Bit-Plane Spike Encoding for Efficient SNNs

• Bit-plane spike encoding is a method that decomposes m-bit tensors into binary bit-planes, mapping each plane to a distinct temporal step in spike trains.
• It is implemented in pure SNNs and hybrid ANN-SNN architectures to enhance diversity in spike codes and enable full surrogate-gradient backpropagation.
• Empirical results show that hybrid schemes reduce MAC operations and improve accuracy on benchmarks like CIFAR-10 and ImageNet, despite increased temporal steps.

Bit-plane spike encoding is a deterministic input and hidden-layer coding strategy for spiking neural networks (SNNs), in which discrete-valued signals (such as pixels or activation tensors) are decomposed into their binary bit-plane representations, and each bit-plane temporally mapped to a distinct step in the spike train. This technique has emerged as a key bridge between precision-limited neuromorphic hardware and high-accuracy artificial neural network (ANN) paradigms, yielding substantial efficiency improvements and supporting full surrogate-gradient backpropagation in both pure SNNs and hybrid ANN-SNN systems (Luu et al., 29 Sep 2025, Luu et al., 2024, Nhan et al., 3 Dec 2025).

1. Mathematical Formulation of Bit-Plane Spike Encoding

Given an $m$-bit integer tensor $X \in \mathbb{R}^{C \times H \times W}$ (e.g., 8-bit pixel or feature intensities), each channel at location $(x,y)$ is decomposed as: $$I_C(x,y) = \sum_{k=0}^{m-1} b_{k,C}(x,y) \, 2^k, \quad b_{k,C}(x,y) \in \{0,1\}$$ where $b_{k,C}(x,y)$ denotes the $k$-th least significant bit (LSB, $k=0$) to the most significant bit (MSB, $k=m-1$). The $k$-th bit-plane is the binary tensor: $$B^{(k)}_{C,x,y} = \left\lfloor \frac{I_C(x,y)}{2^k} \right\rfloor \bmod 2$$

For spike-train conversion, the encoding function presents the $X \in \mathbb{R}^{C \times H \times W}$0 bit-planes sequentially across $X \in \mathbb{R}^{C \times H \times W}$1 time steps such that at time $X \in \mathbb{R}^{C \times H \times W}$2: $X \in \mathbb{R}^{C \times H \times W}$3 This order plays the MSB first, progressing to the LSB last (Luu et al., 29 Sep 2025, Nhan et al., 3 Dec 2025).

2. Implementation in SNN and Hybrid ANN-SNN Architectures

Bit-plane spike encoding has been integrated into both pure SNNs and hybrid ANN-SNN architectures:

• Pure SNNs: Bit-plane decomposed input frames serve as deterministic binary spike input at each time step, optionally combined with conventional rate- or temporal-coding channels. For example, in SEW-ResNet18 backbones, input is formed by concatenating bit-plane and Poisson-rate frames, increasing spike-train diversity while avoiding model size inflation (Luu et al., 2024, Nhan et al., 3 Dec 2025).
• Hybrid ANN-SNNs: Each hybrid block combines a standard ANN sub-block (e.g., Conv+BN+ReLU) and an SNN sub-block (SpikeEncoding $X \in \mathbb{R}^{C \times H \times W}$4 Conv+BN $X \in \mathbb{R}^{C \times H \times W}$5 IF neuron), fusing their outputs via element-wise addition. Layer-wise encode-decode SNN blocks use bit-plane spike encoders together with smooth surrogate-gradient approximations for gradient flow (Luu et al., 29 Sep 2025).

Pseudocode for the bit-plane encoding process (input $X \in \mathbb{R}^{C \times H \times W}$6, bit width $X \in \mathbb{R}^{C \times H \times W}$7):

$(x,y)$8

3. Surrogate Gradient Techniques for Differentiable Bit-Plane Encoding

A primary challenge of bit-plane spike encoding is non-differentiability, both in the hard thresholding of bit-plane extraction (square-wave function) and in downstream spiking neuron Heaviside nonlinearity. Modern methods overcome these with surrogate gradient approximations:

• Encoder Surrogates: The bit extraction $X \in \mathbb{R}^{C \times H \times W}$8 is replaced in backpropagation by smooth surrogates. Notable forms are SigSine, TanhSine, and truncated Fourier series (FourierSine), which interpolate between integer values by a sharp but differentiable transition. For SigSine:

$X \in \mathbb{R}^{C \times H \times W}$9

where $(x,y)$0 is a scale hyperparameter, and $(x,y)$1 is the logistic sigmoid. In the backward pass, $(x,y)$2 is replaced by the smoothed derivative.

• Order-Aware Rescaling: Backward gradients are further rescaled by the bit order,

$(x,y)$3

strengthening gradients for high-order (MSB) planes and damping noise from LSB planes (Luu et al., 29 Sep 2025).

• Neuron Surrogates: The IF neuron's step function is replaced by arctan or similar surrogates, e.g.,

$(x,y)$4

with $(x,y)$5 in practical settings.

This dual surrogate approach allows end-to-end differentiable optimization of deep hybrid architectures (Luu et al., 29 Sep 2025, Luu et al., 2024, Nhan et al., 3 Dec 2025).

4. Extensions: Hybrid Coding Schemes and Color Model Integration

Bit-plane encoding is highly flexible and has been integrated with other temporal and rate-based coding strategies:

• Hybrid Coding: Concatenating bit-plane frames with Poisson-rate or Time-to-First-Spike (TTFS) channels along the time axis (e.g., 8-bit planes plus 10 rate steps yields 18 total input steps). The proposed “HybridEncode” function in (Nhan et al., 3 Dec 2025) efficiently merges TTFS and bit-plane channels, resulting in dual representation and improved downstream performance.
• Color Model Support: Arbitrary device- and user-oriented color spaces (e.g., RGB, CMY, YCbCr, HSL, HSV, CIE-XYZ, LAB) are compatible. Each channel in the converted color space is quantized and bit-plane encoded independently. Empirical results indicate RGB consistently provides the best mean accuracy, but certain datasets exhibit marginal gains in alternative color spaces such as HSV (Luu et al., 2024).

5. Empirical Performance and Impact

Comprehensive experiments demonstrate that bit-plane spike encoding yields measurable accuracy, efficiency, and complexity gains:

Dataset	Baseline (rate/TTFS)	Bit-plane only	Hybrid (rate/TTFS+bits)	Source
CIFAR-10	70.69/72.24	37.28	73.49 (Hybrid)	(Luu et al., 2024)
CIFAR-100	38.57/38.95	11.28	42.15	(Luu et al., 2024)
Caltech101	61.67/61.21	43.28	64.55	(Luu et al., 2024)
ImageNet (Top-1)	52.43 (ResNet18 ANN)	—	52.30 (HAS-8)	(Luu et al., 29 Sep 2025)

• Hybrid ANN-SNN (HAS-8): On ImageNet, achieves 52.30% top-1 vs 52.43% for pure ResNet18, but with half as many parameters and 36% fewer MACs. On CIFAR-10, achieves 81.58% vs 75.89% ANN and 74.60% SNN baselines (Luu et al., 29 Sep 2025).
• Standard SNNs: Across 10 image datasets, hybrid bit-plane + rate or bit-plane + TTFS always matches or exceeds performance of pure rate, pure bit-plane, or pure TTFS, with gains up to 2–11% absolute on color benchmarks and ∼1.4% on typical grayscale, without increasing parameter count (Luu et al., 2024, Nhan et al., 3 Dec 2025).
• Efficiency: Bit-plane streams use 8–9 input timesteps (vs 10+ for common rate codes) and facilitate substantial reductions in MAC operations at inference (e.g., 1.16G MACs for HAS-8-ResNet vs 1.81G for standard ResNet18) (Luu et al., 29 Sep 2025).

Ablation studies highlight the necessity of surrogate gradient rescaling—simply removing the order-aware rescaling results in accuracy drops up to 17.6% (VGG) and 61.6% (ResNet) variants (Luu et al., 29 Sep 2025).

6. Analytical Considerations and Limitations

• Information Content: Bit-plane augmentation increases the Kolmogorov complexity and mean Shannon entropy of the spike stream; the hybrid scheme yields intermediate complexity, suggesting a possible “optimal complexity” for maximum accuracy (Luu et al., 2024).
• Latency and Energy: Total inference steps increase by $(x,y)$6, slightly elevating SNN latency and energy per sample, though remaining much lower than conventional ANNs on neuromorphic platforms.
• Sensitivity to Low-Order Bits: LSB planes may encode noise rather than salient structure, and in some datasets, pure bit-plane encoding can be detrimental or less effective than hybrid variants.
• Parameterization: Smoothing degree (e.g., $(x,y)$7 in SigSine, number of Fourier terms) and bit-plane selection remain empirical; no closed-form optimality conditions have been established.
• Generalization: Existing studies focus on fixed bit widths per channel/image; adaptive region- or sample-wise bit-depth policies and extension to non-binary (multi-bit) or sparse binary encodings are cited as open research areas (Luu et al., 29 Sep 2025, Nhan et al., 3 Dec 2025).

7. Future Directions

• Adversarial Robustness: The differentiability of the surrogate-encoded bit-plane mapping opens the door to input-gradient regularization techniques for SNNs and potentially enhances adversarial robustness (Luu et al., 29 Sep 2025).
• Higher-Order Learning: Sobolev-space training and knowledge distillation using higher-order (bit-plane) derivatives are proposed as means to further close the ANN-SNN accuracy gap.
• Neuromorphic Hardware Co-Design: There is significant scope for hardware-software codesign. Efficient streaming and hardware-native bit-plane transmission could further reduce inference cost and latency (Luu et al., 29 Sep 2025).
• Adaptive and Contextual Coding: Methods to adaptively allocate bit-plane resolution in space, time, or per-sample, and to devise multi-spike temporal codes that transcend single TTFS channels, represent primary research frontiers (Nhan et al., 3 Dec 2025).
• Information-Theoretic Analysis: Systematic study of the interplay between spike-train complexity, information throughput, and network generalization. This suggests richer codes could benefit certain classes of structured or high-entropy tasks (Luu et al., 2024).

• Hybrid Layer-Wise ANN-SNN With Surrogate Spike Encoding-Decoding Structure (Luu et al., 29 Sep 2025)
• Improvement of Spiking Neural Network with Bit Planes and Color Models (Luu et al., 2024)
• Hybrid Temporal-8-Bit Spike Coding for Spiking Neural Network Surrogate Training (Nhan et al., 3 Dec 2025)