TopGQ: Fast GNN Post-Training Quantization Leveraging Topology Information

Deploying deep neural networks on resource-constrained 6G edge devices demands aggressive compression with minimal accuracy loss. Quantization-Aware Training (QAT) has emerged as a leading compression approach; however, existing mixed-precision methods typically operate at coarse layer- or channel-level granularity. These methods often rely on heuristic or search-based bit-allocation strategies, which may overlook fine-grained variability at the neuron level. We propose Neuron-Level Mixed-Precision QAT (NMP-QAT), where each neuron independently learns its own discrete precision during training. Starting from low-bit precision, NMP-QAT expands bit-width only when training signals demand it, via differentiable surrogates and straight-through estimators, while preserving a fully discrete inference graph. This adaptability extends to both weights and activations, reducing memory movement. Evaluated on telecom and non-telecom datasets across MLP and tabular foundation model architectures, NMP-QAT achieves superior compression-accuracy trade-offs over mixed-precision QAT baselines, making it well-suited for Green AI deployments at the network edge.

Multi-hop all-reduce is the de facto backbone of large model training. As the training scale increases, the network often becomes a bottleneck, motivating the reduction of the volume of transmitted data. Accordingly, recent systems have demonstrated significant acceleration of the training process using gradient quantization. However, these systems are not optimized for multi-hop aggregation, where entries are partially summed multiple times along their aggregation topology. We present DynamiQ, a quantization framework that bridges the gap between quantization best practices and multi-hop aggregation. DynamiQ introduces novel techniques to better represent partial sums, codesigned with a decompress accumulate recompress fused kernel to facilitate fast execution. We extend PyTorch DDP to support DynamiQ over NCCL P2P, and across different LLMs, tasks, and scales, we demonstrate consistent improvement of up to 34.2% over the best among state-of-the-art methods such as Omni-Reduce, THC, and emerging standards such as MXFP4, MXFP6, and MXFP8. Further, DynamiQ is the only evaluated method that consistently reaches near-baseline accuracy (e.g., 99.9% of the BF16 baseline) and does so while significantly accelerating the training.

Post-training quantization (PTQ) is widely used to reduce the memory and computational cost of large language models. Existing PTQ methods typically obtain an initial quantized model through heuristic rules or greedy optimization, and once quantization is completed the resulting integer assignments are usually treated as final. This observation motivates a complementary optimization stage within PTQ that keeps quantized weights improvable after an executable quantized model has been produced, while preserving the quantized format. We introduce ReQuant, a backpropagation-free fixed-grid refinement procedure for this stage. Agnostic to the PTQ initializer, ReQuant takes an existing quantized model as a feasible starting point and iteratively revisits its discrete weight assignments on the fixed quantization grid. Accepted updates strictly reduce the mean squared reconstruction error and remain on the original grid. In this way, ReQuant turns the initially fixed PTQ output into an iteratively optimizable discrete solution and serves as a plug-and-play post-processing stage for existing PTQ pipelines. Experiments across diverse model families, bit-widths, and downstream tasks show that ReQuant consistently improves quantized models from heterogeneous PTQ initializers, with especially large gains on simple initializers and lower bit-widths. Notably, ReQuant can refine a simple round-to-nearest initialization across multiple sweeps until it approaches or surpasses GPTAQ under the same quantization format. These results establish ReQuant as a practical complementary stage for further improving existing PTQ pipelines.