$$\rightleftharpoonup{xx}$$
$$\longleftharp{xx}$$,
$$\longrightharp{xx}$$,
Setup
We considered a supervised classification task with a dataset
, where
represents the input features and
denotes the corresponding class labels for a K-class problem. The dataset D is split into a clean training dataset and a test dataset.
The goal is to modify the clean training dataset by introducing small, imperceptible perturbations δ to create an unlearnable dataset
, where
+ δ. The perturbation δ is bounded by
, ensuring that it does not significantly alter the normal utility of the data. The key objective is to disrupt learning by forcing the model fθ, trained on Du, to focus on irrelevant patterns induced by the noise rather than the meaningful features, resulting in poor generalization on a clean test dataset:
![figure-protocol-7 Optimization formula argmin E[(xᵢ,yᵢ)~Dᵤ] L(fₑ(xᵢ),yᵢ), mathematical expression.](/files/ftp_upload/68338/68338eq7.jpg)
Simulating a blockchain environment
To install blockchain tools, the Hardhat framework is used to simulate an Ethereum network on a local environment for deploying smart contracts and testing the generation of Unlearnable Examples. To launch a local network, a simulated blockchain network with multiple nodes and accounts is initialized. Each node is allocated resources like Ether to facilitate transaction simulations. To develop smart contracts, they are implemented to dynamically manage user permissions. Authorized users can access clean data, while unauthorized users are restricted to accessing Unlearnable Examples. First, configure a development environment based on Node.js v16.x and Hardhat 2.8.4, and use the Solidity 0.8.17 compiler to complete the compilation and optimization of the smart contract. The compilation process is executed by the command line using npx hardhat compile to generate build artifacts containing the ABI and bytecode. Subsequently, deploy the contract to the Sepolia test network by running the deployment script npx hardhat run scripts/deploy.js --network sepolia, and record the output contract address and deployment transaction hash. During the performance testing phase, three core tests are sequentially executed: transaction cost test records gas consumption by cyclically invoking the contract's grantAccess method; throughput test uses the Artillery tool to simulate user requests with incrementally increasing load; testing and validation transactions, including data storage and retrieval, are conducted to validate the smart contract's functionality.
Constructing on-chain users and permission mechanisms
Unique user accounts are generated using blockchain wallets (e.g., MetaMask), each comprising a private key and a public key. The prototype implementation employs a simulated blockchain environment where synthetic user entities upload publicly available datasets to the decentralized system, storing only cryptographic hash values on the distributed ledger. This ensures data integrity without storing the actual data on-chain, which would be inefficient and costly. The actual data is stored off-chain, typically using decentralized storage systems like IPFS, ensuring efficient data management while maintaining security and privacy. For non-fungible tokens (NFTs) and access control, this study implements a fine-grained access control mechanism using NFTs compliant with the ERC-721 standard. Each dataset of unlearnable examples is associated with a unique tokenId, which acts as a key to accessing the data. Users request access by submitting Merkle proofs. These proofs verify the user's identity in a secure, decentralized manner. Upon successful proof validation, the contract mints a unique NFT and transfers it to the user's wallet. This NFT represents the user's right to access the data associated with that specific unlearnable example. The use of NFTs ensures that only authorized users can access the data, based on a decentralized, immutable record. This is in contrast to traditional Role-Based Access Control (RBAC), which typically operates at the group level and may not provide the granularity needed for high-security applications30.
The smart contract continuously verifies access permissions through the ownerOf function, checking the ownership of the NFT to ensure that only authorized users can access the clean data. Administrators can revoke access by destroying the NFT through the revokeAccess function, ensuring flexibility in managing user access over time. The operational workflow consists of four critical steps: (1) users submit access requests containing Merkle proofs; (2) the contract verifies the validity of these proofs; (3) upon successful validation, the contract mints the corresponding NFT; (4) users retrieve encrypted data using the IPFS Content Identifier (CID) embedded in the NFT's metadata. By leveraging NFTs, we achieve several benefits over traditional access control mechanisms, such as fine-grained permission control (data-level vs. group-level), better audit capability (immutable on-chain records), and permission transferability (NFT marketplace transactions).
Multi-signature contracts are implemented for updating the Merkle root hash, preventing unauthorized tampering of data. The system incorporates anti-Sybil mechanisms by binding each dataset to a unique tokenId, ensuring that malicious actors cannot generate fraudulent tokens to access unauthorized data. The UEs are encrypted using AES-256 before being uploaded to the InterPlanetary File System (IPFS) network. The encrypted data hashes are stored on-chain, while the complete datasets remain on IPFS, reducing blockchain storage overhead. The hybrid approach of combining on-chain and off-chain storage strikes a balance between ensuring data availability and reducing storage costs, a common concern in blockchain-based applications.
Smart contracts are employed to dynamically manage user permissions. Each user is granted access to clean data only if they hold the appropriate NFT, which serves as their authorization token. Smart contracts log all data access in event logs, providing full traceability. These logs are immutable and can be audited, offering transparency and accountability. The smart contract employs the grantAccess function to validate access requests. The contract checks if the user holds the appropriate NFT and, if valid, grants access to the requested data. Each access event is recorded on the blockchain, ensuring that all data retrieval activities are verifiable. Every data access event is logged in real-time by the smart contract, which triggers an AccessGranted event. This event contains important information such as the user's wallet address, the timestamp of the access, and the corresponding NFT tokenId. The dynamic nature of smart contracts allows for real-time management of permissions. This is particularly useful in decentralized applications, where access control needs to be highly flexible and adaptable to changing conditions.
To address privacy concerns in public blockchain environments, the system stores low-resolution thumbnails (e.g., 64 x 64 pixels) on the blockchain, while the original high-resolution images are encrypted and stored off-chain on IPFS. Only authorized users who possess the corresponding NFT can retrieve the decryption keys for accessing the high-resolution data. Unauthorized users receive versions of the data with real-time DEM perturbations, ensuring that they cannot access the original data.
Generate image perturbation
Load CIFAR10, CIFAR100, and ImageNet datasets. Images in the datasets are uniformly resized and converted into PyTorch tensor, and the image tensor is normalized using the mean and standard deviation. Initialize a random noise δ1, using a Gaussian distribution to generate the initial perturbation. Random noise is applied to each image x, and the loss between the target label and the model prediction is calculated based on the cross-entropy loss. In a data set of class C, for a sample i, yi is the target label value, pi is the model prediction probability, which quantifies the difference between the probability distribution predicted by the model and the actual label, maximizing the loss so that the model produces false predictions. The cross-entropy loss is:

The influence of image perturbation on prediction calculated according to the loss function, the reverse propagation updates the perturbation, and the perturbation range and perturbation value are constantly updated through multiple iterations. For the learning rate η, the update formula for the perturbation is:

Generate text perturbations
Load pre-trained BERT models for generating text embeddings. A custom TextFeatureExtractor network consisting of two Transformer blocks and a fully connected layer is used to extract features from text embeddings generated by BERT models. Input the user information and timestamp of the access user into the pre-trained BERT model and dynamically generate text noise through the customized TextFeatureExtractor network.
The input image I is fed into the Qwen2.5-VL-7B-Instruct multimodal model. Guided by a structured prompt, the model generates a concise textual description Tq. This generated text Tq is input into the pre-trained BERT-base-uncased language model. Through task-specific rewriting prompts, the system generates perturbed text
that preserves semantics while altering expression. A TextFeatureExtractor network maps the perturbed text
into a high-dimensional semantic embedding vector Eg.
Generate multi-target perturbations
To ensure compatibility between text embeddings and image perturbations, we adjust the shape of the text embedding to match the dimensions of the image perturbation. Let ET and Eq represent the text embeddings, and PL the image perturbation. The reshaping process ensures ET and Eq are transformed to the same dimensionality as PL:
, where C, H, W are the dimensions of PL. Define an attention-mechanism fusion module that fuses text embedding perturbations and image perturbations, dynamically adjusting the perturbations according to the attention weights of the text. The fusion is:

where α is the dynamic adjustment of the attention mechanism parameters. δT is the text disturbance generated by the Eq and ET. Add a regularization term to the training process to prevent overfitting. The regularization term is the L2 norm of the text embedding, which penalizes perturbations. The multi-objective loss function combines cross-entropy loss and fusion perturbation, and the multi-objective loss function is as follows:

The goals of the loss function are:

where λ is a regularization coefficient used to control the penalty force of the perturbation, with the purpose of inhibiting excessive perturbation or overfitting. In the study of adversarial attacks, it has been found that
is the perturbation limit perceptible to the human eye. The training and evaluation process is defined, including perturbation generation, loss calculation, model training, etc.
Comparative experiments
We conducted a comprehensive evaluation of the proposed Dynamic Error-Minimizing Noise (DEM) against three existing methods: Error-Minimizing Noise (EM), Transferable Adversarial Perturbations (TAP), and Stable Error-Minimizing Noise (SEM). These methods were tested on three benchmark datasets: CIFAR-10, CIFAR-100, and a subset of ImageNet, using four widely adopted neural network architectures: VGG-16, ResNet-18, ResNet-50, and DenseNet-121, to ensure diverse experimental conditions.
In addition, we examined the robustness of these methods by applying diffusion-based denoising models to remove defensive noise and measuring the accuracy of the denoised examples on the test datasets. This step aimed to evaluate each method's ability to resist recovery attacks and maintain data privacy integrity under adversarial conditions. Results indicate that our DEM outperforms other methods in both robustness and accuracy across all datasets and architectures, demonstrating its efficacy as a privacy-preserving framework.