# STAKE MODEL

### **Model Overview**

NeuraCoin utilizes a stake-weighted model to ensure fair and incentivized participation within the ecosystem. Intelligence within the network is defined as a parameterized function trained over diverse datasets to minimize loss functions. The network comprises multiple peers—users, developers, freelancers—each holding a stake in NeuraCoin, recorded on a transparent digital ledger.

### **Stake Distribution and Peer Contribution**

Peers contribute to the ecosystem by submitting weight updates and interacting with other peers' functions. The collective performance is measured by a stake-weighted machine learning objective:

<figure><img src="https://3720853054-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FkBTOV2ESHByAgpfGgIBB%2Fuploads%2F799ZfNcraMmpZYWsxZui%2FScreenshot%202024-12-26%20at%201.34.39%E2%80%AFAM.png?alt=media&#x26;token=9b8336d2-1842-4775-af61-a39905c84477" alt="" width="192"><figcaption></figcaption></figure>

Where:

* Where Li​ represents the loss associated with the ith peer.
* si​ denotes the stake held by the ith peer.

#### **Peer-Ranking Mechanism**

Peers evaluate each other's contributions by using outputs from other peers as inputs to their functions, creating a dynamic and interconnected network. The ranking RRR of each peer is calculated based on the product of the weight matrix *W* and the stake vector *S*:

<figure><img src="https://3720853054-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FkBTOV2ESHByAgpfGgIBB%2Fuploads%2F2NHHbyGQ0BlctZQwmP2W%2FScreenshot%202024-12-26%20at%201.36.10%E2%80%AFAM.png?alt=media&#x26;token=0f603b8e-2077-4841-8eb5-3be3cd4dade2" alt="" width="122"><figcaption></figcaption></figure>

Subsequently, the stake is inflated proportionally to the peer rankings, ensuring that significant contributors receive greater rewards:

<figure><img src="https://3720853054-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FkBTOV2ESHByAgpfGgIBB%2Fuploads%2FM4SpINWD22tmcY6BtlkS%2FScreenshot%202024-12-26%20at%201.37.24%E2%80%AFAM.png?alt=media&#x26;token=cd37194d-89f5-408e-8117-78a4bfe41bb4" alt="" width="288"><figcaption></figcaption></figure>

Where:

* T is the inflation rate.
* ∥R∥ and ∥S∥ represent the norms of the ranking and stake vectors, respectively.

### **Incentive and Reward System**

The system incentivizes peers to contribute meaningfully by rewarding those who minimize the loss objective effectively. NeuraCoin rewards are distributed based on peer rankings, ensuring that contributors who add the most value to the network receive proportionally higher stakes.

### **Anti-Collusion Measures**

To maintain the integrity of the ranking system, NeuraCoin implements connectivity-based regularization that exponentially rewards trusted peers. This mechanism ensures resilience against collusion attempts, maintaining accurate and fair rankings even when up to 50% of the network stake is involved in collusion.
