Precision of 0.76 achieved by ArKrum and DP-SGD in massive testing of 10 million nodes

The ArKrum algorithm combined with Differential Private Stochastic Gradient Descent (DP-SGD) has demonstrated its operational capability in an extremely demanding environment: a distributed network reaching 10 million participating nodes. This milestone represents a significant advance in the scalability of decentralized learning systems under privacy constraints.

Details of the experimental test

The technical validation was conducted under deliberately adversarial conditions. The noise multiplier was set to 0.3, a critical parameter reflecting the balance between privacy protection and model integrity. During 20 consecutive rounds of distributed training, the system processed data from the CIFAR-10 dataset while simulating the presence of 30% malicious nodes—a significantly high proportion that mimics real-world resilience scenarios.

The simulations were implemented using Torch distributed infrastructure, allowing tens of millions of computational nodes to coordinate gradients synchronously.

Achieved performance

The final result: an accuracy of 0.76. This value shows a moderate reduction compared to the previous simulation with 1 million nodes, a phenomenon mainly attributable to the emerging complexity in coordinating such a massive scale. Despite this factor, the system demonstrated operational robustness without critical collapses, validating that ArKrum maintains its defensive capacity even under exponential coordination pressure.

Future prospects

Researchers have identified two priority directions: integrating blockchain verification to certify the integrity of training rounds, or replicating the current experiment using the MNIST dataset, an option that would validate the consistency of the algorithm’s behavior across different data domains. Both paths aim to strengthen the system’s reliability in scenarios involving multiple millions of nodes.