Quantized Aggregation (QSGD)

QSGD replaces each 32-bit floating-point gradient component with a low-bit representation using a randomized rounding scheme. For a gradient vector v, each coordinate v_i is quantized to one of a discrete set of levels, with the probability of selecting a particular level inversely proportional to its distance from v_i. This stochastic approach ensures the quantized output is an unbiased estimator of the original gradient, preserving convergence guarantees while achieving compression ratios of up to 32× when using 1-bit quantization. The server reconstructs the aggregated update by averaging the dequantized client contributions.

In healthcare federated learning, hospitals often exchange models with millions of parameters. Transmitting full-precision gradients for a ResNet-50 model requires approximately 97 MB per round per client. QSGD with 4-bit quantization reduces this to roughly 12 MB, enabling feasible synchronization over constrained hospital network links. Key benefits include:

• Reduced communication time: Critical when coordinating across time zones
• Lower infrastructure costs: Decreased data transfer fees for cloud-hosted aggregation servers
• Improved scalability: Allows participation of resource-limited rural clinics with limited uplink bandwidth

QSGD maintains strong theoretical convergence guarantees even when clinical data across hospitals is non-IID—a common scenario where patient demographics, imaging protocols, and disease prevalence differ significantly. The stochastic quantization introduces controlled variance into the gradient estimates, which can be bounded analytically. For strongly convex objectives, QSGD achieves a convergence rate of O(1/√(T)) where T is the number of communication rounds, matching the asymptotic rate of uncompressed SGD. Practical deployments often combine QSGD with error feedback mechanisms to accumulate quantization residuals locally, further improving convergence on heterogeneous medical datasets.

QSGD naturally complements Differential Privacy (DP) mechanisms in healthcare FL pipelines. The quantization process itself introduces a form of information loss that can amplify privacy guarantees. When combined with DP-FedAvg:

• Quantization noise adds a layer of obfuscation before Gaussian noise injection
• Communication efficiency allows more frequent privacy budget accounting
• Composability: The privacy loss of quantized updates can be formally analyzed under the subsampled Gaussian mechanism This synergy is particularly valuable for cross-institutional medical imaging collaborations where both bandwidth constraints and HIPAA compliance are paramount.

Vanilla QSGD can suffer from slow convergence due to quantization variance. Error Feedback (EF) mitigates this by storing the local quantization error and adding it to the next round's gradient before compression. The implementation loop:

• Compute local gradient g_t on clinical data
• Add accumulated error e_t from previous round: g̃_t = g_t + e_t
• Quantize g̃_t using QSGD and transmit to server
• Update error buffer: e_{t+1} = g̃_t - Q(g̃_t) This ensures no gradient information is permanently lost, achieving convergence rates comparable to uncompressed FedAvg while maintaining the full compression benefits.

QSGD offers a tunable compression parameter s (number of quantization levels) that controls the bandwidth-accuracy trade-off:

• s = 1 (1-bit): Maximum compression, highest variance. Suitable for early training rounds or bandwidth-constrained edge devices
• s = 4 (2-bit): Balanced compression with moderate variance. Recommended for most cross-silo healthcare deployments
• s = 16 (4-bit): Low variance, modest compression. Preferred for fine-tuning sensitive diagnostic models where precision is critical
• s = 256 (8-bit): Minimal compression, near-lossless. Used when regulatory requirements demand exact gradient fidelity Selecting the optimal s depends on the specific clinical task, network topology, and acceptable convergence delay.