📊Determining Subnet Yield

There are two critical values that TaiNet’s algorithms consider when determining each subnet’s share of the total TAO emissions; Weight (W) and Stake (S). They are defined as follows:

Stake: Represents the stake of each neuron in the Bittensor network. Stake is an important concept in the Bittensor ecosystem, signifying the amount of network weight (or “stake”) each neuron holds. The stake influences a subnet’s ability to contribute to and benefit from the network, playing a crucial role in the distribution of incentives and decision-making processes.

Neurons in Bittensor refer to nodes; either subnet miners or subnet validators. When measuring emissions issued to subnets, it refers to the subnet as a single neuron.

Weight: Represents the weights assigned to each subnet in the Bittensor network. In the context of Bittensor, weights are crucial for determining the influence and interaction between subnets. Each neuron is responsible for setting its weights, which are then recorded on a digital ledger. These weights are reflective of the neuron’s assessment or judgment of other subnets in the network.The weight matrix W=[Wij] is a key component of the network’s architecture, where the ith row is set by neuron i and represents its weights towards other neurons. These weights influence the ranking and incentive mechanisms within the network.

Both W and S values can be found using Bittensor’s metagraph, so there’s no need to calculate the weight matrix for each value of i. The following code snippet solves it for us:

import bittensor as bt

subnet = bt.metagraph( netuid = 1, lite = False)

print ('subnet 1 validator stake', subnet.S )

print ('subnet 1 validator weights', subnet.W )

TaiNet is responsible for automatically running this function on a regular basis, and using the outputs to determine which subnet is currently earning the greatest share of rewards. However, the subnet earning the greatest share of rewards is not necessarily the most profitable for validation - it is a combination of selecting a high yielding subnet and ensuring that yTAO makes up a large portion of that validator’s effective stake, that yields the greatest share of yield. For academic purposes, the factors that go into the W and S values are calculated as follows:

There are four values needed to compute the stake and weight per subnet per subnet: Trust (T), Consensus (C), Rank (R), which will be used to find Emission (E).

Trust: Defined as a sum of only those stakes that set non-zero weights.

Where Wn is defined as:

Rank: Defined as the sum of weighted stake, S.

Consensus: Defined as the k-centered sigmoid of trust

Where: