Neuromorphic Candidate Ensembles¶

The NeuromorphicExplorationEnsemble and NeuromorphicExploitationEnsemble operators are grounded in spike-driven neural dynamics.

Neuromorphic Mechanisms¶

1. Poisson Spike Generation¶

Each neural population encodes input via stochastic spiking:

rates_hz = max_rate / (1 + exp(-(encoders @ x + intercepts)))
spike_raster = poisson(rates_hz * dt)

Biological basis: Cortical neurons fire Poisson-distributed spikes around a rate governed by tuning curves.
Stochasticity: Intrinsic spike-time jitter provides natural exploration noise without hand-tuned Gaussian parameters.
Energy relevance: Sparse spike codes are computationally efficient on neuromorphic hardware (Loihi, SpiNNaker).

2. Synaptic Filtering¶

Spike trains are filtered through exponential synapses (τ-dependent):

τ dS/dt = -S + spikes  →  S(t+1) = (1-α)S(t) + α*spikes(t)

where α = dt / (τ + dt).

Fast synapses (τ=5 ms, exploration): Rapid response to input changes; high-frequency passband.
Slow synapses (τ=20 ms, exploitation): Smooth, stable state evolution; attractor-like dynamics.
Biological basis: AMPA (fast), NMDA (slow), and GABA receptors have distinct timescales.

3. Neural Population Coding (NEF)¶

Candidates are decoded from time-averaged firing rates via learned decoders:

candidate = mean_spike_rate @ decoders

Basis: Neural Engineering Framework (Eliasmith & Anderson, 2003).
Emergent representation: Multi-dimensional information encoded in population vectors.
Noise resilience: Population coding naturally averages out single-neuron noise.

4. Reward-Modulated Hebbian Learning (STDP-like)¶

Decoders update on improvements using dopamine-gated plasticity:

if delta_reward > 0:
    decoders += learning_rate * delta_reward * (mean_rates outer target)

Biological basis: Reward-modulated synaptic plasticity via dopamine neurotransmitter.
Online learning: Adapts decoder weights to reinforce successful search directions.
Locus: Basal ganglia and dopaminergic midbrain (SNc/VTA).

5. Attractor Dynamics (Exploitation)¶

The exploitation ensemble maintains a slow attractor via:

Slow synaptic filtering (τ=20 ms).
Sharp tuning curves concentrated around the attractor centre.
Implicit recurrence through synaptic state persistence.

attractor(t+1) = 0.9 * attractor(t) + 0.1 * new_target

Biological basis: Persistent neural activity in prefrontal cortex and superior colliculus.
Computational benefit: Natural drift towards optimal solutions without explicit gradient information.
Hardware efficiency: Asynchronous spike events reduce power relative to continuous updates.

6. Broad vs. Sharp Tuning¶

Exploration: Random broad encoders (all dimensions equally represented).

Encoders ~ N(0, 1) / ||·||
Intercepts ~ Uniform(-1, 1)
Result: Wide receptive fields, diverse exploration directions.

Exploitation: Sharply tuned encoders concentrated around the current solution.

Encoders ~ N(0, sharp_tuning^2) / ||·|| (smaller variance)
Intercepts ~ Uniform(-0.5, 0.5) (narrow range)
Result: Narrow, aligned tuning; stable convergence.

Benchmark Comparison¶

Sphere Function (5D, 0.5 s sim time)¶

Mode	Mean Best F	Interpretation
`"trad"`	7.0e-4	Hand-crafted operators, strong baseline
`"nm_dual"`	1.8e-3	Spike stochasticity adds exploration noise
`"nm_softmix"`	1.8e-3	Blended spike populations

Note: Sphere is convex, so heuristic operators excel. Neuromorphic ensembles trade some near-optimum precision for spike-driven robustness.

Rastrigin Function (5D, 0.5 s sim time, highly multimodal)¶

Mode	Mean Best F	Interpretation
`"trad"`	1.0e+0	Heuristics struggle on multimodal landscapes
`"nm_dual"`	0.124	Spike stochasticity + STDP learning outperform
`"nm_softmix"`	0.372	Soft blending is less aggressive than hard switching

Key insight: On hard multimodal problems, spike-driven dynamics outperform tuned heuristics.

Usage¶

Dual-Ensemble Mode (`"nm_dual"` — Hard WTA Switching)¶

from nevo import NEVOptimiser

optimiser = NEVOptimiser(
    objective_function=my_function,
    bounds=(-5, 5),
    dimension=10,
    operator_mode="nm_dual",
    population_size=30,
    memory_size=15,
)
optimiser.run(time=5.0)

Soft-Mix Mode (`"nm_softmix"` — Continuous Blending)¶

optimiser = NEVOptimiser(
    objective_function=my_function,
    bounds=(-5, 5),
    dimension=10,
    operator_mode="nm_softmix",
    population_size=30,
    memory_size=15,
)
optimiser.run(time=5.0)

Constructor Parameters¶

`NeuromorphicExplorationEnsemble`¶

Parameter	Type	Default	Description
`n_neurons`	int	150	Number of LIF neurons
`tau_synapse`	float	0.005	Synaptic time constant (seconds; 5 ms)
`max_rates`	tuple	(100, 200)	Min/max peak firing rates (Hz)
`intercepts`	tuple	(-1.0, 1.0)	Neuron activation thresholds
`use_numpy_fallback`	bool	False	Use NumPy path (no Nengo simulator required)

`NeuromorphicExploitationEnsemble`¶

Parameter	Type	Default	Description
`n_neurons`	int	200	Number of LIF neurons
`tau_synapse`	float	0.020	Synaptic time constant (seconds; 20 ms)
`max_rates`	tuple	(50, 100)	Min/max peak firing rates (Hz)
`intercepts`	tuple	(-0.5, 0.5)	Neuron activation thresholds
`trust_radius`	float	0.2	Radius of the trust region in v-space
`use_numpy_fallback`	bool	False	Use NumPy path (no Nengo simulator required)

Important: Both operators require access to state["simulator"], which is injected automatically during NEVOptimiser.run(). Setting use_numpy_fallback=True removes this requirement.

References¶

Neural Engineering Framework: Eliasmith, C., & Anderson, C. H. (2003). Neural Engineering: Computation, Representation, and Dynamics in Neurobiological Systems.
Reward-Modulated Plasticity: Florian, R. V. (2007). Reinforcement learning through modulation of spike-timing-dependent synaptic plasticity.
Population Coding: Georgopoulos, A. P. (2000). Neural aspects of cognitive control.
Neuromorphic Hardware: Davies, M., et al. (2018). Loihi: A neuromorphic manycore processor with on-chip learning.