Interval Coding in Axon

This document explains how Axon implements the interval-based encoding and computation as defined by the STICK (Spike Time Interval Computational Kernel) model.

1. Neuron & Synapse Model

Axon uses a simplified Integrate-and-Fire neuron model, supporting three synapse types:

  • V-synapses: instantaneously modify membrane potential (excitatory w_e = V_t or inhibitory w_i = -V_t)
  • gₑ-synapses: conductance-based, model temporal integration
  • g_f-synapses: fast-gated conductance-based

Each synapse includes a configurable delay (≥ T_syn, the minimal delay) :contentReference[oaicite:1]{index=1}.

2. Interval-Based Value Encoding

Values x ∈ [0,1] are encoded in the time difference Δt between two spikes:

Δt = T_min + x · T_cod
x   = (Δt − T_min) / T_cod

where:

  • T_min: minimum time difference (e.g., 1 ms)
  • T_cod: coding interval (e.g., 10 ms)
  • Δt: time difference between two spikes

3. Interval-Based Computation

Spiking networks can be build to process these interval-encoded values. The network dynamics are governed by the synaptic weights and delays, allowing for complex computations based on the timing of spikes.

  • Value x is represented by timing between spikes Δt.
  • Spiking networks manipulate these intervals via synaptic delays, integration, and gating, executing operations like addition, multiplication, and memory.

4. Memory & Control Flow Patterns

Axon includes reusable network patterns for symbolic SNN algorithms, such as:

4.1 Volatile Memory

  • Uses an accumulator neuron (acc) to store value in membrane potential.

  • Spike-to-store encodes interval into potential; recall emits output with the same interval once.