Data Encoding in Axon

The DataEncoder class is responsible for converting scalar values into inter-spike intervals (ISIs) and decoding them back. This functionality is central to how Axon implements symbolic computation using the STICK (Spike Time Interval Computational Kernel) framework.

1. Concept

In STICK-based networks, numerical values are encoded not in voltage amplitude or spike rate, but in the time difference between two spikes. This allows for:

• High temporal resolution
• Symbolic logic without rate coding
• Hardware-friendly encoding (e.g., for ADA)

2. Encoding Equation

A normalized value ( x \n [0, 1] ) is encoded as a spike interval:

Δt = Tmin + x * Tcod

where:

• ( Tmin ) is the minimum interval (e.g., 1 ms
• ( Tcod ) is the coding range (e.g., 100 ms)
• ( dt ) is the resulting inter-spike interval (ISI)

Example:

Δt = 10 + 0.4 * 100 = 50 ms

Decoding Equation

To decode a spike interval back into a value:

x = (interval - Tmin) / Tcod

where:

• interval is the time difference between two spikes. This is the inverse of the encoder.

3. DataEncoder Class

The DataEncoder class provides methods for encoding and decoding values:

class DataEncoder:
    def __init__(self, Tmin=10.0, Tcod=100.0):
        ...

    def encode_value(self, value: float) -> tuple[float, float]:
        ...

    def decode_interval(self, spiking_interval: float) -> float:
        ...

Attributes:

Integration

The DataEncoder is used during simulation and output processing:

from axon_sdk.simulator import Simulator
from axon_sdk.encoders import DataEncoder

encoder = DataEncoder(Tmin=10.0, Tcod=100.0)
spike_pair = encoder.encode_value(0.6)  # returns (0.0, 70.0)

This spike pair can then be injected into the network, and the simulator will handle the timing based on the encoded intervals.

sim.apply_input_value(value=0.6, neuron=input_neuron)

Output Decoding

interval = spike2_time - spike1_time
decoded_value = encoder.decode_interval(interval)