UltraLIF: Fully Differentiable Spiking Neural Networks via Ultradiscretization

Official code for the ICML 2026 paper:

UltraLIF: Fully Differentiable Spiking Neural Networks via Ultradiscretization and Max-Plus Algebra Jose Marie Antonio Miñoza. ICML 2026. Paper | arXiv | Project Page

Overview

Standard Spiking Neural Networks (SNNs) are trained with surrogate gradients that approximate the non-differentiable Heaviside spike function. UltraLIF replaces the entire neuron — membrane dynamics and spike function — with a fully differentiable formulation derived from max-plus (tropical) algebra.

The membrane update becomes a soft max-plus operation (logsumexp), parameterized by a learnable temperature ε that interpolates between hard tropical dynamics (ε→0) and linear averaging (ε→∞):

V(t+1) = LSE_ε(V(t) + log(τ),  I(t))          # UltraLIF  (temporal, 2-term)
V_i(t) = LSE_ε(V_{i-1}, V_i, V_{i+1}) + I_i   # UltraDLIF (spatial,  3-term)

No surrogate gradients. No neuromorphic hardware required.

Results at T=1 (Ultra-Low Latency)

Dataset	Best Ultra	Best Baseline	Gain
SHD	51.24% (UltraDLIF)	40.02% (FullPLIF)	+11.22pp
DVS-Gesture	60.23% (UltraPLIF)	52.27% (PLIF)	+7.96pp
N-MNIST	94.14% (UltraDLIF)	90.23% (DSpike)	+3.91pp
CIFAR-10	43.27% (UltraPLIF)	40.26% (DSpike+)	+3.01pp
Fashion-MNIST	83.02% (UltraPLIF)	82.67% (DSpike+)	+0.35pp
MNIST	95.67% (UltraDLIF)	95.58% (DSpike+)	+0.09pp

See the project page for interactive visualizations and full results.

Model Reference

Paper Name	CLI Key	Description
UltraLIF	ultratlif	Temporal, 2-term LSE, fixed τ
UltraPLIF	ultratplif	Temporal, 2-term LSE, learnable τ
UltraDLIF	ultradlif	Spatial, 3-term LSE, fixed τ
UltraDPLIF	ultradplif	Spatial, 3-term LSE, learnable τ
LIF	lif	Standard LIF (surrogate gradient)
PLIF	plif	LIF with learnable τ
DSpike	dspike	Li et al. NeurIPS 2021
DSpike+	dspike+	DSpike with learnable τ
SigmaLIF	sigmalif	Sigmoid-only ablation baseline

Installation

git clone https://github.com/JomaMinoza/UltraLIF.git
cd UltraLIF
pip install -r requirements.txt

Quick Start

# Download static datasets
python scripts/download_datasets.py --static

# Train UltraLIF (temporal) on MNIST
python experiments/train.py --model ultratlif --dataset mnist \
    --epochs 100 --hidden 64 --track-spikes

# Train UltraDLIF (spatial) on SHD
python experiments/train.py --model ultradlif --dataset shd \
    --epochs 100 --hidden 64 --timesteps 10

# Train all single-layer models on CIFAR-10
python experiments/train.py --model all --dataset cifar10 --epochs 100 --hidden 64

# ResNet18 backbone experiments
python experiments/train_resnet.py --dataset cifar10 --backbone resnet18 \
    --timesteps 1 5 10

# Epsilon ablation (Appendix B.1)
python ablations/eps_ablation.py --epochs 100 --timesteps 1 --seed 42

Python API

from ultralif import UltraLIF, SNN, get_dataset, train_model, set_seed

set_seed(42)
train_loader, test_loader, in_dim, n_cls = get_dataset('mnist')

neuron = UltraLIF(dim=256)
model = SNN(neuron, in_dim=in_dim, hid_dim=256, out_dim=n_cls)

best_acc, history, _ = train_model(
    model, train_loader, test_loader,
    epochs=100, lr=1e-3, device='cuda',
    track_spikes=True,
)
print(f"Best accuracy: {best_acc:.2%}")
print(f"Learned eps: {neuron.eps.item():.3f}")

Supported Datasets

Dataset	Type	Classes	Input dim
mnist	Static	10	784
fashion	Static	10	784
cifar10	Static	10	3072
nmnist	Neuromorphic	10	2x34x34
dvs_gesture	Neuromorphic	11	2x128x128
shd	Audio spike	20	700
ssc	Audio spike	35	700

Structure

UltraLIF/
├── ultralif/           # Python library
│   ├── neurons/        # UltraLIF, UltraDLIF, LIF, DSpike, SigmaLIF
│   ├── networks/       # SNN, DeepSNN, ConvSNN, SpikingResNet18
│   ├── datasets/       # get_dataset(), rate_encode(), set_seed()
│   └── training/       # train_model(), TeeLogger, metrics
├── experiments/
│   ├── train.py        # Main FC/Conv/ResNet training script
│   └── train_resnet.py # ResNet backbone experiments
├── ablations/
│   └── eps_ablation.py # eps ablation (Appendix B.1)
├── docs/               # Project page (GitHub Pages)
└── scripts/
    └── download_datasets.py

Citation

@inproceedings{minoza2026ultralif,
  title     = {UltraLIF: Fully Differentiable Spiking Neural Networks via Ultradiscretization and Max-Plus Algebra},
  author    = {Mi{\~n}oza, Jose Marie Antonio},
  booktitle = {International Conference on Machine Learning},
  year      = {2026},
}