Final-Model-Only Data Attribution with a Unifying View of Gradient-Based Methods

TL;DR

The paper tackles the challenge of training data attribution when only the final model is available (FiMO), reframing attribution as model sensitivity to training instances and introducing FiMODA as a gold-standard sensitivity probe via further training. It unifies gradient-based TDA methods under a common Taylor-expansion framework, showing first-order methods approximate the further-training process well early on, while influence-function-based approaches are more stable but may not reach early peak quality. Empirical results across tabular, image, and text modalities reveal a clear decay in first-order method accuracy with more further training, whereas IF-based methods maintain steadier performance, though not always outperforming first-order methods at peak. The work provides theoretical generalizations, practical approximations, and extensive numerical comparisons, highlighting the potential and limitations of FiMODA methods for data attribution when training details are unavailable, with significant implications for real-world data understanding and auditing.

Abstract

Training data attribution (TDA) is concerned with understanding model behavior in terms of the training data. This paper draws attention to the common setting where one has access only to the final trained model, and not the training algorithm or intermediate information from training. We reframe the problem in this "final-model-only" setting as one of measuring sensitivity of the model to training instances. To operationalize this reframing, we propose further training, with appropriate adjustment and averaging, as a gold standard method to measure sensitivity. We then unify existing gradient-based methods for TDA by showing that they all approximate the further training gold standard in different ways. We investigate empirically the quality of these gradient-based approximations to further training, for tabular, image, and text datasets and models. We find that the approximation quality of first-order methods is sometimes high but decays with the amount of further training. In contrast, the approximations given by influence function methods are more stable but surprisingly lower in quality.

Figures (11)

• Figure 1: Given only a final model with parameters ${\bm{\theta}}^f$, the proposed further training gold standard measures the model's sensitivity to training sample $i$ by further training on the full training set $\mathcal{D}$ as well as leaving out sample $i$ ($\mathcal{D}_{-i}$), resulting in changed parameters ${\bm{\theta}}^f + \Delta{\bm{\theta}}(\mathcal{D})$ and ${\bm{\theta}}^f + \Delta{\bm{\theta}}(\mathcal{D}_{-i})$. The difference in outputs $g({\bm{z}}, {\bm{\theta}}^f + \Delta{\bm{\theta}}(\mathcal{D}_{-i})) - g({\bm{z}}, {\bm{\theta}}^f + \Delta{\bm{\theta}}(\mathcal{D}))$ indicates the sensitivity to $i$. For stochastic training, this process is repeated to obtain the expected sensitivity.
• Figure 2: Cosine similarity between attribution scores of gradient-based TDA methods and further training, as a function of the number of epochs or steps of further training. The legend in panel (b) applies to (a)--(d). In panel (a), Grad-Cos occludes Grad-Dot; in panel (c), LiSSA occludes CG.
• Figure 3: Maximum cosine similarity between attribution scores of gradient-based TDA methods and further training, as a function of the number of random seeds averaged.
• Figure 4: Cosine similarity between attribution scores of gradient-based TDA methods and further training as a function of the amount of further training, using a different further training algorithm (Adam) than the initial training algorithm (SGD).
• Figure 5: Cosine similarity between attribution scores of gradient-based TDA methods and further training using the same further training algorithms as in Figure \ref{['fig:cos_sim_epochs_sgd']}, but with adjustment done according to \ref{['eqn:output_diff_averaged']}.

Theorems & Definitions (4)

• Proposition 1
• Corollary 2
• proof : Proof of Proposition \ref{['prop:IF']}
• proof : Proof of Corollary \ref{['cor:IF_GN']}