LIAF-Net: Leaky Integrate and Analog Fire Network for Lightweight and Efficient Spatiotemporal Information Processing

I. INTRODUCTION

• LIF-SNNs transmit only a spike or nothing at each step, limiting activation precision and often reducing performance despite their simplicity and energy efficiency.The paper notes that LIF-SNNs are used for temporal and spatiotemporal processing and supported by neuromorphic chips.Source: §I · p. 1
• ANN neurons lack LIF-like membrane accumulation, firing, and reset dynamics, while LSTM and GRU use recurrent hidden-state updates and gates that require extra connections and weights.The paper contrasts these gate mechanisms with biology-inspired threshold firing.Source: §I · p. 1
• Spike-based inputs and outputs complicate digital vision processing and ANN-layer integration, requiring spike-generation or conversion modules for analog pixels and ANN mechanisms.The cited examples include pooling, residual connections, activations, and normalization alternatives.Source: §I · pp. 1–2
• LIF-SNN accuracy can require longer temporal coding, increasing synaptic integration and computational workload, while event-driven efficiency depends on sufficient spike sparsity.The introduction notes that more than 100 time steps may be used for temporal coding and that 1% sparsity over 100 steps yields ANN-equivalent dendritic workload.Source: §I · p. 2
• LIAF-Net transmits analog activations while retaining traditional LIF temporal dynamics, and its ANN-compatible data format supports networks mixing LIAF and ANN layers.The authors frame LIAF as a spatiotemporal layer that can be used like Conv3D or ConvLSTM in a deep network.Source: §I · p. 2
• LIAF-Net achieves performance comparable to GRU and LSTM on bAbI QA and state-of-the-art results on three DVS datasets, with fewer weights and lower computational overhead than the compared networks.The DVS datasets are MNIST-DVS, CIFAR10-DVS, and DVS128 Gesture; the stated comparisons are to GRU/LSTM for bAbI and ConvLSTM/Conv3D for the DVS tasks.Source: §I · p. 2

A. Evolution from ANN and SNN models

• Unlike LIF, LIAF receives analog input and outputs analog activations; its fire signal resets membrane potential while an activation function determines output from that potential.LIAF otherwise retains LIF-like dendritic integration, threshold comparison, and membrane reset.Source: A. Evolution from ANN and SNN models · p. 2

• LIF is described by differential dynamics, while the paper uses an iterative discrete-time representation for easier inference and training.The passage identifies τ as the neuron’s timing factor and Vreset as its reset potential; firing occurs at Vth and resets the potential.Source: B. Mathematical description of the… · p. 2
• Spatial integration can use dense multiplication, convolution, or direct input without integration.The convolutional option is 2D convolution (Conv2D).Source: B. Mathematical description of the… · p. 3
• LIAF uses an analog activation instead of LIF’s fire signal while retaining membrane accumulation and threshold-based firing dynamics.The activation may be threshold-related (TR) or non-threshold-related (NTR).Source: B. Mathematical description of the… · pp. 2–3
• Vth, Vreset, α, and β may be shared across all neurons, shared by channel, or varied per neuron; non-sharing is avoided in ConvLIAF/ConvLIF to save parameter storage.Neurons within a channel share the channel-specific parameter values.Source: B. Mathematical description of the… · p. 3

Relationship to LIF

• With a Heaviside step activation, LIAF degrades to LIF.The passage defines Act(x) as the threshold test V ≥ Vth.Source: C. Model degradation · p. 3

Relationship to perceptron or convolution

• Setting α = 0 and β = 0 removes temporal information, reducing LIAF to a perceptron or Conv2D.Source: C. Model degradation · p. 3

Relationship to RNN model

• LIAF can be viewed as a higher-order RNN with more nonlinear features than traditional RNNs, and has equivalent expressional capability to LIF and ANN perceptron/convolution models.The passage attributes the higher-order view to a recurrent term involving the previous state.Source: C. Model degradation · p. 3

D. Easily integration with ANN layers

• LIAF and LSTM/GRU use a (B,T,L) interface, while ConvLIAF, Conv3D, and ConvLSTM use (B,T,H,W,L), allowing LIAF to function as a spatiotemporal layer alongside ANN layers.The tensor dimensions represent batch size, time steps, height, width, and feature maps for the 5D interface; L denotes neuron count or hidden size for the 3D interface.Source: D. Easily integration with ANN layers · pp. 3–4
• Unlike LIAF, LIF requires spike trains to represent multivalued analog inputs and may require conversion back to analog values for subsequent ANN layers.Fig. 2 describes mixed LIAF–ANN networks without spike/analog conversion; LIF communication with ANN layers requires a converter.Source: D. Easily integration with ANN layers · p. 4, Figure 2 · p. 4

• BPTT training unfolds the recurrent time domain into a 2D grid of node functions, with membrane potential as hidden state and activations as inputs.The network uses the same backpropagation rule as recurrent networks above the node level; the difference lies inside each LIAF node.Source: §III · p. 4
• Because the Dirac Delta derivative of the Heaviside step function is unsuitable for backpropagation, LIAF approximates it with a rectangle window of width set by a small positive μ.The window is 1 when |x| < μ and 0 otherwise.Source: §III · p. 4
• Derivatives for other LIAF-Net operations are straightforward and can be handled automatically by deep-learning frameworks.Source: §III · p. 4

IV. LIAF AS A LIGHTWEIGHT SPATIOTEMPORAL MODEL

• RNN uses recurrent fully connected hidden-state exchange, LSTM uses three gate calculations, and GRU uses one shared gate calculation, unlike LIAF/LIF’s gate-free network design.The paper describes these gate calculations as gFCs.Source: §IV · pp. 4–5
• DenseLIAF/DenseLIF use fire, reset, and leak as gates controlled by the cell neuron; omitting input and output gates eliminates gFCs and reduces implementation cost.Unlike LSTM and GRU, these gates consider only hidden-state information.Source: §IV · pp. 4–5
• ConvLIAF retains parameter and computation savings over ConvLSTM; ConvLSTM additionally requires a convolution for the previous hidden state, while Conv3D uses several times the multiply-adds of LIAF’s Conv2D.Source: §IV · p. 5
• LIAF can be combined with classical models in a network to balance performance and complexity.Source: §IV · p. 5

V. EFFICIENCY EVALUATION

• LIAF has the same additions and weights as LIF but slightly more multiplications; LIF can replace some matrix and reset multiplications with selection operations.The analysis excludes activation, lookup-table, selection, and comparison costs, and does not count LIF’s event-driven property because LIAF can also benefit from event-driven operation with suitable activations.Source: §V · p. 5
• LIAF and LIF use far less computation and fewer parameters than GRU and LSTM, while ConvLIAF saves computation and storage relative to ConvLSTM and Conv3D.The comparisons are summarized in the temporal- and spatiotemporal-layer complexity tables.Source: §V · p. 5, Table I · p. 6, Table II · p. 6
• ConvLIAF’s overhead is not significantly different from time-distributed Conv2D, and it shares ConvLIF’s additions and parameter count.The comparison fixes batch size at one and represents the hidden state and output as tensors of size (T, H, W, L).Source: §V · p. 5, Table II · p. 6
• Appending an 8-bit analog value to a 32-bit TrueNorth spike packet adds 20% bandwidth, while LSTM may require more internal communication or memory access despite equal output-activation size.The passage also notes that Tianjic packets can carry either an 8-bit analog value or a spike.Source: §V · p. 6

VI. PERFORMANCE EVALUATION

• The performance-evaluation section compares LIAF-Net’s temporal processing on QA tasks and spatiotemporal classification on DVS datasets.This subsection reports the temporal-model evaluation on bAbI QA tasks.Source: §VI · p. 6

A. Experiment: LIAF-Net on bAbI QA tasks

• The evaluation compares temporal models on bAbI, a 20-task question-answering dataset [42] requiring networks to retain statement information and answer questions.The setup encodes statements and questions as vectors, uses one-hot vocabulary outputs, and compares DenseLIF, DenseLIAF, GRU, LSTM, and RNN under shared input/output and training parameters.Source: A. Experiment: LIAF-Net on bAbI QA tasks · p. 6
• In the equivalent-condition comparison, LIAF is 3.3% below LSTM/GRU and 0.5% below RNN, but exceeds same-weight LIF by 3.9%.RNN has an additional fully connected layer, resulting in higher storage and computation than LIAF.Source: A. Experiment: LIAF-Net on bAbI QA tasks · p. 6
• Finetuned LIAF reaches accuracy comparable to LSTM and GRU and exceeds LIF by 4.6%.The finetuning configuration uses more epochs and a lower learning rate of 0.0005; LSTM and GRU gain only modestly under that configuration.Source: A. Experiment: LIAF-Net on bAbI QA tasks · p. 6
• LIAF/LIF may outperform LSTM/GRU on limited-support, simple-reasoning tasks, while LSTM/GRU may do better on complex relationships and multi-hop reasoning.The authors suggest the absence of gating in LIAF/LIF may explain the latter pattern.Source: A. Experiment: LIAF-Net on bAbI QA tasks · p. 6
• With 100 hidden units, LIAF uses 63.5%, 90.8%, and 87.7% fewer weights than RNN, LSTM, and GRU, respectively.Its computational overhead is 91.5% lower than LSTM and 88.8% lower than GRU.Source: A. Experiment: LIAF-Net on bAbI QA tasks · p. 6

1) Datasets and preparation:

• MNIST-DVS and CIFAR10-DVS encode light-intensity changes as events containing pixel coordinates, timestamps, and polarity.The event datasets provide temporal information beyond image-based data.Source: 1) Datasets and preparation · pp. 6–7
• Spike trains are accumulated into event frames every 5 ms, with separate channels for lightening and darkening and adjacent frames ordered chronologically.Each sample has shape (T, 128, 128, 2).Source: 1) Datasets and preparation · p. 7
• MNIST-DVS uses T = 20, cropped 40×40 frames, and scale8, while CIFAR10-DVS uses T = 10 and the full 128×128 resolution.Larger T represents more temporal information.Source: 1) Datasets and preparation · p. 7

2) Network structure:

• The VGG-like network repeats LIAF Blocks N times and Dense Blocks M times; each LIAF Block contains ConvLIAF, time-distributed layer normalization, ReLU, and average pooling.ConvLIAF uses a (3, 3) kernel with padding 1.Source: 2) Network structure · p. 8
• The selected LIAF configuration uses TR-mode activation with Channel-Sharing and Act(x) = x, while Vth, Vreset, α, and β are trained by BPTT.For the LIF-SNN comparison, LIAF Blocks are replaced with LIF Blocks containing TD-Conv2D, TD-layer-normalization, TD-AvgPooling, and DirectLIF.Source: 2) Network structure · p. 8
• Layer normalization is used to stabilize hidden-state dynamics, accelerate training and inference, and prevent overfitting; Sumlayer averages activations across time before a 10-unit softmax classifier.Sumlayer reduces the activation shape from (T, H, W, L) to (H, W, L).Source: 2) Network structure · p. 8

3) Training setup:

• For MNIST-DVS and CIFAR10-DVS classification, the network used Adam with an initial learning rate of 5e-5, divided by 5 when validation loss failed to improve for five epochs.The same network structure was used for both datasets.Source: 3) Training setup · pp. 8–9, Figure 6 · p. 9

4) Performance analysis:

• 70.4% accuracy on CIFAR10-DVS was the best result, 9.9% higher than the previous best result.The authors also report extremely high accuracy on MNIST-DVS and better event-based data analysis than LIF-SNN.Source: 4) Performance analysis · p. 9, Table VI · p. 9
• LIAF-Net’s accuracy and loss curves were smoother than LIF-SNN’s, with less overfitting, possibly because LIAF’s continuous-activation differential function is smoother than LIF’s Heaviside firing function.The reported curves cover training on MNIST-DVS and CIFAR10-DVS.Source: 4) Performance analysis · p. 9, Figure 7 · p. 10

5) Evaluating the efficiency of LIAF-Net with other spatiotemporal networks:

• The spatiotemporal model comparison used CIFAR10-DVS with shared inputs and outputs, Adam, binary cross-entropy, and a (3, 3, 3) Conv3D kernel.Initial learning rates were 5e-4 for Conv2D and 5e-5 for Conv3D and ConvLSTM; ConvLSTM used a 0.2 reduction factor after two monitoring epochs without improvement.Source: 5) Evaluating the efficiency of… · p. 9
• Conv3D- and ConvLSTM-based networks had higher training accuracy than LIAF-Net but severe overfitting, while Conv2D underperformed LIAF-Net after 30 epochs despite similar convergence speed.The authors suggest redundant weights as a possible cause of the overfitting.Source: 5) Evaluating the efficiency of… · p. 9, Figure 8 · p. 10
• LIAF-Net achieved approximate performance with 68% and 92% fewer weight parameters than Conv3D- and ConvLSTM-based networks; ConvLIAF computational overhead was 64% and 92% lower, respectively.The comparison is on CIFAR10-DVS; the authors characterize the overall result as the best performance-cost balance among the compared spatiotemporal models.Source: 5) Evaluating the efficiency of… · pp. 9–10, Table VII · p. 9

1) Dataset and preparation:

• The DVS128 Gesture Dataset contains 1,342 event-based instances of 11 hand and arm gestures recorded under three illumination conditions; this experiment used the 11-class classification task.Source: 1) Dataset and preparation · pp. 10–11
• Events were accumulated into 32 × 32 frames every 25 ms, split into two channels by pixel intensity-change polarity, and stacked chronologically into 60-frame samples.The original 128 × 128 resolution was down-sampled by one quarter; input batches had dimensions (36, 2, 32, 32, 60).Source: 1) Dataset and preparation · p. 11

2) Network structure and training setup:

• The DVS128 network used ConvLIAF and DenseLIAF blocks throughout, with optional PoolingLIAF in ConvLIAF blocks.PoolingLIAF combines a pooling layer with a DirectLIAF layer.Source: 2) Network structure and training setup · p. 11
• LIAF settings included NTR and All-Sharing configurations, Vth = 0.5, α = 0.3, β = 0, and SELU activation in DirectLIAF.For comparisons, LIAF layers were replaced by LIF layers or ConvLSTM layers; training used Adam with learning rate 1e-4 and weight decay 1e-4, with learning-rate fine-tuning.Source: 2) Network structure and training setup · p. 11

3) Performance analysis:

• 91.6% less computation overhead and 90.0% less storage were reported for ConvLIAF versus ConvLSTM, counting convolutional layers only.The comparison was restricted to convolutional-layer weights and computation to reflect the efficiency difference between LIAF and LSTM.Source: Table IX · p. 12, 3) Performance analysis · p. 12
• 97.56% accuracy was reported for LIAF-Net, 3.46% higher than both LIF-SNN and the ConvLSTM-based network on DVS128 Gesture.The comparison used the 11-class task.Source: 3) Performance analysis · pp. 11–12, Table X · p. 12

A. Rethinking of the bio-plausibility of LIAF

• LIAF-like analog action potentials may model stimulus-dependent amplitude variation observed in human cortical L2/3 pyramidal neurons, supporting the model’s biological plausibility.Source: A. Rethinking of the bio-plausibility… · p. 12

B. Artificial neuron models using analog value

• Some spiking models derive analog values from spike-train traces, while compartmental dendrites and intrinsic homeostasis also involve analog currents or normalization.Source: B. Artificial neuron models using… · p. 12
• SpArNet transmits only above-threshold analog spikes to reduce synaptic operations, unlike LIAF-Net, which trains directly on spatiotemporal data rather than converting a pretrained CNN.Source: B. Artificial neuron models using… · p. 12

C. From LIAF to SNN

• LIAF can form a pure SNN through rate or temporal coding, representing analog values as spike trains within a time step or using limited sub-intervals for quantized activations.It can also serve as an intermediate representation for converting rate-coded and temporally coded spike trains between schemes.Source: C. From LIAF to SNN · p. 12

VIII. CONCLUSION

• LIAF-Net solves real temporal and spatiotemporal tasks with higher accuracy and lower computational and storage costs than existing traditional networks.The conclusion reports these results across the performance evaluation, without specifying task-level values here.Source: §VIII · p. 12
• LIAF combines LIF dynamics with a flexible activation that eases backpropagation, leverages ANN layers and training frameworks, and enables ANN–SNN communication without coding conversion.The authors propose it as a framework for building large-scale networks.Source: §VIII · p. 12
• Because LIF is a special case of LIAF, the authors describe LIAF as a “3.5th generation” evolution of LIF SNNs that addresses their backpropagation difficulty.Source: §VIII · p. 12

1) RNN:

• Elman RNN is used as the reference, with tanh as the default σc activation.Its variables include input, hidden state, and output vectors, alongside trainable weights and biases.Source: 1) RNN · p. 14
• The RNN model excludes its second equation because a fully connected layer outside can realize it, leaving a part more similar to LIF/LIAF.Source: 1) RNN · p. 14

2) LSTM and ConvLSTM:

• LSTM and ConvLSTM define forget, input/update, and output gates, a cell-input vector, and a hidden-state vector using trainable parameters.Source: 2) LSTM and ConvLSTM · p. 14
• The configurable LSTM/ConvLSTM activations default to sigmoid for σg and tanh for σc and σh.Source: 2) LSTM and ConvLSTM · p. 14
• In LSTM and ConvLSTM, ◦ denotes the Hadamard product, while ∗ denotes matrix multiplication or convolution, respectively.Source: 2) LSTM and ConvLSTM · p. 14

3) GRU [18]:

• The GRU [18] reset gate is rt = σg(Wrxt + Urht−1 + br), and its candidate state is ˜ht = σh(Whxt + Uh(rt ◦ht−1) + bh).Source: 3) GRU [18] · p. 14
• GRU variables include update and reset gates, candidate activation, input and output vectors, and trainable weights and biases; default activations are sigmoid and tanh.Source: 3) GRU [18] · p. 14