August 1, 2024

Model Influence Functions: Measuring Data Quality


As AI plays a larger economic role in society, a critical question emerges: who should own AI? Recent controversies, such as the Youtube creators realizing their videos had been used to train leading AI video models, highlight the urgent need for data ownership and transparency in AI.

Vana is building user-owned AI through user-owned data. That means users who contribute the data that teaches AI are the ones who own it. Aligning these incentives is key to pushing the frontiers of AI. But a critical question is: how exactly do you quantify what good data is, and what data teaches AI models? 

This is where AI model influence functions come in—a powerful tool for measuring data's value in AI training.

AI Model Influence Functions

Model influence functions provide a mathematical framework to measure how much a single data point contributes to an AI model's performance. Essentially, they quantify the "teaching power" of each piece of data. Model influence functions measure the change in a model's output when a specific data point is added or removed from the training set (1).

Mathematical Foundation:

Influence of a Data Point

The influence of a data point \(z_m\) is approximated by:

\[I(z_m) \approx -H^{(-1)} \nabla_\theta L(z_m, \theta^*)\]

Where:

  • \(H\) is the Hessian matrix of the loss function
  • \(\nabla_\theta L(z_m, \theta^*)\) is the gradient of the loss with respect to the model parameters

Illustrative MNIST Example

To illustrate, consider the MNIST dataset of handwritten digits, a classic dataset used in AI. Model influence functions reveal that the most influential data points are often "edge cases"—ambiguous digits that could be mistaken for others (e.g., a '2' that resembles a '7'). These challenging examples force the model to refine its decision boundaries, thus having a more significant impact on its learning. It’s the unique data points like these that are most important to teaching AI. 

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Training data points with a high model influence score (N Panickssery)

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Implications for User-Owned AI

Model influence functions serve as a cornerstone for proof of contribution systems in user-owned AI. By providing a quantifiable measure of data impact, they enable:

  • Transparent Reward Systems: Users can be compensated based on their data's actual influence on AI model performance, earning financial rewards and governance rights of the data DAO.
  • Verifiable Contributions: The impact of each data point can be independently verified, ensuring fairness in data marketplaces.
  • Iterative Improvement: By understanding which types of data are most influential, we can guide users to contribute more valuable information over time.

For a deeper dive into proof of contribution mechanisms, see the docs. As we advance towards truly user-owned AI, model influence functions will play a crucial role in ensuring fair attribution, compensation, and governance in the AI ecosystem. For those interested in diving deeper into the technical aspects of model influence functions and user-owned AI, join the conversation on X and dm if you're interested in joining our technical reading group on user-owned AI.