Supplementary Materials for Evolving Connectivity for Recurrent Spiking Neural Networks

Appendix A Detailed Experiment Settings

A.1 Hardware

All experiments were conducted on a single GPU server with the following specifications. Additionally, all efficiency experiments, including those that measure wall-clock time, were executed on a single GPU within this server.

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8x NVIDIA Titan RTX GPU (24GB VRAM)
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2x Intel(R) Xeon(R) Silver 4110 CPU
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252GB Memory

A.2 Hyperparameters

In this section, we provide the hyperparameters for our framework, Evolving Connectivity (EC), and the baselines, including Evolution Strategies (ES) and Surrogate Gradient (SG). All methods utilize the same hyperparameter set for all three locomotion tasks. We also list the settings of neural networks below.

Table 1: Hyperparameters for Evolving Connectivity (EC)

Hyperparameter	Value
Population size $N$	10240
Learning rate $\eta$	0.15
Exploration probability $\epsilon$	$10^{-3}$

Table 2: Hyperparameters for Evolution Strategies

Hyperparameter	Value	Target
Population size $N$	10240	All
Learning rate $\eta$	0.15	RSNN
	0.01	Deep RNN
Noise standard deviation $\sigma$	0.3	RSNN
	0.02	Deep RNN
Weight decay	0.1	All

Table 3: Hyperparameters for Surrogate Gradient

Proximal Policy Optimization (PPO)
Hyperparameter	Value
Batch size	2048
BPTT length	16
Learning rate $\eta$	$3\times 10^{-4}$
Clip gradient norm	0.5
Discount $\gamma$	0.99
GAE $\lambda$	0.95
PPO clip	0.2
Value loss coefficient	1.0
Entropy coefficient	$10^{-3}$
Surrogate Gradient
Surrogate function	SuperSpike
Surrogate function parameter $\beta$	10

Table 4: Settings of neural networks

Recurrent Spiking Neural Network (RSNN)
Hyperparameter	Value
Number of neurons $d_{h}$	256
Excitatory ratio	$50\%$
Simulation time per environment step	16.6 ms
Simulation timestep $\Delta t$	0.5 ms
Synaptic time constant $\tau_{syn}$	5.0 ms
Membrane time constant $\tau_{m}$	10.0 ms
Output time constant $\tau_{out}$	10.0 ms
Input membrane resistance ¹¹1Resistance is set following snn_initialization to preserve variance. $R_{in}$	$0.1\cdot\tau_{m}\sqrt{\frac{2}{d_{in}}}$
Hidden membrane resistance ¹¹1Resistance is set following snn_initialization to preserve variance. $R_{h}$	$1.0\cdot\frac{\tau_{m}}{\tau_{syn}}\sqrt{\frac{2}{d_{h}}}$
Output membrane resistance ¹¹1Resistance is set following snn_initialization to preserve variance. $R_{out}$	$5.0\cdot\tau_{out}\sqrt{\frac{2}{d_{h}}}$
Gated Recurrent Unit (GRU)
Hidden size	256
Long-short term memory (LSTM)
Hidden size	128

Appendix B License

In this work, we utilized the locomotion tasks and physics simulator from brax, as well as the JAX framework (jax). Both are released under the Apache 2.0 License.

Appendix C Source Code

Upon publication, we will release the source code and trained 1-bit RSNN models used in this paper to ensure reproducibility and facilitate further research, in line with NeurIPS’s commitment to open and reproducible research. The code and data will be made available through a public repository (e.g., GitHub, GitLab, or Bitbucket) and will include detailed documentation and instructions for use.