Optimizing Neural Networks Across Axonal Propagation Delays with Human-in-the-Loop Adaptation
Optimizing Neural Networks Across Axonal Propagation Delays with Human-in-the-Loop Adaptation
Biological Foundations of Axonal Propagation Delays
In biological neural networks, the transmission of electrical signals across axons is not instantaneous.
Axonal propagation delays—ranging from 0.1 ms to 100 ms in human neurons—play a critical role in
information processing, temporal coding, and synchronization. These delays arise due to myelination,
axon diameter, and internodal distance, influencing spike-timing-dependent plasticity (STDP) and network dynamics.
Artificial neural networks (ANNs), however, often neglect these temporal constraints, relying instead on
synchronous or uniformly delayed activations. By integrating biologically plausible axonal delays into ANNs,
we unlock new optimization pathways for temporal learning tasks, such as speech recognition, motor control,
and real-time decision-making.
Modeling Axonal Delays in Artificial Systems
Mathematical Formulation
The propagation delay (Δij) between neuron i and neuron j can be modeled as:
Δij = Lij / vij
where:
- Lij: Axonal length between neurons (μm)
- vij: Conduction velocity (m/s), varying with myelination (50–120 m/s in myelinated fibers; 0.5–2 m/s in unmyelinated fibers)
Implementation in Spiking Neural Networks (SNNs)
Spiking neural networks naturally accommodate axonal delays through:
- Delay buffers: Explicit storage of spike times with dynamic adjustment.
- Synaptic filters: First-order differential equations simulating post-synaptic potential delays.
For example, the Izhikevich neuron model integrates delays via:
v' = 0.04v² + 5v + 140 - u + I
u' = a(bv - u)
if v ≥ 30 mV: v ← c, u ← u + d
Human-in-the-Loop (HITL) Adaptation
Feedback Mechanisms
Human feedback refines delay optimization through:
- Reinforcement signals: Binary or scalar rewards for temporal accuracy.
- Direct manipulation: Adjusting delay distributions via interactive visualizations.
Case Study: Real-Time Motor Control
In a prosthetic limb controller, axonal delays were tuned using HITL:
| Parameter |
Without HITL |
With HITL |
| Delay Standard Deviation |
8.2 ms |
3.1 ms |
| Task Completion Rate |
72% |
91% |
Computational Challenges and Solutions
Non-Differentiability of Delay Parameters
Unlike weights, delays are non-differentiable. Workarounds include:
- Evolutionary strategies: Genetic algorithms for delay optimization.
- Surrogate gradients: Approximating gradients for backpropagation.
Scalability in Deep Networks
Scaling delay-adjusted networks requires:
- Sparse connectivity: Prioritizing critical pathways.
- Hardware acceleration: FPGA/ASIC implementations for parallel delay computations.
Legal and Ethical Considerations
"Where silicon mimics synapse, the law must bridge mind and machine." — Adapted from AI jurisprudence literature.
Key issues include:
- Data privacy: Human feedback may contain identifiable neural patterns.
- Agency: Ensuring users retain override capabilities in HITL systems.
Future Directions
Dynamic Delay Modulation
Investigating real-time delay adjustment via:
- Neuromodulators: Simulating dopamine/serotonin effects on conduction velocity.
- Closed-loop HITL: Continuous adaptation during operation.
Cross-Species Validation
Comparative studies with:
- Cephalopods: Unmyelinated giants (e.g., squid axon delays ~25 ms).
- Mammals: Myelinated cortico-thalamic pathways (~2–5 ms delays).