GEX: A flexible method for approximating influence via Geometric Ensemble

Through a deeper understanding of predictions of neural networks, Influence Function (IF) has been applied to various tasks such as detecting and relabeling mislabeled samples, dataset pruning, and separation of data sources in practice. However, we found standard approximations of IF suffer from performance degradation due to oversimplified influence distributions caused by their bilinear approximation, suppressing the expressive power of samples with a relatively strong influence. To address this issue, we propose a new interpretation of existing IF approximations as an average relationship between two linearized losses over parameters sampled from the Laplace approximation (LA). In doing so, we highlight two significant limitations of current IF approximations: the linearity of gradients and the singularity of Hessian. Accordingly, by improving each point, we introduce a new IF approximation method with the following features: i) the removal of linearization to alleviate the bilinear constraint and ii) the utilization of Geometric Ensemble (GE) tailored for non-linear losses. Empirically, our approach outperforms existing IF approximations for downstream tasks with lighter computation, thereby providing new feasibility of low-complexity/nonlinear-based IF design. N n=1 ℓ(z n , θ)/N for a sample-wise loss ℓ(z n , θ) (e.g., cross-entropy between ŷn and y n ). In general, θ * is trained using a stochastic optimization algorithm (e.g., stochastic gradient descent (SGD) with momentum). For the reader's convenience, we provide the notation table in Appendix A for terms used in the paper.