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PPLNs: Parametric Piecewise Linear Networks for Event-Based Temporal Modeling and Beyond
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Proposes Parametric Piecewise Linear Networks (PPLNs), which predict coefficients of a smoothed, integral-normalized piecewise linear membrane-potential function per node, and applies them to event-based steering prediction, human pose estimation, and motion deblurring.
Problem
Temporal vision inference from event camera data needs models that handle continuous timestamps; existing GPU temporal models and SNNs do not directly model the membrane potential as a function of time.
Approach
Represent each neuron's membrane potential as an input-dependent n-segment piecewise linear function of time whose slopes, intercepts and segment endpoints are predicted from the input, with temperature-based smoothing for gradient flow at endpoints and integral normalization so all coefficients receive dense gradients.
Key results
- Motion deblurring on HQF: MSE 0.152, PSNR 24.284, SSIM 0.728, improving DeblurSR by 5.6% in MSE.
- Steering prediction on DDD20: RMSE 3.15 vs 4.55 for baseline Hu (30.8% improvement overall) with similar parameter count.
- Human pose on DHP19: 3D MPJPE 73.05 mm vs 82.17 mm for reproduced Calabrese baseline (11.1% improvement).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace U-Net convolution layers with PPLN nodes | U-Net · HQF motion deblurring | MSE: 0.334 -> 0.152 | Helped |
| Replace U-Net convolution layers with PPLN nodes | U-Net · HQF motion deblurring | PSNR: 17.834 -> 24.284 | Helped |
| Replace U-Net convolution layers with PPLN nodes | U-Net · HQF motion deblurring | SSIM: 0.508 -> 0.728 | Helped |
| Replace the baseline linear component with PPLN nodes | HuMod · DDD20 dual-modal steering prediction (all) | RMSE: 3.34 ± 0.048 -> 3.15 ± 0.081 | Helped |
| Replace the baseline linear component with PPLN nodes | HuMod · DDD20 dual-modal steering prediction (all) | EVA: 0.917 ± 0.003 -> 0.926 ± 0.004 | Helped |
| Introduce PPLN layers in the prediction network | Calabrese · DHP19 human pose estimation | 3D MPJPE: 82.17 -> 73.05 | Helped |
| Use frame-only PPLN instead of the dual-modal model | PPLN steering model · DDD20 frame-only steering prediction (all) | RMSE: 3.55 ± 0.154 -> 3.16 ± 0.130 | Helped |
| Add integral normalization (ablation) | PPLN · HQF motion deblurring | MSE: 0.264 -> 0.152 | Helped |
| Add integral normalization (ablation) | PPLN · HQF motion deblurring | PSNR: 19.721 -> 24.284 | Helped |
| Add integral normalization (ablation) | PPLN · HQF motion deblurring | SSIM: 0.554 -> 0.728 | Helped |
| Add integral normalization (ablation) | PPLN · DDD20 steering prediction (all) | RMSE: 3.82 ± 0.339 -> 3.15 ± 0.081 | Helped |
| Add integral normalization (ablation) | PPLN · DDD20 steering prediction (all) | EVA: 0.897 ± 0.018 -> 0.926 ± 0.004 | Helped |
Surprising findings
- Frame-based PPLN steering model performs similarly to the dual-modal PPLN, suggesting PPLN overcomes imperfect input data.
- Authors could not reproduce baseline numbers for steering and pose tasks, reporting notably worse baseline performance than originally published.
Limitations
- Number of line segments n is a hyperparameter with no theoretical guideline for selection.
- Baseline results could not be reproduced exactly, making comparisons less certain.
- Gains in steering prediction are based on five seeds; proposed future work is a dynamic number of segments.
Experimental setup
Datasets: HQF DDD20 DHP19
Benchmarks: HQF DDD20 DHP19
Metrics: MSE PSNR SSIM RMSE EVA MPJPE
Baselines: EDI eSL-Net eSL-Net++ E-CIR DeblurSR U-Net Hu HuMod Calabrese CalabreseMod
Builds on: Kolmogorov-Arnold Networks Piecewise Linear Unit Leaky Integrate-and-Fire model U-Net
Closest papers by meaning
- A Chaotic Dynamics Framework Inspired by Dorsal Stream for Event Signal Processing (ICML 2025 · similarity 0.83)
- Leveraging Asynchronous Spiking Neural Networks for Ultra Efficient Event-Based Visual Processing (AAAI 2025 · similarity 0.83)
- Recurrent neural network dynamical systems for biological vision (NeurIPS 2024 · similarity 0.83)
- Temporal Flexibility in Spiking Neural Networks: Towards Generalization Across Time Steps and Deployment Friendliness (ICLR 2025 · similarity 0.82)
- Causal pieces: analysing and improving spiking neural networks piece by piece (NeurIPS 2026 · similarity 0.82)
- State Space Models for Event Cameras (CVPR 2024 · similarity 0.82)
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