Interpretable and Sparse Linear Attention with Decoupled Membership-Subspace Modeling via MCR2 Objective

Maximal Coding Rate Reduction (MCR2)-driven white-box transformer, grounded in structured representation learning, unifies interpretability and efficiency, providing a reliable white-box solution for visual modeling. However, in existing designs, tight coupling between "membership matrix" and "subspace matrix U" in MCR2 causes redundant coding under incorrect token projection. To this end, we decouple the functional relationship between the "membership matrix" and "subspaces U" in the MCR2 objective and derive an interpretable sparse linear attention operator from unrolled gradient descent of the optimized objective. Specifically, we propose to directly learn the membership matrix from inputs and subsequently derive sparse subspaces from the fullspace S. Consequently, gradient unrolling of the optimized MCR2 objective yields an interpretable sparse linear attention operator: Decoupled Membership-Subspace Attention (DMSA). Experimental results on visual tasks show that simply replacing the attention module in Token Statistics Transformer (ToST) with DMSA (we refer to as DMST) not only achieves a faster coding reduction rate but also outperforms ToST by 1.08%-1.45% in top-1 accuracy on the ImageNet-1K dataset. Compared with vanilla Transformer architectures, DMST exhibits significantly higher computational efficiency and interpretability.

Dynamic Stochastic Ensemble with Adversarial Robust Lottery Ticket Subnetworks

Adversarial attacks are considered the intrinsic vulnerability of CNNs. Defense strategies designed for attacks have been stuck in the adversarial attack-defense arms race, reflecting the imbalance between attack and defense. Dynamic Defense Framework (DDF) recently changed the passive safety status quo based on the stochastic ensemble model. The diversity of subnetworks, an essential concern in the DDF, can be effectively evaluated by the adversarial transferability between different networks. Inspired by the poor adversarial transferability between subnetworks of scratch tickets with various remaining ratios, we propose a method to realize the dynamic stochastic ensemble defense strategy. We discover the adversarial transferable diversity between robust lottery ticket subnetworks drawn from different basic structures and sparsity. The experimental results suggest that our method achieves better robust and clean recognition accuracy by adversarial transferable diversity, which would decrease the reliability of attacks.