In this section, we mainly introduce the axiomatic properties of Shapley value. Weber et al. [17] have proved that Shapley value is the unique metric that satisfies the following axioms: Linearity, Symmetry, Dummy, and Efficiency. If two independent games u and v can be linearly merged into one game w(S) = u(S)+v(S), then the Shapley value of each player i N in the new game w is the sum of Shapley values of the player i in the game uand v, which can be formulated as: ϕw(i|N) = ϕu(i|N)+ϕv(i|N) (1) Symmetry Axiom. Considering two players i and j in a game v, if they satisfy: S N \{i,j},v(S {i}) = v(S {j}) (2) then ϕv(i|N) = ϕv(j|N). The dummy player is defined as the player that has no interaction with other players. Formally, if a player i in a game v satisfies: S N \{i},v(S {i}) = v(S)+v({i}) (3) then this player is defined as the dummy player.

Fine-Grained Visual Classification (FGVC) is a critical and challenging area within computer vision, demanding the identification of highly subtle, localized visual cues. The importance of FGVC extends to critical applications such as biodiversity monitoring and medical diagnostics, where precision is paramount. While large-scale Vision Transformers have achieved state-of-the-art performance, their decision-making processes often lack the interpretability required for trust and verification in such domains. In this paper, we introduce The Loupe, a novel, lightweight, and plug-and-play attention module designed to be inserted into pre-trained backbones like the Swin Transformer. The Loupe is trained end-to-end with a composite loss function that implicitly guides the model to focus on the most discriminative object parts without requiring explicit part-level annotations. Our unique contribution lies in demonstrating that a simple, intrinsic attention mechanism can act as a powerful regularizer, significantly boosting performance while simultaneously providing clear visual explanations. Our experimental evaluation on the challenging CUB-200-2011 dataset shows that The Loupe improves the accuracy of a Swin-Base model from 85.40% to 88.06%, a significant gain of 2.66%. Crucially, our qualitative analysis of the learned attention maps reveals that The Loupe effectively localizes semantically meaningful features, providing a valuable tool for understanding and trusting the model's decision-making process.

Acquisition of Magnetic Resonance Imaging (MRI) scans can be accelerated by under-sampling in k-space (i.e., the Fourier domain). In this paper, we consider the problem of optimizing the sub-sampling pattern in a data-driven fashion. Since the reconstruction model's performance depends on the sub-sampling pattern, we combine the two problems. For a given sparsity constraint, our method optimizes the sub-sampling pattern and reconstruction model, using an end-to-end learning strategy. Our algorithm learns from full-resolution data that are under-sampled retrospectively, yielding a sub-sampling pattern and reconstruction model that are customized to the type of images represented in the training data. The proposed method, which we call LOUPE (Learning-based Optimization of the Under-sampling PattErn), was implemented by modifying a U-Net, a widely-used convolutional neural network architecture, that we append with the forward model that encodes the under-sampling process. Our experiments with T1-weighted structural brain MRI scans show that the optimized sub-sampling pattern can yield significantly more accurate reconstructions compared to standard random uniform, variable density or equispaced under-sampling schemes.