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How Yuma Consensus 3 Makes Bittensor More Fair

YC3 is the next evolution of Bittensor's consensus mechanism. It optimizes emissions to reward validators for recognizing innovation quickly.

Introduction: Understanding Yuma Consensus

At the heart of every Bittensor subnet lies a fundamental challenge: how do you fairly distribute rewards for work, when that work can include a wide range of different digitial commodities or services? Bittensor approaches this as a distributed judgment problem: Validators serve as judges for the whole community, with trust in them being measured by the total stake they have been delegated. Their ratings of the performance of miners (who produce the commodities and services for each subnet) determine emissions to those miners.

But how can we keep validators honest and hard-working to make sure that they do their best effort to accurately judge the miners?

Yuma Consensus is Bittensor's solution. Validators continuously rank the quality of work done by miners in their subnet, with the rankings of validators being trusted in proportion to how much stake they have received from the community. Lazy or dishonest validators lose emissions for submitting inaccurate rankings, which is likely to cause the community to move their stake to more relabile validators. Hence the community's trust in a given validator, embodied as stake, is linked over time to the emissions earned by the miners that validator rates. Hence validators are kept honest and miners are kept working hard to produce the best commodities possible.

But how does this work in detail? Each validator submits their rankings of miners they've evaluated. The algorithm then looks at all these rankings and tries to figure out which validators are giving the most reliable, honest evaluations. Validators who consistently make good predictions about which miners other validators will eventually recognize as the best, get more influence in the system. Meanwhile, validators give stale or otherwise inaccurate evaluations lose out.

The system builds "bonds" between validators and miners over time. When a validator consistently recognizes a miner's good work, their bond with that miner strengthens, leading to better rewards for both parties. This creates a powerful incentive for validators to be diligent, honest, and forward-thinking in their evaluations.

But the earlier versions of this system had some significant flaws—particularly when it came to rewarding validators who were ahead of the curve in recognizing promising miners, and ensuring fairness for validators with smaller stakes. Yuma Consensus 3 solves these problems.

The Evolution of Consensus

The Yuma Consensus mechanism, which determines how emissions are distributed, has evolved through several iterations to address fairness concerns.

The Limitations of Earlier Versions

Yuma Consensus V1

The first version of the algorithm distributed validator rewards based on stake and consensus weight, but had significant limitations:

• Small validators faced unfair rounding issues
• Limited mechanisms for recognizing early adopters of promising miners

Yuma Consensus V2

The second version introduced a more sophisticated bonding mechanism with exponential moving averages, but still struggled with:

• Unfair penalties for small validators due to rounding errors
• Insufficient rewards for validators who recognized good miners early
• Uniform alpha parameters that didn't account for individual validator-miner relationships
• A serious bug in bond distribution, when validator participation changed dramatically.

The last and most serious of these issues was that bonds were only redistributed when validators holding at least 50% of total stake cast votes for a given miner. This created a situation where:

1. Bonds would freeze when validators stopped actively voting for a miner.
2. Historical allocations persisted for months, even when those validators were no longer evaluating the miner.
3. New evaluators were locked out until enough high-stake validators resumed voting.
4. Unfair reward distribution occurred when miners became relevant again - old bond holders received rewards despite not currently evaluating, while active evaluators received minimal bonds

Yuma Consensus V3

Yuma Consensus 3 addresses these fundamental issues with several breakthrough improvements:

Per-Bond EMA Scaling

The most significant innovation in YC3 is that each validator-miner bond pair now gets its own adjustment rate (alpha value) rather than using a single rate for all bonds. This allows individual relationships to evolve at different speeds based on performance and consensus differences.

When Liquid Alpha is enabled, the system calculates individual alpha values for each validator-miner pair using a sigmoid function. When Liquid Alpha is disabled, it falls back to a uniform alpha calculation based on the bonds moving average parameter.

Fair Scaling for All Validators

Bond values are computed using fixed-point arithmetic and then converted to u16 for storage efficiency, allowing precise fractional relationships while maintaining a 0-65535 storage scale. This fixes the disadvantages that plagued small-stake validators in previous versions.

Early Recognition Rewards

Validators who identify promising miners before they become widely recognized can now start accumulating bonds early. This creates proper incentives for proactive evaluation rather than just following the crowd.

The alpha sigmoid function calculates adjustment rates based on the difference between a validator's current weights and the network consensus. When a validator's weight for a miner differs significantly from consensus, the sigmoid determines whether to increase or decrease the bond adjustment rate, rewarding early recognition while preventing manipulation.

Understanding Bonds: The Key to Validator Rewards

Bonds are the mechanism by which validators earn rewards for their evaluation work. Think of them as shares or stakes that validators accumulate with specific miners over time.

Bonds held by a validator for a given miner, produce emissions in proportion to the strength of the bond and the emissions to the miner. See source code.

The Technical Implementation:

1. Storage: Bonds are stored as sparse matrices on a 0-65535 scale for efficiency
2. Computation: Each epoch, bonds are updated via Exponential Moving Average (EMA) based on validator weights and previous bond values
3. Rewards: Validator dividends are computed by multiplying bonds with miner incentives

Mathematical Foundation: Under the hood, bonds following the EMA equation. Here, $\Delta B_{ij}$ is the "instant bond" based on a validator's stake-weighted evaluation of a miner.

$$B_{ij}^{(t)} = \alpha \,\Delta B_{ij} + (1-\alpha)\,B_{ij}^{(t-1)}$$

However, YC3's innovation is that α can now be different for each validator-miner pair rather than uniform across all bonds. The system also applies a bonds penalty factor β when validator weights exceed consensus, helping maintain anti-fraud protection. For the complete mathematical treatment, see the main article on Yuma Consensus.

How Validators Acquire Bonds

In Yuma v2 (the problematic version): A validator needed to vote on a miner while at least 50% of validators were also voting for that miner. This meant early discoverers got locked out until big validators joined.

In Yuma v3: Validators can build bonds independently through the EMA process. When Liquid Alpha is enabled, each validator-miner pair gets its own alpha value, allowing bonds to accumulate even when others haven't recognized the miner yet.

Liquid Alpha Integration

YC3 works seamlessly with Liquid Alpha, providing additional rewards for validators who vote for miners that aren't yet receiving votes from others. This further encourages independent evaluation and early recognition. YC3 integrates with Liquid Alpha when specific conditions are met:

1. Liquid Alpha must be enabled for the subnet
2. Consensus values must exist and contain non-zero values
3. The network must have sufficient activity

When these conditions are satisfied, validators receive additional rewards for voting for miners that aren't yet receiving votes from others. If conditions aren't met, the system falls back to traditional EMA bonding.

Enhanced EMA Smoothing

The system maintains strong anti-fraud protection while providing smoother bond transitions. The adjustment rate is controlled by the bonds moving average parameter, which can be configured up to 97.5% (meaning bonds change by 2.5% per epoch toward their target values).

Technical note: The EMA calculation uses alpha = 1 - (bonds_moving_average / 1_000_000), where bonds_moving_average is typically set to 975,000, resulting in approximately 2.5% adjustment per epoch.

The Real-World Impact

YC3 creates a healthier ecosystem by encouraging validators to:

• Make independent evaluations rather than copying popular validators
• Recognize promising miners early through differentiated bond adjustment rates
• Maintain consistent evaluations while being rewarded for good prediction accuracy
• Participate meaningfully regardless of stake size through fair scaling mechanisms

This transformation means innovation and early recognition are properly rewarded, while maintaining the security and reliability that makes Bittensor networks trustworthy.

For Subnet Owners

Yuma 3 works best in subnets where validators can independently evaluate miners and benefit from early recognition of promising innovations. The system distributes dividends more fairly than previous versions, and when combined with Liquid Alpha, provides powerful tools to encourage independent evaluation.

YC3 can be toggled per subnet through governance mechanisms. The alpha parameter controls allow fine-tuning of the sigmoid steepness and adjustment ranges for your specific subnet needs.

Important considerations:

• Liquid Alpha must be enabled to get full YC3 benefits
• The system requires active consensus formation to function optimally
• Bond reset functionality is available for subnets that need it

Looking Forward

As Bittensor continues to grow, YC3 provides a solid foundation for fair and efficient consensus. The system's ability to reward early recognition while maintaining security makes it well-suited for the network's future development.

For subnet owners ready to embrace more sophisticated consensus mechanisms, YC3 combined with Liquid Alpha provides a powerful toolkit for creating equitable and efficient subnet ecosystems.

YC3 was introduced to the Subtensor Code base in PR 1593.