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PPLNs: Parametric Piecewise Linear Networks for Event-Based Temporal Modeling and Beyond

Chen Song, Zhenxiao Liang, Bo Sun, Qixing Huang

TL;DR

Parametric Piecewise Linear Networks (PPLNs) introduce a bio-inspired temporal model for event-based vision by approximating neuron membrane potentials with a learnable, parametric piecewise-linear function $\tilde{V}_\Theta(t)$ and producing outputs via $f(\mathbf{x},t)=\sigma(\tilde{V}_\Theta(t))$. Coefficients $\Theta=\{\mathbf{m},\mathbf{b},\mathbf{s}\}$ are predicted from input $\mathbf{x}$ and timestamp $t$ is normalized within $[0,1]$, with a smoothing operator and integral normalization ($\sigma$) to ensure learnable segment boundaries and rich gradients. A convolutionally-extended version enables practical deployment, and the approach yields state-of-the-art results on motion deblurring, steering prediction, and 3D human pose estimation for both event-based and frame-based inputs. The work provides convergence theory under smoothing and demonstrates robustness through extensive ablations, highlighting PPLNs as a general, neuromorphic alternative to traditional temporal layers in vision models with broad applicability.

Abstract

We present Parametric Piecewise Linear Networks (PPLNs) for temporal vision inference. Motivated by the neuromorphic principles that regulate biological neural behaviors, PPLNs are ideal for processing data captured by event cameras, which are built to simulate neural activities in the human retina. We discuss how to represent the membrane potential of an artificial neuron by a parametric piecewise linear function with learnable coefficients. This design echoes the idea of building deep models from learnable parametric functions recently popularized by Kolmogorov-Arnold Networks (KANs). Experiments demonstrate the state-of-the-art performance of PPLNs in event-based and image-based vision applications, including steering prediction, human pose estimation, and motion deblurring. The source code of our implementation is available at https://github.com/chensong1995/PPLN.

PPLNs: Parametric Piecewise Linear Networks for Event-Based Temporal Modeling and Beyond

TL;DR

Parametric Piecewise Linear Networks (PPLNs) introduce a bio-inspired temporal model for event-based vision by approximating neuron membrane potentials with a learnable, parametric piecewise-linear function and producing outputs via . Coefficients are predicted from input and timestamp is normalized within , with a smoothing operator and integral normalization () to ensure learnable segment boundaries and rich gradients. A convolutionally-extended version enables practical deployment, and the approach yields state-of-the-art results on motion deblurring, steering prediction, and 3D human pose estimation for both event-based and frame-based inputs. The work provides convergence theory under smoothing and demonstrates robustness through extensive ablations, highlighting PPLNs as a general, neuromorphic alternative to traditional temporal layers in vision models with broad applicability.

Abstract

We present Parametric Piecewise Linear Networks (PPLNs) for temporal vision inference. Motivated by the neuromorphic principles that regulate biological neural behaviors, PPLNs are ideal for processing data captured by event cameras, which are built to simulate neural activities in the human retina. We discuss how to represent the membrane potential of an artificial neuron by a parametric piecewise linear function with learnable coefficients. This design echoes the idea of building deep models from learnable parametric functions recently popularized by Kolmogorov-Arnold Networks (KANs). Experiments demonstrate the state-of-the-art performance of PPLNs in event-based and image-based vision applications, including steering prediction, human pose estimation, and motion deblurring. The source code of our implementation is available at https://github.com/chensong1995/PPLN.
Paper Structure (30 sections, 3 theorems, 41 equations, 6 figures, 7 tables)

This paper contains 30 sections, 3 theorems, 41 equations, 6 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Method
  4. Overview
  5. Coefficient prediction
  6. Smoothing
  7. Integral normalization
  8. Supporting the convolution operation
  9. Evaluation
  10. Task I: motion deblurring
  11. Task II: steering angle prediction
  12. Task III: human pose estimation
  13. Ablation studies
  14. Conventional frame-based vision
  15. Conclusion and Future Work
  16. ...and 15 more sections

Key Result

Theorem 3.1

(Informal) Consider an underlying n-segment piecewise linear function parameterized by $\Theta^{\star} = \{\mathbf{m}^{\star},\mathbf{b}^{\star}, \mathbf{t}^{\star}\}$ as defined in (Eq:MembraneApprox). Let $(\tau_j, v_j)$, $j = 1, \dots, m$ be $m$ point samples, where $v_j = \tilde{V} _{\Theta^{\st Denote by $\Theta_T^{\star}$ the weights at which the minimum of (Eq:Smoothed:Training:Loss) is att

Figures (6)

  • Figure 1: (Left): A biological neuron has three main components: the dendrites (blue), the axon (orange, pink), and the soma (green). The dendrites are responsible for receiving external inputs. The axon transmits signals to the dendrites of other neurons through the synapses. The soma is the body of the cell and connects the dendrites to the axon. (Middle): The membrane potential, defined as the voltage difference between the interior and the exterior of the cell, regulates the neuron's behavior and can be approximately modeled by a piecewise linear function. ① When the neuron is at rest, the potential stays at a constant level $V_0$. ② An external input is received by the dendrites, causing an instantaneous perturbation to the membrane potential. ③ The perturbation is not significant enough to excite the neuron, and the potential leaks over time exponentially (i.e., linearly in the logarithmic space). ④ Another external input happens. ⑤ The input fails to excite the neuron. ⑥ A third input causes the membrane potential to exceed the threshold voltage $V_\text{th}$. The neuron becomes excited and generates a spike. ⑦ The excitement opens ion channels, and the ion flow causes a reset to the membrane potential. ⑧ After the excitement, the ion channels close again, and the potential continues to decay. ⑨ The neuron returns to the resting state, waiting for new inputs. (Right): A PPLN node. Given inputs $\{x_i\}_{i=1}^{k}$, we predict the linear coefficients $\Theta$ for the membrane potential function, including the slope, intercept, and endpoints of each line segment. The resulting parametric function $\tilde{V}_\Theta$ is then used to evaluate the neuron output at the timestamp of interest $y(x_1, \dots, x_k, t)=\sigma(\tilde{V}_\Theta(t))$, where $\sigma(\cdot)$ is the integral normalization defined in Section \ref{['Sec:Method:IntegralNormalization']}.
  • Figure 2: (a) A linear PPLN node, which maps the input $(\mathbf{x}, t)$ to output $f$. The trainable parameters are $W_m$, $W_b$, $W_b$, and $\mathbf{w}_V$. (b) A similarly structured 2D convolutional PPLN node. (c) The baseline architecture for steering angle prediction (Hu). (d) Our model. (e) The modified baseline (HuMod).
  • Figure 3: Motion deblurring visualizations. More are available in the supplementary material.
  • Figure 4: Motion deblurring visualizations on the HQF dataset.
  • Figure 5: Randomly sampled piecewise linear predictions.
  • ...and 1 more figures

Theorems & Definitions (4)

  • Theorem 3.1
  • proof
  • Proposition A.1
  • Corollary A.2