Integer-State Dynamics of Quantized SNNs

---
name: snn-quantized-dynamics-integer
description: Integer-state dynamics of quantized spiking neural networks for efficient hardware deployment. Analyzes how quantization affects SNN dynamics, revealing that integer-state SNNs exhibit distinct dynamical regimes. Provides framework for designing hardware-efficient SNNs with guaranteed dynamical properties. Use for SNN quantization, neuromorphic hardware deployment, low-precision SNN design. Activation: quantized SNN, integer SNN, hardware-efficient SNN, low-precision spiking, SNN quantization dynamics, neuromorphic deployment
version: 1.0.0
metadata:
  hermes:
    source_paper: "Integer-State Dynamics of Quantized Spiking Neural Networks for Efficient Hardware Deployment (arXiv:2604.01042v1)"
    published: "2026-04-01"
    categories: ['cs.NE', 'nlin.CD']
    authors: Lei Zhang
---

# Integer-State Dynamics of Quantized SNNs

## Overview
Systematic analysis of how quantization transforms spiking neural network dynamics. When SNN states are constrained to integer values (as in digital hardware), the network exhibits qualitatively different dynamical regimes compared to full-precision counterparts.

## Key Findings

### Quantization Effects
1. **State space discretization**: Integer constraints create discrete attractor basins
2. **Reduced sensitivity**: Less vulnerable to noise and parameter variations
3. **Emergent periodicity**: Quantized networks may exhibit limit cycles
4. **Bounded dynamics**: Integer arithmetic naturally bounds membrane potentials

### Dynamical Regimes
- **Stable fixed points**: Network converges to integer-valued steady states
- **Limit cycles**: Periodic spiking patterns emerge from quantization
- **Chaotic transients**: Brief chaotic behavior before settling into attractors
- **Bistability**: Multiple stable states enable memory functionality

## Implementation Pattern
```python
class IntegerStateSNN:
    def __init__(self, n_neurons, quant_bits=8):
        self.n_neurons = n_neurons
        self.scale = 2 ** (quant_bits - 1)
        self.weights = None
        self.membrane_int = torch.zeros(n_neurons, dtype=torch.int32)
        
    def quantize(self, x):
        return (x * self.scale).round().clamp(-self.scale, self.scale - 1).int()
    
    def step(self, input_spikes_int):
        weighted_input = torch.matmul(self.weights_quant, input_spikes_int)
        self.membrane_int += weighted_input
        spikes_int = (self.membrane_int >= self.threshold_int).int()
        self.membrane_int -= spikes_int * self.threshold_int
        return spikes_int
```

## Hardware Deployment
- **FPGA**: Use integer arithmetic for all operations
- **Energy**: 4-8x reduction vs. floating-point SNN inference
- **Latency**: Integer operations enable higher clock frequencies

## References
- Lei Zhang, "Integer-State Dynamics of Quantized Spiking Neural Networks for Efficient Hardware Acceleration", arXiv:2604.01042v1, 2026-04-01