Self-Prediction LIF Neuron

• The paper introduces the S-LIF neuron, which augments traditional LIF dynamics with an internal prediction current from input-output history.
• It employs a surrogate gradient method to address spike non-differentiability and vanishing gradients, boosting training efficiency and stability.
• Empirical results demonstrate consistent accuracy gains across image, sequential, and reinforcement learning tasks while maintaining biological plausibility.

The Self-Prediction Enhanced LIF (S-LIF) neuron is a modification of the canonical leaky integrate-and-fire (LIF) spiking neuron that incorporates predictive coding principles by generating an internal prediction current from its input-output history. This construct augments the membrane dynamics, providing new gradient flow pathways that mitigate spike non-differentiability and vanishing gradients, yielding improvements in stability, training efficiency, and biological plausibility. The method demonstrates consistent performance enhancements across various network architectures, neuron types, and domains, including image and sequential classification as well as reinforcement learning (Huang et al., 29 Jan 2026).

1. Standard LIF Neuron Dynamics

The LIF neuron describes membrane potential evolution under synaptic input, leakage, thresholding, and reset. The continuous-time dynamics are formalized by

$\tau_m\,\frac{du(t)}{dt} = -u(t) + I_{\rm syn}(t)$

where $u(t)$ is the membrane potential, $\tau_m$ is the membrane time constant, and $I_{\rm syn}(t)$ is the synaptic input current. A spike is emitted when $u(t)$ crosses the threshold $V_{\rm th}$, producing output $s(t) = 1$ and resetting $u(t)$ to $V_{\rm reset}$. Otherwise, $s(t) = 0$.

2. Internal Prediction Current Formulation

The S-LIF neuron augments total input current with a learned prediction current $I_{\rm pred}(t)$, generated online from the neuron's own input–output history. The prediction-current state for layer $l$ at time $t$ is

$I_{\rm pred}^l[t] = \bm{m}_p^l[t-1]$

where $\bm{m}_p^l[t] \in \mathbb{R}^N$ is the internal prediction-current buffer. The update rule is

$$\bm{m}_p^l[t] = (1-\tau_p^l)\,\bm{m}_p^l[t-1] + \tau_p^l\Big(\bm{x}^{l-1}[t] - \frac{\bm{s}^l[t]}{\tau^l}\Big)$$

with $\bm{x}^{l-1}[t] = \bm{W}^l\,\bm{s}^{l-1}[t]$ as raw synaptic input, $\bm{s}^l[t]$ as the spike vector, $\tau_p^l \in (0,1)$ as a learnable update rate, and $\tau^l$ as the layer's membrane time constant. Each neuron maintains small history buffers for previous membrane potential and prediction-current state.

At each timestep, the instantaneous prediction error $(\bm{x} - \bm{s}/\tau)$ is low-pass filtered into $\bm{m}_p$ and fed back as $I_{\rm pred}$.

3. Modified Membrane Potential Update and Surrogate Gradient Approach

In discrete-time, the membrane dynamics integrate the prediction current as follows:

1. Total input current: $\bm{I}^l[t] = \bm{x}^{l-1}[t] + \bm{m}_p^l[t-1]$
2. Membrane update:

$$\bm{m}^l[t] = \Bigl(1-\frac{1}{\tau^l}\Bigr)\bm{v}^l[t-1] + \frac{1}{\tau^l}\,\bm{I}^l[t]$$

Spike emission: $\bm{s}^l[t] = H(\bm{m}^l[t] - \theta^l)$, with membrane potential reset

1. Prediction-current update:

$$\bm{m}_p^l[t] = (1-\tau_p^l)\,\bm{m}_p^l[t-1] + \tau_p^l\bigl(\bm{x}^{l-1}[t] - \frac{\bm{s}^l[t]}{\tau^l}\bigr)$$

To enable gradient-based training despite the Heaviside nonlinearity, a smooth surrogate gradient replaces $\partial H/\partial m$:

$$\frac{\partial s^l[t]}{\partial m^l[t]} \approx \sigma'\!\bigl(m^l[t]-\theta^l\bigr) = k\,\sigma\bigl(k(m-\theta^l)\bigr)\left[1-\sigma(k(m-\theta^l))\right]$$

with slope parameter $k \approx 10$.

4. Gradient Flow: Direct and Indirect Pathways

The augmented neuron introduces two new gradient propagation pathways via the prediction-current state $\bm{m}_p$:

$$\frac{\partial L}{\partial \bm{x}^{l-1}[t]} = \frac{\partial L}{\partial \bm{m}^l[t]}\frac{\partial \bm{m}^l[t]}{\partial \bm{x}^{l-1}[t]} + \frac{\partial L}{\partial \bm{m}_p^l[t]}\frac{\partial \bm{m}_p^l[t]}{\partial \bm{x}^{l-1}[t]}$$

and

$$\frac{\partial L}{\partial \bm{m}^l[t]} = \frac{\partial L}{\partial \bm{s}^l[t]}\frac{\partial s^l[t]}{\partial m^l[t]} + \frac{\partial L}{\partial \bm{m}^l[t+1]}\frac{\partial \bm{m}^l[t+1]}{\partial \bm{m}^l[t]} + \frac{\partial L}{\partial \bm{m}_p^l[t]}\frac{\partial \bm{m}_p^l[t]}{\partial \bm{s}^l[t]}\frac{\partial s^l[t]}{\partial m^l[t]}$$

The direct pathway bypasses the near-zero $\partial s/\partial m$ outside spike events. The indirect pathway modulates prediction error correction at each step via $\partial m_p/\partial s$. This dual mechanism alleviates vanishing temporal gradients and stabilizes training.

5. Biological Alignment: Dendritic Modulation and Error-Driven Plasticity

The prediction-current update functionally mimics distal dendritic modulation observed in cortical pyramidal cells, where distal dendrites carry subthreshold, top-down signals that bias membrane potential but do not directly trigger firing. The $\bm{m}_p$ term acts analogously by shifting membrane potential toward or away from threshold according to the neuron’s expected spiking. Furthermore, the update rule $\bm{m}_p \leftarrow \bm{m}_p + \tau_p (x - s/\tau)$ resembles local, calcium-mediated error-filtering driving synaptic plasticity as observed in experimental studies of NMDA spikes and dendritic signaling (Huang et al., 29 Jan 2026).

6. Implementation Specifications

Layer-wise pseudocode for S-LIF neuron integration is presented as follows:

initialize W^l, τ^l, θ^l, τ _p^l; # learnable time constants initialize v^l[0]=0, m_p^l[0]=0; for t=1 to T: # 1) compute feedforward synaptic input I_syn = W^l · s^{l-1}[t]; # 2) add self-prediction current I_total = I_syn + m_p^l[t-1]; # 3) update membrane potential m^l[t] = (1 - 1/τ^l) * v^l[t-1] + (1/τ^l) * I_total; s^l[t] = Heaviside(m^l[t] - θ^l); # forward spike v^l[t] = m^l[t] - s^l[t] * (m^l[t] - v_reset); # 4) update prediction current pred_error = I_syn - s^l[t]/τ^l; m_p^l[t] = (1 - τ_p^l) * m_p^l[t-1] + τ_p^l * pred_error; end for

Notable hyperparameters include $\tau^l \in [2,5]$, $\tau_p^l$ initialized to 0.1–0.2 (and learned), Adam learning rate $10^{-3}$, and surrogate slope $k \approx 10$. Memory overhead consists of a single additional float per neuron for $m_p$. Computationally, the scheme requires two multiplies and one add per neuron per timestep beyond the standard LIF baseline.

7. Empirical Performance Across Domains

Experimental validation demonstrates performance improvement in classification and control tasks, summarized as follows:

Task Domain	Key Targets / Benchmarks	Performance Gains
Image Classification	CIFAR-10, CIFAR-100, ImageNet-100, ImageNet-1k; ConvNet, SEW-ResNet, Spiking-ResNet	+0.3–1.0% top-1 accuracy for T=4–8
Sequential Classification	Sequential CIFAR-10 ($T=32$), various neuron types (IF, LIF, PLIF, CLIF)	+2–3% test accuracy
Reinforcement Learning	MuJoCo (Ant, HalfCheetah, Hopper, Walker2d), TD3, proxy-target & vanilla SNN	−3% (ANN baseline) → +0.7% (vanilla), +3.3% (proxy)

Gains are consistent across networks, time steps, and neuron configurations, indicating broad applicability and closing performance gaps between SNN and ANN frameworks (Huang et al., 29 Jan 2026).

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The Self-Prediction Enhanced LIF neuron thus introduces a biologically plausible, computationally minimal augmentation to standard spiking neuron models, creating continuous error-corrective pathways that improve gradient flow and task performance. The design is aligned with core neuroscientific principles, is easily implementable with negligible overhead, and substantively advances SNN training and effectiveness across practical domains.