Sharding is one of the most effective techniques for addressing scalability challenges in blockchain systems. However, existing sharding schemes often fail to balance security and scalability, primarily due to unavoidable cross-shard communication costs. Some schemes rely on additional roles like TEEs or alliances to streamline cross-shard consensus, introducing security risks such as hardware attacks or node collusion. Others mitigate cross-shard consensus costs by periodically distributing nodes or states based on predefined rules, yet inefficient distribution rules lead to poor scalability. In response, this article proposes SAC, a novelshardingallocation service that efficiently trades scalability and security via a two-stage allocation strategy. First, SAC employs lightweight state graph clustering to group frequently interacting states within the same shards based on historical transaction data, reducing cross-shard transactions significantly. Second, it formulates node allocation as a multi-objective evolutionary problem (MoSA) that jointly maximizes system throughput, minimizes confirmation latency, and balances malicious node distribution. Next, SAC selects FV-MOEA as the foundational solver for MoSA after comprehensive preliminary experiments. Based on this, SAC proposes an improved algorithm, LeFV, to explore optimal shard allocation solutions. Specifically, LeFV retains and mutates low-contributing but potentially high-quality solutions to enhance population diversity. It allows for a wider exploration of shard allocations, thereby identifying optimal ones that effectively balance scalability and security of the sharding system. Extensive experiments on a sophisticated blockchain emulator demonstrate that SAC outperforms two advanced state-of-the-art methods in balancing scalability and security.

We prove that when we do the Taylor series expansion of the loss function, the BN operation will block the influence of the first-order term and most influence of the second-order term of the loss. We also find that such a problem is caused by the standardization phase of the BN operation. We believe that proving the blocking of certain loss terms provides an analytic perspective for potential detects of a deep model with BN operations, although the blocking problem is not fully equivalent to significant damages in all tasks on benchmark datasets. Experiments show that the BN operation significantly affects feature representations in specific tasks.