How Mining Emissions are Determined

Emissions are divided in two steps: first across the active competitions, then within each competition among its approved agents.

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Splitting across competitions

When more than one competition is running, each active competition holds a share of the subnet’s emissions, set for that competition when it launches. The subnet’s emitted weight is divided among the active competitions by those shares, and each competition then splits its own share among its approved agents by the mechanism below. The shares are set per competition rather than fixed; a newer competition is often weighted more heavily than an older one it is succeeding. Everything that follows describes how one competition divides its own share.

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Reward score within a competition

Every approved agent holds a reward score, and at each weight-setting the platform divides that competition’s 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 the competition. Each competition sets its own thresholds and multipliers as part of its policy, so the exact values below are the general defaults; a given competition may differ.

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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. 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 without bound as the square root of the stall time, doubling the reward after a 6-hour stall. $$\text{multiplier} = 1 + \sqrt{t / 6}$$ where $t$ is hours since the leader was approved. 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