PTQ4SNN: Membrane-Aware Post-Training Quantization for Spiking Neural Networks

Summary of the Paper

This paper, PTQ4SNN: Membrane-Aware Post-Training Quantization for Spiking Neural Networks by Hui Xie, Tong Shi, Haotong Qin, Aishan Liu, Xiaode Liu, and Jinyang Guo, addresses the problem of low-bit deployment of spiking neural networks (SNNs). The authors note that SNNs enable sparse and event-driven computation, but their low-bit deployment remains incomplete because recurrent membrane states are commonly retained in floating point even after weight quantization. Quantizing these states is difficult because their distributions differ across channels and from the preceding weights, while small perturbations near the firing threshold may alter spike decisions and accumulate over time.

The authors propose PTQ4SNN, a membrane-aware post-training quantization framework that jointly quantizes weights and recurrent membrane states using only a small calibration set. The framework operates on reusable projection–LIF pairs and supports both convolutional SNNs and spike-driven Transformers without backbone retraining, keeping backbone parameters fixed and determining only the quantization variables used during inference.

Method Highlights

• Channel-wise Unified Scale Bridge. This component constrains the membrane scale as s mem,c = s w,c · 2 k c, adapting to membrane distributions while enabling shift-compatible scale conversion. Compared to direct weight-scale reuse, this allows the membrane quantization step to expand or shrink according to calibration statistics; compared to an independent membrane scale, the conversion is a power of two and implementable as a shift. The authors show that direct weight-scale reuse suffers severe clipping and that the bridge retains shift-compatible conversion while closely tracking independently calibrated observer scales.

• Mixed-Precision Bit Allocation (MPBA). This mechanism assigns 2/4/8-bit precision to membrane channels according to firing activity and quantization sensitivity under an average-bit budget. For each channel, a combined score is formed from firing rate r̂ c and quantization sensitivity ĝ c as a c = βr̂ c + γĝ c. Channels are assigned 2, 4, or 8 membrane bits by score quantiles, with the 8/4-bit boundary grid-searched on a small calibration subset and the 4/2-bit boundary determined by binary search so the element-count-weighted average membrane precision satisfies the budget. The first spiking layer, classifier-adjacent layers, and a small set of highly important channels can be protected with higher precision for stability. Although individual channels may use 2/4/8 bits, the operating point is reported as M4 because the average precision is close to 4 bits.

Main Contributions

• Introduction of a channel-wise Unified Scale Bridge for membrane-aware PTQ, adapting to weight–membrane distribution mismatch while preserving power-of-two, shift-compatible scale conversion.

• Proposal of activity- and sensitivity-aware Mixed-Precision Bit Allocation for recurrent membrane states, which assigns 2/4/8-bit precision at channel level under an element-count-weighted average-bit budget.

• Extensive experiments on diverse SNN architectures and tasks, including conventional convolutional SNNs and spike-driven Transformers for static-image classification, event-based recognition, and semantic segmentation, demonstrating that PTQ4SNN consistently preserves competitive accuracy under W4 quantization and an approximately 4-bit membrane budget.

Experimental Results

• ImageNet-1K classification. On SDT-8-768, PTQ4SNN reaches 75.16%... corresponding to only 0.74... percentage-point drop[] from [the] floating-point checkpoint[]. On Meta-SpikeFormer it reaches 78.50%, a 0.38-point drop. On the conventional convolutional SNN SEW-ResNet18, PTQ4SNN achieves 59.62% at W4/M4, outperforming direct weight-scale reuse (58.28%), GPTQ reuse (56.85%), and the layer-wise FlowQ baseline (58.30%).

• Event-based classification. On CIFAR10-DVS with SDT-2-256 at T=10, PTQ4SNN obtains 70.80% at W4/M4, limiting the drop from the floating-point checkpoint to 1.00 percentage point, versus larger drops for BRECQ (-10.10), GPTQ (-10.60), and FlowQ (-4.50).

• Semantic segmentation. On an SDT-based FPN for Pascal VOC2012, PTQ4SNN achieves 59.77 mIoU at W4/M4, only 0.67 point below the floating-point model, whereas the layer-wise FlowQ baseline reaches 49.41 mIoU, an 11.03-point drop, showing the framework transfers to dense prediction without task-specific retraining.

• Ablations. In the Unified Scale Bridge ablation on SEW-ResNet18/CIFAR-100 under W4/M4, the bridge improves Acc@1 by 1.66 points over reuse and by 0.17 points over the independent observer, while retaining shift-compatible conversion. In the MPBA ablation on SEW-ResNet18, MPBA improves Acc@1 by 0.440 points on CIFAR-10 and 0.522 points on ImageNet-1K, demonstrating channel-wise allocation uses the same average bit budget more effectively than uniform precision. A hyperparameter scan on VGG16/CIFAR-10 selected P99 with β = 0.6 (93.06%) and confirms that combining activity and sensitivity is preferable to either signal alone.

• Hardware model estimate. Using an 8×16-PE hardware model with 32-bit SRAM words for SEW-ResNet18/CIFAR-10, the mixed-precision allocation achieves 4.002-bit average non-stem precision with 0.177 normalized state-SRAM read/write energy versus 1.000 for the 32-bit M32 mode, and 0.174 for uniform M4, while packing resident membrane states into 5.282 MiB versus 30.293 MiB for M32.

Conclusion. The authors "presented PTQ4SNN, a membrane-aware PTQ framework that quantizes weights and recurrent membrane states without full-network retraining. Its channel-wise Unified Scale Bridge provides shift-compatible scale adaptation, while Mixed-Precision Bit Allocation allocates membrane precision according to channel activity and sensitivity. Results across convolutional SNNs, spike-driven Transformers, event-based recognition, and semantic segmentation support membrane states as first-class PTQ targets."

• Low-bit SNN deployment without retraining: Improved AI systems can quantize both weights and recurrent membrane states to ~4 bits using only a small calibration set, while keeping backbone parameters frozen. This makes low-power, low-memory SNN inference practical for edge devices.

• Membrane-adaptive quantization with shift-compatible scales: Improved systems use a channel-wise Unified Scale Bridge, setting membrane scale as s mem,c = s w,c · 2 k c. This adapts to the distribution mismatch between weights and membrane states without clipping, and requires only bit shifts rather than expensive multiplications during inference.

• Sensitivity- and activity-aware mixed precision: Improved systems assign 2/4/8-bit membrane precision per channel based on firing activity and quantization sensitivity, under an average-bit budget. They automatically protect critical channels, e.g., first spiking layer and classifier-adjacent layers, improving accuracy compared to uniform precision at the same average bit count.

• Stable temporal behavior: By allocating more bits to channels whose small perturbations near the firing threshold might flip spikes, the improved system prevents errors from accumulating over time steps, keeping spike decisions reliable.

• Broad architecture and task coverage: Improved systems can quantize both conventional convolutional SNNs and spike-driven Transformers, and support static-image classification, event-based recognition, and semantic segmentation without task-specific retraining.

• Significantly reduced memory and energy: The improved system packs recurrent membrane states into ~5.3 MiB instead of ~30.3 MiB and reduces normalized state-SRAM read/write energy to ~0.177, enabling deployment in memory-constrained, energy-constrained hardware while preserving accuracy.

• Demonstrated accuracy preservation: Improved systems can achieve, for example, 75.16% ImageNet-1K on SDT-8-768 at W4/M4 (0.74-point drop), 70.80% on CIFAR10-DVS (1.00-point drop), and 59.77 mIoU on Pascal VOC2012 semantic segmentation (0.67-point drop), outperforming prior PTQ methods that reuse weight scales or use layer-wise baselines.

Spiking neural networks (SNNs) enable sparse and event-driven computation, but their low-bit deployment remains incomplete because recurrent membrane states are commonly retained in floating point even after weight quantization. Quantizing these states is challenging because their distributions differ across channels and from the preceding weights, while small perturbations near the firing threshold may alter spike decisions and accumulate over time. We propose PTQ4SNN, a membrane-aware post-training quantization framework that jointly quantizes weights and recurrent membrane states using only a small calibration set. First, a channel-wise Unified Scale Bridge constrains the membrane scale as s mem,c = s w,c * 2 k c, adapting to membrane distributions while enabling shift-compatible scale conversion. Second, Mixed-Precision Bit Allocation assigns 2/4/8-bit precision to membrane channels according to firing activity and quantization sensitivity under an average-bit budget. The framework operates on reusable projection-LIF pairs and supports both convolutional SNNs and spike-driven Transformers without backbone retraining. Experiments on static and event-based classification and semantic segmentation show that PTQ4SNN effectively preserves model accuracy under W4 quantization and approximately 4-bit membrane precision.