97/0.89 | 0.98/0.96 | 0.98/0.93 | 0.98/0.91 | |
+| Ours | 0.96/0.84 | 0.97/0.88 | 0.98/0.92 | 0.96/0.83 | 0.98/0.92 | 0.99/0.98 | 0.99/0.99 | 0.99/0.99 | 0.99/0.98 | 0.99/0.99 | |
+*Table 2.* Performance Comparison on Mimir datasets with 7 subsets across 5 target models using AUROC scores.
+<span id="page-5-1"></span>
+| | | Wikipedia | | | | Github | | | | Pile CC | | | | PubMed Central | | |
+|-------------------------------------------------------------------------------------------------------------|----|-----------------------------------------------------------------------------------------------------|-----------|---------|----|--------|----------------|---------|----|------------|-----------|---------|----|----------------|-----------|----|
+| Method 2.7B | 6B | | 6.7B 6.9B | 7B 2.7B | 6B | | 6.7B 6.9B | 7B 2.7B | 6B | | 6.7B 6.9B | 7B 2.7B | 6B | | 6.7B 6.9B | 7B |
+| PPL | | 0.56 0.57 0.56 0.56 0.56 0.78 0.79 0.78 0.90 0.83 0.56 0.57 0.56 0.56 0.52 0.78 0.79 0.78 0.78 0.72 | | | | | | | | | | | | | | |
+| ZLib | | 0.62 0.65 0.59 0.65 0.58 0.90 0.91 0.79 0.91 0.86 0.55 0.55 0.55 0.55 0.52 0.78 0.78 0.73 0.77 0.71 | | | | | | | | | | | | | | |
+| Min-k | | 0.66 0.68 0.65 0.68 0.63 0.88 0.89 0.76 0.90 0.83 0.56 0.57 0.56 0.56 0.52 0.81 0.80 0.74 0.79 0.72 | | | | | | | | | | | | | | |
+| Min-k++ 0.65 0.68 0.60 0.69 0.56 0.84 0.86 0.56 0.86 0.73 0.54 0.55 0.54 0.56 0.51 0.71 0.72 0.60 0.70 0.59 | | | | | | | | | | | | | | | | |
+| FSD | | 0.61 0.67 0.60 0.65 0.60 0.77 0.80 0.62 0.77 0.72 0.55 0.55 0.54 0.55 0.52 0.71 0.79 0.63 0.56 0.63 | | | | | | | | | | | | | | |
+| Ours | | 0.63 0.64 0.65 0.65 0.64 0.90 0.92 0.88 0.92 0.91 0.59 0.59 0.59 0.57 0.59 0.84 0.85 0.84 0.79 0.82 | | | | | | | | | | | | | | |
+| | | ArXiv | | | | | DM Mathematics | | | HackerNews | | | | Average | | |
+| Method 2.7B | 6B | | 6.7B 6.9B | 7B 2.7B | 6B | | 6.7B 6.9B | 7B 2.7B | 6B | | 6.7B 6.9B | 7B 2.7B | 6B | | 6.7B 6.9B | 7B |
+| PPL | | 0.78 0.79 0.65 0.78 0.70 0.78 0.79 0.65 0.91 0.31 0.65 0.62 0.59 0.62 0.59 0.64 0.66 0.62 0.73 0.59 | | | | | | | | | | | | | | |
+| ZLib | | 0.77 0.78 0.68 0.77 0.71 0.82 0.81 0.80 0.81 0.23 0.68 0.60 0.58 0.60 0.58 0.65 0.67 0.63 0.72 0.58 | | | | | | | | | | | | | | |
+| Min-k | | 0.78 0.79 0.65 0.78 0.70 0.93 0.93 0.92 0.92 0.32 0.65 0.62 0.59 0.62 0.59 0.71 0.73 0.69 0.75 0.60 | | | | | | | | | | | | | | |
+| Min-k++ 0.60 0.64 0.53 0.70 0.57 0.77 0.79 0.67 0.75 0.22 0.53 0.57 0.51 0.60 0.53 0.60 0.63 0.56 0.67 0.53 | | | | | | | | | | | | | | | | |
+| FSD | | 0.72 0.78 0.55 0.70 0.52 0.58 0.85 0.60 0.74 0.53 0.61 0.60 0.57 0.56 0.51 0.61 0.66 0.59 0.62 0.55 | | | | | | | | | | | | | | |
+| Ours | | 0.78 0.79 0.78 0.78 0.77 0.95 0.95 0.94 0.95 0.95 0.58 0.60 0.60 0.57 0.58 0.73 0.75 0.74 0.76 0.70 | | | | | | | | | | | | | | |
+# 5. Experiments
+#### 5.1. Experimental Setup
+Datasets Following prior work, we evaluate on five prevalent datasets: WikiMIA, BookMIA [\(Shi et al.,](#page-9-0) [2024\)](#page-9-0),ArxivTection, BookTection [\(Duarte et al.\)](#page-8-11), and MIMIR [\(Duan](#page-8-12) [et al.\)](#page-8-12), a widely recognized challenging benchmark for pretraining data detection.
+Target Models We evaluate five open-source LLMs with diverse architectures: Neo-2.7B [\(Black et al.,](#page-8-13) [2021\)](#page-8-13), GPT-J-6B [\(Wang & Komatsuzaki,](#page-9-6) [2021\)](#page-9-6), OPT-6.7B [\(Zhang et al.,](#page-9-7) [2022\)](#page-9-7), Pythia-6.9B [\(Biderman et al.,](#page-8-14) [2023\)](#page-8-14), and LLaMA-7B [\(Touvron et al.,](#page-9-8) [2023\)](#page-9-8) from Hugging Face.
+Comparison Methods We select five representative stateof-the-art baselines. Four scoring function–based methods
+include PPL [\(Carlini et al.,](#page-8-3) [2021\)](#page-8-3), ZLib [\(Carlini et al.,](#page-8-3) [2021\)](#page-8-3), Min-k [\(Shi et al.,](#page-9-0) [2024\)](#page-9-0), and Min-k++ [\(Zhang et al.,](#page-9-1) [2025\)](#page-9-1). The fine-tuning–enhanced method includes FSD [\(Zhang](#page-9-2) [et al.\)](#page-9-2). More details are shown in Appendix [A.](#page-10-0)
+Evaluation Metrics Two metrics evaluate the binary pretraining data detection task: AUROC measures overall discriminative performance, and TPR@5%FPR captures practical effectiveness by assessing detection rate under a 5% false positive constraint.
+Implementation Details We use the PEFT library [\(Man](#page-8-15)[grulkar et al.,](#page-8-15) [2022\)](#page-8-15) for LoRA-based [\(Hu et al.,](#page-8-16) [2022\)](#page-8-16) gradient feature extraction without parameter updates. The MLP is trained on 30% of the data, with the remaining 70% used for inference evaluation under FSD settings. More Details can be seen in Appendix [A.6.](#page-11-0)
+{6}------------------------------------------------
+<span id="page-6-2"></span>![](_page_6_Figure_1.jpeg)
+*Figure 4.* Distribution differences of eight gradient features between member(red) and non-member(blue) samples. Dashed lines indicate distribution means. The x-axis represents feature values, and the y-axis denotes probability density.
+<span id="page-6-0"></span>*Table 3.* Ablation results using AUROC on WikiMIA and Arxiv-Tection. - denotes the removal of related features.
+| Dataset | -Magnitude | -Concentration | -Position |
+|--------------|--------------|----------------|--------------|
+| WikiMIA | 0.94 (↓0.02) | 0.94 (↓0.02) | 0.93 (↓0.03) |
+| ArxivTection | 0.96 (↓0.01) | 0.95 (↓0.02) | 0.95 (↓0.02) |
+<span id="page-6-1"></span>*Table 4.* Ablation results using AUROC and TPR@5%FPR. ATT-Only refers to performance validation using only attention module.
+| Dataset | ATT-Only | FFN-Only | Origin |
+|--------------|-------------|-------------|-------------|
+| WikiMIA | 0.94 / 0.68 | 0.93 / 0.64 | 0.96 / 0.84 |
+| ArxivTection | 0.95 / 0.76 | 0.93 / 0.72 | 0.97 / 0.85 |
+# 5.2. Main Results
+Table [1](#page-5-0) shows detection performance on WikiMIA, Arxiv-Tection, BookTection, and BookMIA. Specifically, when tested on WikiMIA with LLaMA-7B, GDS achieves an AUC score of 0.96, which is an improvement of 0.04 compared to the best baseline FSD and significantly higher than score-function-based methods such as Min-k++. GDS outperforms the best baseline in most settings, with especially large gains in TPR@5%FPR on BookTection and Book-MIA. Notably, with LLaMA-7B, BookTection performance improves by nearly 67.3%.
+Table [2](#page-5-1) reports results on seven MIMIR subsets. Although all methods degrade due to similar data distributions, GDS achieves the best average improvements +2.8%, +2.7%, +7.2%, +1.3%, +16.6% across different models, and shows clear advantages on PubMed Central, DM Mathematics, and GitHub. Using the LLaMA model, the three subsets achieve AUC scores of 0.82, 0.95, and 0.91. Our method shows the most stable performance across models, with AUC variations mostly within 0.04, demonstrating strong generalization across different models.
+#### 5.3. Ablation Study
+We perform two ablation studies: (1) removing each gradient feature category individually, and (2) using features from only the Attention or FFN module. Table [3](#page-6-0) shows that all feature categories contribute to performance, with Position Offset and Magnitude being the most important. Concentration features have smaller effects, and the full combination performs best, highlighting the complementary nature of multi-dimensional features (see Appendix [C](#page-14-0) for sub-feature ablations). Table [4](#page-6-1) shows that Attention features are more discriminative than FFN features. Both single-module variants underperform the full model, indicating that Attention and FFN capture complementary gradient patterns and must be combined for optimal performance.
+#### 5.4. Analysis
+# 5.4.1. FEATURE DISTRIBUTION
+To explain the classifier's effectiveness, we quantify feature distributions across all layers and sub-modules for member and non-member samples. Figure [4](#page-6-2) shows the eight features with the largest discrepancies. Member samples exhibit smaller Abs Mean and Row Mean Max, indicating lower gradient magnitudes due to higher data familiarity, along with higher Sparsity, smaller Std and Row Mean Std, reflecting more concentrated and stable gradients. They also maintain a consistently higher 10p Ratio, occupying the core of gradient propagation. For locations Row Ecc and Col Ecc, member samples cluster at lower values, while non-members shift higher, suggesting that member-related parameters lie more centrally in weight matrices.
+We collect sub-features with the largest distribution differences between the two sample types and analyze their overall distribution patterns. Figure [5](#page-7-0) show that discriminative sub-features are predominantly concentrated in low layers, while middle and high layers contribute far less. Among sub-modules, attention-related modules are the main sources
+{7}------------------------------------------------
+<span id="page-7-1"></span>*Table 5.* Performance Comparison between LoRA and Full-Parameter Update using AUROC on WikiMIA and ArxivTection.
+| Dataset | Metric | LLaMA-7B | | GPT-J-6B | | OPT-6.7B | | Pythia-6.9B | | Neo-2.7B | |
+|--------------|------------|----------|------|----------|------|----------|------|-------------|------|----------|------|
+| | | LoRA | Full | LoRA | Full | LoRA | Full | LoRA | Full | LoRA | Full |
+| WikiMIA | AUC | 0.96 | 0.96 | 0.93 | 0.90 | 0.94 | 0.92 | 0.92 | 0.89 | 0.90 | 0.88 |
+| | TPR@5% FPR | 0.84 | 0.79 | 0.66 | 0.58 | 0.67 | 0.56 | 0.63 | 0.50 | 0.60 | 0.51 |
+| ArxivTection | AUC | 0.97 | 0.96 | 0.97 | 0.96 | 0.94 | 0.93 | 0.95 | 0.94 | 0.94 | 0.94 |
+| | TPR@5% FPR | 0.85 | 0.84 | 0.86 | 0.79 | 0.75 | 0.67 | 0.83 | 0.73 | 0.73 | 0.75 |
+<span id="page-7-0"></span>![](_page_7_Figure_4.jpeg)
+*Figure 5.* Distribution Difference Statistics of Discriminative Features. The y-axis shows the statistical count.
+of discriminative features, with obvious differences in contribution across modules. In terms of gradient features, grad sparsity exhibits the strongest discriminative power, significantly outperforming other indicators.
+# 5.4.2. FULL PARAMETER TRAINING
+In LoRA training, only FFN and MLP modules are updated, while LayerNorm, despite containing meaningful training dynamics, is excluded. To account for this, we evaluate our method under full-parameter training on two small-scale datasets, BookMIA and ArxivTection, for computational feasibility. As shown in Table [5,](#page-7-1) although full-parameter updates cause a slight performance drop compared to LoRA, our method still outperforms most baselines. We attribute this gap to reduced gradient magnitudes in full training, which weaken discriminative signals between sample types.
+#### 5.4.3. WIKIMIA MODIFICATION
+Dataset partitioning can introduce distribution shifts or dataset-specific artifacts. For example, WikiMIA is split by publication time, with all non-member samples labeled as 2023. To ensure our method does not exploit such artifacts, we remove all timestamp tokens and reevaluate all methods. As shown in Table [6,](#page-7-2) although token removal degrades performance, our method suffers a much smaller drop than the strongest baseline, FSD, and still achieves SOTA results.
+<span id="page-7-2"></span>*Table 6.* Comparison of Temporal Feature Perturbation via AU-ROC. Deletion denotes the removal of all year timestamps.
+| Method | Origin | Deletion |
+|---------|--------|----------|
+| PPL | 0.69 | 0.62 |
+| Min-k | 0.73 | 0.63 |
+| Min-k++ | 0.82 | 0.59 |
+| FSD | 0.92 | 0.76 |
+| Ours | 0.96 | 0.84 |
+<span id="page-7-3"></span>*Table 7.* Cross-Dataset Generalization Performance using AU-ROC. Wiki(arXiv) indicates training on ArxivTection with test on WikiMIA, while Mix indicates mixed datasets.
+| Method | Wiki (arXiv) | arXiv (Wiki) | Mix |
+|--------|--------------|--------------|------|
+| FSD | 0.52 | 0.58 | 0.92 |
+| Ours | 0.66 | 0.68 | 0.95 |
+### 5.4.4. TRANSFERABILITY
+Although our method shares the same feature extraction framework, it requires dataset-specific classifiers. To examine whether a unified classifier is feasible, we train classifiers on WikiMIA and ArXiv separately and evaluate crossdataset generalization, as well as train a unified classifier on mixed data. Table [7](#page-7-3) shows that cross-dataset transfer leads to notable performance degradation due to dataset shifts (e.g., distribution, difficulty, and pre-training differences), which cause classifiers to overfit dataset-specific gradient features. In contrast, the unified classifier performs well on mixed data, indicating that our method can capture universal feature discrepancies arising from model familiarity.
+# 6. Conclusion
+We revisit pre-training data detection from an optimization and training-dynamics perspective and introduce GDS, a fine-tuning–free method for inferring pre-training membership. By analyzing how models transition from unfamiliarity to familiarity, we show that member and non-member samples exhibit stable, interpretable differences in gradient magnitude, location, and concentration across datasets and architectures. Experiments show that GDS is effective and generalizable, outperforming strong baselines. Future work can focus on developing more generalizable detectors by contrastive learning or deeper feature extraction.
+{8}------------------------------------------------
+# Limitations
+This work investigates pre-training data detection, a form of membership inference that determines whether a given sample was included in a LLM's pre-training corpus. While our proposed GDS method improves detection accuracy and generalization without fine-tuning, it also raises important ethical concerns. Pre-training data detection methods could be misused to probe proprietary or confidential training corpora, potentially revealing sensitive information about data sources or collection practices. Although GDS does not reconstruct or expose training samples directly, it contributes to capabilities that may be exploited if applied irresponsibly. Our primary motivation is to support transparency, accountability, and safety. As pre-training datasets become increasingly large and opaque, tools like GDS can help researchers, auditors, and regulators verify data usage claims, identify potential copyright violations, and detect benchmark contamination. In this sense, GDS is intended as a diagnostic and auditing mechanism rather than a data extraction attack. We release code and models to promote reproducibility while encouraging responsible deployment. Overall, we hope this work advances trustworthy and transparent large-scale model development while highlighting the need for careful governance of pre-training data.
+# References
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+{10}------------------------------------------------
+# <span id="page-10-0"></span>A. Details of Baseline
+Shared Notations: We first define the universal notations used across all baseline methods for consistency:
+- x: Input text sample for membership inference detection.
+- {x1, x2, . . . , x<sup>N</sup> }: Token sequence of input text sample x, where N denotes the total number of tokens in the text.
+- x<t: Prefix token sequence of the t-th token xt, i.e., x<t = {x1, . . . , xt−1}.
+- θ: Trainable parameters of the pre-trained language model.
+- p(· | ·; θ): Conditional probability distribution parameterized by the model parameters θ.
+- k%: Percentage threshold for selecting low-probability outlier tokens (used in Min-k% and Min-k%++).
+#### A.1. PPL
+Perplexity (PPL) is a classic global likelihood-based metric that measures the model's uncertainty in predicting a given text, with lower PPL indicating higher text familiarity (more likely to be a member sample). First, the text is tokenized into a sequence of tokens {x1, x2, . . . , x<sup>N</sup> }. Then, the log-likelihood of each token is calculated conditional on the preceding tokens, and the final PPL is derived by normalizing the sum of log-likelihoods by the token sequence length and performing an exponential transformation.
+$$PPL = \exp\left(-\frac{1}{N} \sum_{i=1}^{N} \log p(x_i|x_1, ..., x_{x-1}; \theta)\right)$$
+(16)
+#### A.2. Zlib
+Zlib is a compression-based global likelihood-related method that leverages compression entropy to distinguish member and non-member samples, which calibrates the loss using the input's Zlib entropy. For an input text sample x and a pre-trained model M, the Zlib score is defined as the ratio of the loss related to the text and model to the Zlib compression entropy of the input text:
+Zlib Score =
+$$\frac{L(x, M)}{\text{zlib}(x)}$$
+(17)
+where L(x, M) denotes the loss value associated with the input text x under the model M and zlib(x) represents the Zlib compression entropy of the input text x, which is derived from the length of the text after Zlib compression.
+#### A.3. Min-k%
+Min-k% is a local likelihood-based method that mitigates global word frequency interference by focusing on low-probability outlier tokens. For an input text token sequence x = {x1, x2, . . . , x<sup>N</sup> } (where N denotes the total number of tokens), it first calculates the conditional log-likelihood of each token x<sup>i</sup> given its preceding context:
+$$\log p(x_i \mid x_1, x_2, \dots, x_{i-1}; \theta)$$
+Subsequently, it sorts all token conditional probabilities in ascending order, selects the bottom k% tokens (i.e., the k% tokens with the smallest conditional probabilities) to form the low-probability set Tmin(k%) = Min-K%(x). The final Min-k% score is defined as the average conditional log-likelihood of tokens in Tmin(k%):
+Min-k% Score(x) =
+$$\frac{1}{|T_{\min(k\%)}|} \sum_{x_i \in T_{\min(k\%)}} \log p(x_i \mid x_1, \dots, x_{i-1}; \theta)$$
+(18)
+where |Tmin(k%)| = ⌊k% × N⌋ denotes the cardinality of the low-probability token set (rounded down to the nearest integer). During detection, a threshold is set on Min-k% Score(x): text with a score below the threshold is classified as a member sample (since member samples tend to contain more low-probability outlier tokens), and vice versa.
+{11}------------------------------------------------
+#### A.4. Min-k%++
+Min-k%++ is an optimized variant of Min-k% that enhances detection robustness by integrating vocabulary-level probability statistics, addressing the text-length dependency and short-text fluctuation issues of the original method. For an input text token sequence $x = \{x_1, x_2, \dots, x_N\}$ , it first computes the normalized conditional log-likelihood for each token $x_t$ (given prefix $x_{< t} = \{x_1, \dots, x_{t-1}\}$ ) by normalizing with the vocabulary-wide log-probability statistics of the prefix $x_{< t}$ .
+#### **Core Token-Level Score Calculation**
+For each token $x_t$ , the token-level Min-k%++ score is defined as:
+$$Min-k\% + +_{token}(x_{< t}, x_t) = \frac{\log p(x_t \mid x_{< t}; \theta) - \mu_{x_{< t}}}{\sigma_{x_{< t}}}$$
+(19)
+where $\mu_{x_{< t}} = \mathbb{E}_{z \sim p(\cdot \mid x_{< t}; \theta)} [\log p(z \mid x_{< t}; \theta)]$ : Expectation of the next-token log-likelihood over the model's vocabulary, given prefix $x_{< t}$ ; $\sigma_{x_{< t}} = \sqrt{\mathbb{E}_{z \sim p(\cdot \mid x_{< t}; \theta)} \left[ (\log p(z \mid x_{< t}; \theta) - \mu_{x_{< t}})^2 \right]}$ : Standard deviation of the next-token log-likelihood over the vocabulary, given prefix $x_{< t}$ .
+Both $\mu_{x_{< t}}$ and $\sigma_{x_{< t}}$ can be computed analytically using the model's output logits (since $p(\cdot \mid x_{< t}; \theta)$ follows a categorical distribution), requiring no additional computational overhead beyond standard LLM inference.
+#### **Final Sequence-Level Score Calculation**
+Similar to Min-k%, Min-k%++ selects the bottom k% tokens with the smallest Min-k%++<sub>token</sub> scores to form the low-probability set $T_{\min(k\%)}^+$ . The final sequence-level score is the average of the token-level scores in this set:
+$$Min-k\% ++ Score(x) = \frac{1}{|T_{\min(k\%)}^+|} \sum_{(x_{< t}, x_t) \in T_{\min(k\%)}^+} Min-k\% ++_{token}(x_{< t}, x_t)$$
+(20)
+where $|T_{\min(k\%)}^+| = \lfloor k\% \times N \rfloor$ denotes the cardinality of the low-probability token set. During detection, a threshold is applied: text with a lower Min-k%++ score is more likely to be a member sample, as the normalized score better distinguishes low-probability outlier tokens of member samples from non-member ones.
+#### A.5. FSD
+Fine-tuned Score Deviation (FSD) is a fine-tuning enhanced method that leverages score discrepancies between pre-trained and fine-tuned models for member sample detection. Its core workflow includes two key steps: first, constructing a domain-matched non-member fine-tuning dataset (using post-model-release unseen data), then performing self-supervised next-token prediction fine-tuning on the pre-trained model. Finally, it calculates the score difference between the pre-trained and fine-tuned models to distinguish member and non-member samples. The self-supervised fine-tuning loss is defined as:
+$$\mathcal{L}_{\text{fine-tuning}}(x) = -\frac{1}{n} \sum_{i=1}^{n} \log f_{\theta}(x_i \mid x_1, \dots, x_{i-1})$$
+(21)
+The final FSD score is the deviation between the sample scores obtained from the pre-trained model $f_{\theta}$ and the fine-tuned model $f_{\theta'}$ (with parameters $\theta'$ ):
+$$FSD(x; f_{\theta}, f_{\theta'}) = S(x; f_{\theta}) - S(x; f_{\theta'})$$
+(22)
+where $S(\cdot)$ represents a base scoring function (e.g., Perplexity, Min-k%). A large FSD score indicates the sample is likely a non-member (fine-tuning reduces non-member perplexity significantly), while a small score suggests a member sample (fine-tuning has negligible impact on member perplexity). A validation-set optimized threshold $\varepsilon$ is used for final classification.
+#### <span id="page-11-0"></span>A.6. Experimental Settings
+We use the PEFT library (Mangrulkar et al., 2022) for LoRA-based (Hu et al., 2022) gradient feature extraction without parameter updates. The base model is initialized from pre-trained checkpoints, and for LoRA configuration, we adopt
+{12}------------------------------------------------
+default settings with rank r = 16, LoRA scaling factor α = 32, and dropout set to 0 since we only focus on gradients from a single backpropagation step and no parameter updates are required. Target modules include all submodules of attention and FFN, including query, key, value, output, gate, up, and down projections. For different datasets, we select the tokenizer sequence length based on the overall length distribution: 256 for the WikiMIA dataset and 512 for all other datasets. When training the MLP classifier, the dataset is uniformly split into training and validation sets at a ratio of 3:7. The MLP classifier is configured with two hidden layers of dimensions 128 and 64, respectively, and uses the default Adam optimizer with a learning rate of 0.001. An early stopping strategy is implemented to avoid overfitting.
+# <span id="page-12-0"></span>B. Motivation Experiment Supplementary Details
+To verify the parameter update law driven by the training process, we conduct LoRA fine-tuning with 8 epochs on LLaMA-7B using the unseen set of BookMIA dataset, counting LoRA matrix parameter updates per epoch to extract dynamic change curves of target features. Experiments are performed under three learning rates (1e − 5, 3e − 5, 5e − 5). We present the variation trends of the four feature categories across different modules and layers under each learning rate.
+We present the variation trends of the four feature categories across different modules and layers under each learning rate. Across all learning rates, ∆Θ<sup>t</sup> and S<sup>t</sup> exhibit clear epoch-wise patterns: ∆Θ<sup>t</sup> continuously decreases with training epochs, while S<sup>t</sup> gradually increases. For Et, distinct opposite trends are observed between the ATT and MLP modules—the update positions of the ATT module tend to be centralized, whereas those of the MLP module tend to be marginalized. Despite this divergence, E<sup>t</sup> values of both modules converge to the same stable range across the three learning rates. In contrast, T10,t shows a different dynamic: under large learning rates, it first increases and then decreases, yet remains stably around 0.27 throughout training. Notably, the inflection point of T10,t decline coincides with the stage when E<sup>t</sup> stabilizes. This aligns with our core hypothesis: during training, the model identifies core parameters correlated with the input data and performs concentrated updates on them; once this process is completed, the overall parameter update dynamics tend to stabilize. Regarding different hierarchical levels, only E<sup>t</sup> shows noticeable discrepancies, while all other features follow the same evolutionary laws.
+![](_page_12_Figure_5.jpeg)
+*Figure 6.* Feature Dynamic Changes During LoRA Fine-Tuning (Learning Rate 1e−5). Top row: Features in ATT/MLP modules; Bottom row: Features in low/middle/high layers.
+{13}------------------------------------------------
+![](_page_13_Figure_1.jpeg)
+*Figure 7.* Feature Dynamic Changes During LoRA Fine-Tuning (Learning Rate 3e − 5).
+![](_page_13_Figure_3.jpeg)
+*Figure 8.* Feature Dynamic Changes During LoRA Fine-Tuning (Learning Rate 5e − 5).
+{14}------------------------------------------------
+# 771 774
+# 776 778
+# 779 780 781 782 783 784 785
+# 787 788 789 790 791
+# 794 796 798 799 800 801
+# 806 807 808 809 810 811 812
+# <span id="page-14-0"></span>C. Ablation Experiments on Sub-features and Sub-modules
+To further explore the discriminative power of fine-grained components in our method, we conduct two additional ablation experiments: sub-feature category ablation (8 sub-features) and sub-module ablation (7 sub-modules). All experiments follow the same configuration as the main text (LLaMA-7B model, WikiMIA/ArxivTection datasets), with AUC and TPR@5% FPR as evaluation metrics.
+# C.1. Sub-feature Category Ablation Experiment
+The four core feature categories are decomposed into 8 sub-features, as follows:
+- Magnitude Distribution Features: Abs Mean, Std
+- Core Contribution Features: 10p Ratio, Sparsity
+- Position Offset Features: Row Ecc, Col Ecc
+- Row-Dimension Consistency Features: Row Mean Max, Row Mean Std
+<span id="page-14-1"></span>Ablation is performed by removing one sub-feature at a time (retaining the other 7), and the results are shown in Table [8.](#page-14-1)
+*Table 8.* Ablation Experiment Results of Sub-features (AUC Scores).
+| Dataset | Sub-feature (Ablation Variant) | | | | | | | | | | |
+|--------------|--------------------------------|---------------------------------------------------------------------------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|--|--|
+| | -Abs Mean | -Std<br>-10p Ratio<br>-Sparsity<br>-Row Ecc<br>-Col Ecc<br>-Row Max<br>-Row Std | | | | | | | | | |
+| WikiMIA | 0.95/0.71 | 0.95/0.72 | 0.95/0.70 | 0.94/0.67 | 0.95/0.70 | 0.93/0.62 | 0.95/0.73 | 0.95/0.72 | 0.96/0.84 | | |
+| ArxivTection | 0.96/0.82 | 0.96/0.81 | 0.96/0.83 | 0.96/0.82 | 0.96/0.83 | 0.95/0.78 | 0.96/0.83 | 0.96/0.83 | 0.97/0.85 | | |
+The sub-feature ablation results verify that all sub-features contribute to detection performance, with their combination achieving optimal AUC and TPR scores across both datasets. Among these sub-features, Col Ecc (a Position Offset Feature) is the most critical: its removal leads to the sharpest performance decline (AUC drops to 0.93 on WikiMIA and 0.95 on ArxivTection, with TPR falling to 0.62 and 0.78 respectively). In contrast, removing Abs Mean, Std, 10p Ratio, Row Ecc, Row Max, or Row Std induces only mild performance degradation, with AUC remaining above 0.95 on both datasets, indicating their relatively moderate importance; Sparsity also shows a slight impact on WikiMIA, with its ablation resulting in an AUC of 0.94. Overall, the fine-grained sub-feature design is rational, as each component provides complementary discriminative information for pre-training data detection.
+#### C.2. Sub-module Ablation Experiment
+The ATT and FFN modules are decomposed into 7 sub-modules based on Transformer architecture details:
+- ATT-related sub-modules: Q-Proj, K-Proj, V-Proj, Out-Proj
+- FFN-related sub-modules: Gate-Proj, Up-Proj, Down-Proj
+<span id="page-14-2"></span>Ablation is performed by removing one sub-module's features at a time, and the results are shown in Table [9.](#page-14-2)
+*Table 9.* Ablation Experiment Results of Sub-modules (AUC / TPR@5% FPR Scores).
+| Dataset | Sub-module (Ablation Variant) | | | | | | | | | |
+|--------------|-------------------------------|-----------|--------------------------------------------------------------|-----------|-----------|-----------|-----------|-----------|--|--|
+| | -Q-Proj | -K-Proj | -V-Proj<br>-Out-Proj<br>-Gate-Proj<br>-Up-Proj<br>-Down-Proj | | | | | | | |
+| WikiMIA | 0.95/0.72 | 0.95/0.71 | 0.94/0.69 | 0.94/0.67 | 0.95/0.69 | 0.94/0.65 | 0.94/0.61 | 0.96/0.84 | | |
+| ArxivTection | 0.96/0.80 | 0.96/0.82 | 0.95/0.79 | 0.96/0.80 | 0.96/0.82 | 0.95/0.78 | 0.96/0.82 | 0.97/0.85 | | |
+The sub-module ablation results demonstrate that all sub-modules provide complementary gradient information, as singlesub-module ablation consistently leads to performance degradation while integrating all sub-modules' features achieves
+{15}------------------------------------------------
+<span id="page-15-0"></span>![](_page_15_Figure_1.jpeg)
+*Figure 9.* Impact Analysis of Training Set Size on WikiMIA. The abscissa denotes the training-validation set ratio, the ordinate represents the scores of two metrics, yellow indicates the AUROC score, and blue indicates the TPR@5% FPR.
+the optimal AUC and TPR@5% FPR scores across both datasets. Though the performance differences between individual ablation variants are mild, ATT-related sub-modules show slightly stronger discriminative power than FFN-related ones, with K-Proj performing prominently among ATT sub-modules; in contrast, among FFN sub-modules, Down-Proj and Gate-Proj contribute more to detection performance than Up-Proj, as retaining the former two yields slightly higher AUC and TPR scores. The performance gap between single-sub-module variants and the full model further confirms the necessity of multi-sub-module feature fusion, which enables the capture of comprehensive gradient patterns across the Transformer architecture. It can be seen from this that our method also achieves excellent performance with smaller LoRA adaptation parameters and lower computational complexity.
+#### C.3. Low-Data Scenarios
+To evaluate the data efficiency of our method in scenarios with limited training data, we adjust the training-testing split ratio of the WikiMIA dataset to five settings: 1:9, 2:8, 3:7 and 4:6, while keeping the total sample size fixed. Figure Y shows AUC and TPR@5% FPR scores across different split ratios.
+Figure [9](#page-15-0) show our method's performance improves steadily with increasing training set size. Notably, it achieves an AUC of 0.9 even with only 10% of data, accompanied by a TPR@5% FPR of 0.48, confirming that it can also achieve excellent performance with a small amount of data.