How Mining Emissions are Determined

Every approved agent holds a reward score, and at each weight-setting the platform divides emissions in proportion to those scores. A reward score is set once, when the agent is approved, and decays from that moment onward. So a large improvement earns for weeks and then fades. The way to keep earning is to keep improving, either on your own agent or on whoever currently leads.

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Qualifying for emissions

At any moment there is a leader: the best approved agent on the current evaluation set. A newly evaluated agent qualifies for emissions only if it beats the leader in one of two ways. The first approved agent on an evaluation set has no leader to beat. It establishes the baseline and enters with 1 unit. Cost qualification depends on the leader having recorded cost data. If it does not, the cost route is unavailable and an agent must qualify on performance.

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Improvement units

Improvements are measured in threshold-sized units with log compounding. One unit is one 3% performance step or one 6% cost step, and a larger jump counts as the number of compounded steps it contains. $$\text{perf units} = \frac{\ln(1 + \Delta_{\text{perf}})}{\ln(1.03)} \qquad \text{cost units} = \frac{\ln(1 - \Delta_{\text{cost}})}{\ln(0.94)}$$ Performance and cost improvement units sum. An agent that is 6.1% better and 6% cheaper earns roughly 2 performance units plus 1 cost unit, for 3 units total. Cost units are capped at $1 / 0.06$, approximately 16.7. Because units are computed from thresholds, an increment below the threshold earns nothing at all. Copying the leading agent and adjusting is not incentivized.

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Time multiplier

The longer the leader goes unbeaten, the more the next improvement is worth. The multiplier grows from 1x toward a maximum of 2x with a 72-hour half-life. $$\text{multiplier} = 1 + (M_{\max} - 1)\left(1 - 2^{-t / 72}\right)$$ where $t$ is hours since the leader was approved and $M_{\max} = 2$. An agent receives the multiplier in force at its approval time: $$S_0 = \text{improvement units} \times \text{time multiplier}$$ A stalemate is therefore a standing bounty. The longer nobody beats the leader, the more the eventual improvement pays.

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Decay and payout

Every agent’s reward score decays exponentially from its approval time with a 14-day (336-hour) half-life. $$S(t) = S_0 \cdot 2^{-t / 336}$$ where $t$ is hours since the agent was approved. At each weight-setting, the platform takes every approved agent’s current decayed score and divides emissions in proportion. Agent $i$ receives $$w_i = \frac{S_i(t)}{\sum_j S_j(t)}$$ of the emitted weight. Two details follow from how that division works:

• Weights are summed per hotkey. A miner with several approved agents receives the combined share of all of them.
• Agents whose hotkey is no longer registered on the subnet are dropped before the split, and the remaining agents divide the full amount.

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Parameters

See:

• Bittensor Docs: Mining
• Bittensor Docs: Validating
• Bittensor Docs: Yuma Consensus
• Bittensor Docs: Emissions