# Validator

Validators are responsible for evaluating the work submitted by training nodes. Similarly, validators have to stake before the evaluation tasks, and can be rewarded upon task completion. This is essential to maintaining the quality and reliability of the FLock network.

### 0. Overview: reward drivers for validators

The reward percentage for validator depends on:

1. how close the score is to the consensus among all the validators, measured by score variance (calculated off-chain)
2. amount the validator (and its delegators) staked
3. the number of submissions that the validator validated

Specifically, the reward distribution for validators follows a two-step calculation:

### 1. Reward distribution within a single AI Arena task

Similar to reward calculation for training nodes, the rewards for all validators in the same given AI Arena task is:

$$
R\_0 \cdot \left( \gamma + (1 - 2\gamma) \cdot \frac{\sum\_{j=1}^{m} s\_j}{\sum\_{i=1}^{n} t\_i + \sum\_{j=1}^{m} s\_j} \right)
$$

Here, we assume there are 𝑛 submissions $$(𝑂1, . . . , 𝑂𝑛 )$$from $$n$$ training nodes with stakes $$(t\_1, . . . , 𝑡\_n)$$, and 𝑚 validators $$(𝑉\_1, . . . , 𝑉\_𝑚 )$$ with stakes $$(𝑠\_1, . . . , 𝑠\_𝑚 )$$. Each validator $$𝑉𝑗 (1 ≤ 𝑗 ≤ 𝑚)$$ evaluates the $$n$$ models submitted by the training nodes.  The total daily reward allocated to a task is denoted as $$R\_0$$​ and the parameter $$\gamma$$ controls the split rewards, defining the balance between fixed and stake-dependent reward components.

### 2. Reward distribution for validators

The formula for a given validator’s daily return is calculated as such:

Consider a validator' stake in the task is $$s\_v$$ and stakes delegated to validator is $$s\_d$$ i.e. $$s\_i = s\_v + \epsilon \cdot s\_d$$, in which $$\epsilon$$ refers to the effective delegation amount. Specifically, effective delegation amount adjusts how much of the delegated stake $$s\_d$$​ is actually counted (i.e., how “effective” it is) when computing validator's total stake $$si$$.  When $$\epsilon = 1$$, then the delegated stake $$s\_d$$ ​ is counted fully—delegations are treated just like the training node’s own stake. When $$\epsilon < 1$$, then the delegated stake is “discounted,” so the validator only gets a fraction of $$s\_d$$ when accounting for its total stake, and vice versa.&#x20;

$$
f\_i\cdot F \cdot (\sigma + (1-\sigma) \cdot \frac{s\_v}{s\_v+ s\_d})
$$

Specifically,

* F refers to the performance of the validation, which is calculated through off-chain consensus
* $$f\_i$$ is the rewards for all validators
* σ is the guaranteed validator return against delegators
* $$S\_v$$​ is the stake amount of this validator
* $$S\_d$$ is the stake amount delegated to this validator

### 3. Example

Let’s assume daily total rewards for all AI Arena tasks for a given day is 309,157.68. We have 1 task with 2 nodes and 3 validators.

Nodes A and B stake 3,000 and 3,500 FLOCK respectively, while validators A, B and C stake 3,000, 6,000 and 3,000 respectively. Node A also receives an additional 1,000 FLOCK from its delegators, which brings the $$t\_i$$(total stake including delegated stake) to be 4,000 for Node A. For simplicity, we assume $$\gamma$$ to be 0, and $$\epsilon$$ to be 1 in this example.

First, for this given task, total rewards for \*all\* validators are:

$$
R\_0 \times \frac{\sum\_{j=1}^m s\_j}{\sum\_{i=1}^n t\_i + \sum\_{j=1}^m s\_j}
\= 309{,}157.68 \times \frac{12000}{6500 + 12000}
\approx 200{,}534.0
$$

Then, if we assume validator A has a score of 0.472768, the the reward for \* validator A only\* is:

$$
f\_i \cdot F \cdot \Bigl(\sigma + (1 - \sigma),\tfrac{S\_v}{S\_v + S\_d}\Bigr)
\= 200{,}534 \times 0.369 \times \Bigl(0.4 + 0.6 \times \tfrac{3000}{3000 + 0}\Bigr)
;\approx;
73{,}997
$$


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