GEX: A flexible method for approximating influence via Geometric Ensemble
Authors: SungYub Kim, Kyungsu Kim, Eunho Yang
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Empirically, our approach outperforms existing IF approximations for downstream tasks with lighter computation, thereby providing new feasibility of low-complexity/nonlinear-based IF design. 1 Introduction In the last decade, neural networks (NNs) have made tremendous advances in various application areas [49, 24, 47]. To make reasonable predictions with NN-based systems, models must be able to explain their predictions. For example, those who doubt the model s prediction can gain insight and foresight by referencing the explanation of the model. Moreover, mission-critical areas like finance and medicine require a high degree of explainability to ensure that the predictions are not biased [30]. Understanding the mechanism of predictions also allows researchers and engineers to improve prediction quality, ensuring that NNs are performing as intended [32]. To this end, Influence Function (IF) was proposed to explain predictions of pre-trained NNs through training data [25]. Intuitively, IF measures how the leave-one-out (LOO) retraining of a training sample changes the loss of each sample. Therefore, the sign of influence determines whether the training sample is beneficial to others, and the scale of influence measures its impact. Specifically, self-influence, the increase in loss when a sample is excluded, was used to measure how much the sample is memorized [48, 15]: When LOO training is performed on a memorized training sample, its loss will increase substantially since matching its (corrupted) label will be difficult. Therefore, self-influence is used to detect mislabeled samples [48, 52] where memorization occurs. Furthermore, 37th Conference on Neural Information Processing Systems (Neur IPS 2023). Correspondence to recent works successfully applied IF to various downstream tasks, including dataset pruning [58] and data resampling [59, 63]. Despite its broad applicability, we found that IF and its approximations [25, 48, 52] suffer from oversimplified self-influence distributions due to their bilinear form1. Although these approximations are introduced to avoid prohibitive retraining costs of IF, they impose a structural constraint that self-influence becomes quadratic to gradients of pre-trained NNs. Due to this constraint, self-influence follows an unimodal distribution, as gradients of pre-trained NNs typically follow a zero-centered Stable distribution [7, 56]. Unfortunately, unimodal distributions are too restrictive for representing self-influence in real-world datasets containing mislabeled samples. While self-influence distributions estimated by LOO retraining may become bimodal depending on the proportion of (high selfinfluential) mislabeled samples, unimodal distributions cannot handle this case. To resolve this problem, we propose a non-linear IF approximation via Geometric Ensemble (GE; [16]). Our method is motivated by a novel connection between IF approximation and linearized Laplace approximation (LA; [38]) that we discovered: IF approximations can be translated to an averaged relationship between two linearized losses over parameters sampled from LA. As linearized losses in this connection cause bilinear forms of IF approximations, we consider an IF approximation without linearization. However, we then identify an additional issue of this approximation due to the singularity of Hessian and its solutions (e.g., damping and truncation). To mitigate this issue, we propose a novel approach using GE to manage the relationship of non-linear losses more effectively. As a result, our approach, Geometric Ensemble for sample e Xplanation (GEX), accurately represents the multimodal nature of LOO retraining, leading to improved performance in downstream tasks across various scenarios. Furthermore, IGEX is easy to estimate as it does not require Jacobian-vector products (JVPs) for batch estimation or sub-curvature approximations like LA. We summarize our contributions as follows: We identify a distributional bias in commonly used IF approximations. We demonstrate how this bias results in oversimplified distributions for self-influences. We provide a novel connection between IF approximations and LA. By identifying an inherent issue of LA, we provide a non-linear IF approximation via GE, named IGEX. Due to its non-linear nature, IGEX can express various influence distributions depending on the characteristic of the datasets. We verify that IGEX outperforms standard IF approximations in downstream tasks, including noisy label detection, relabeling, dataset pruning, and data source separation. We also show that IGEX is competitive with well-known baselines of downstream tasks with lighter computation.2 |
| Researcher Affiliation | Collaboration | Sung-Yub Kim Graduate School of AI, KAIST sungyub.kim@kaist.ac.kr Kyungsu Kim Massachusetts General Hospital and Harvard Medical School kskim.doc@gmail.com Graduate School of AI, KAIST and AITRICS eunhoy@kaist.ac.kr |
| Pseudocode | Yes | We provide the pseudocode for computing IGEX in Appendix C. [...] C Implementations C.1 Pseudocode of LA for IF approximation Algorithm 1 ILA with KFAC [39, 17] sub-curvature approximation [...] C.2 Pseudocode of GEX Algorithm 2 IGEX |
| Open Source Code | Yes | Code is available at https://github.com/sungyubkim/gex. |
| Open Datasets | Yes | We use standard datasets in the computer vision domain: MNIST [33], CIFAR-10/100 [27], and SVHN [42]. [...] To verify the scalability of our method, we also use Image Net [12] with Vision Transformer [13] and MLP-Mixer [60]. [...] To verify the effectiveness of our method in another modality, we train SWEM [53] to DBpedia [34], following Pruthi et al. [48]. |
| Dataset Splits | Yes | We use 30 train samples for each class (circle) and add ten influential samples at the center. [...] For CL, we use two-fold cross-validation. |
| Hardware Specification | Yes | We use 8 NVIDIA RTX 3090 GPUs for all experiments. |
| Software Dependencies | No | The paper mentions software components like "jax.hessian function" and "pytorch implementation" but does not provide specific version numbers for these or other libraries/frameworks, which are essential for reproducible software dependencies. |
| Experiment Setup | Yes | We use a batch size of 1024 for all datasets. For all datasets, we use the cosine learning rate annealing [36] with a linear warm-up where the peak learning rate is 0.4, and the warm-up ratio (percentage of warm-up steps to training steps) is 10%. We use 0.0005 for the L2 regularization coefficient. We use 200 training epochs for all datasets. |