# Efficient and Secure Federated Learning for Financial Applications
## 2 Related Works  
### Gradient Sparsification  
In the field of FL communication optimization, numerous approaches have been suggested to address the communication bottleneck issue. [PERSON] et al. (2010) [18] proposed an asynchronous update system that allows each node to independently update the model, free from the influence of other nodes with slower update rates, from a system perspective. In the area of communication transmission, reducing the traffic for each round is a direct method used to decrease communication time. Gradient sparsification, a prevalent gradient compression method, is employed to decrease the communication burden [19].  
[PERSON] et al. (2015) [20] proposed a gradient-dropping method, which only sends gradients larger than a predefined constant threshold, and all other gradients are accumulated in the locally saved residuals and are temporarily not sent. This method can achieve up to 3 orders of magnitude compression ratio of uploaded data. However, in the actual training task, it is difficult to choose the appropriate values for the threshold. Due to the different thresholds for the different tasks and models, artificial scheduling can introduce significant experimental costs. In order to overcome this problem, [PERSON] et al. (2016) [21] enhanced [PERSON]'s sparsification method. In contrast to the fixed threshold of the Storm method, the sparsity rate \(s\) is fixed. For example, when \(s\) = 0.001, only the top 0.1% of the gradient update vector is transmitted and other parts of the gradient update are kept locally for the time being. Their experiments showed that with a sparsity rate of \(s\) = 0.001, their method could only slightly reduce the convergence speed and the final accuracy of the speed training model.  
[PERSON] et al. (2016) [22] argued that normalizing each layer is crucial for gradient convergence. [PERSON] et al. (2018) [23] proposed the Deep Gradient Compression (DGC) algorithm, which includes momentum correction, a local gradient client, momentum factor masking, and warm-up training, to address the issue of gradient redundancy in distributed training.  
This algorithm can achieve a compression ratio of 270\(\times\) to 600\(\times\) without compromising accuracy. [PERSON] et al. (2019) [8] proposed the Sparse Ternary Compression (STC) framework to compress the locality of deeply compressed Top-k gradient compression and optimal Golomb coding, effectively reducing communication costs in non-IID FL scenarios. [PERSON] et al. [24] proposed a fairness-aware gradient descent method that ensures all clients provide an equal number of updates. Additionally, they proposed a novel online learning formulation and algorithm that can determine the near-optimal communication and computational trade-off while minimizing the overall training time. This trade-off is controlled by the degree of gradient sparsity. [PERSON] et al. [25] presented the first study on the unique issues that arise when introducing sparsity at training time in FL workloads. They then proposed ZeroFL, a framework that relies on highly sparse operations to accelerate on-device training. Some studies quantified the sparse gradient based on gradient sparsification [23; 26], ensuring that non-zero element values in the updated gradient vector belonged to a preset numerical set. Subsequently, the parameter update vector could be coded based on the parameter update vector's sparsity to further reduce transmission volume. However, although the above-mentioned works significantly reduced the communication overhead, there was an obvious impact on the model performance. Moreover, privacy issues arose as they directly exposed the model updates to other entities.