## Proposed Modifications

OpML uses a multi-phase fault-proof to ensure the accuracy of machine learning results onchain. This mechanism is similar to experimental Canon Fault Proofs from the OP stack. Both technologies use a Fault Dispute Game to allow verifiers to resolve challenges on a game tree. Within this process, we aim to expand the merklized data on the OP stack FPVM to include the state transition in the opML Multi-Phase dispute game. By doing this, we aim to potentially achieve a unified framework capable of natively processing machine learning inferences onchain. By digging a bit deeper, we intend to find out if this framework’s implementation can help with the current specs or be an alternative version to the existing specs of FPVM.

### **1. State Transition Function Modeling**

The FPVM functions as a state transition system where a function $f$ maps a pre-state $S_{pre}$ to a post-state ($S_{post}$) based on an executed instruction:
$f(S_{pre}$) $\rightarrow$ $S_{post}$

For integration:
- **Proposed Framework Modification**: Introduce an additional layer that handles complex decision trees or neural network outputs, which adjusts how the state transitions are computed, especially in handling error states or exceptions.
- Consider a modified state transition function $f'(S_{pre}, D)$ where $D$ represents data or decisions derived from opML processes, impacting the transition to $S_{post}$.

> $f'(S_{pre}, D) \rightarrow S_{post}'$

- **State Expansion**: Define a new state component that includes neural network inference results, which influences the transition process, particularly in how exceptions are handled.

### **2. Memory Management Analysis**

Given the detailed memory specifications:
- **Heap and Memory Operations**: Analyze the implications of integrating a mechanism for handling large datasets required by machine learning models directly within the memory structure of FPVM.
- Suppose $M(S)$ is the memory utilization state function. Introduce $M'(S, D)$ to handle additional data structures or caching mechanisms to optimize ML data handling.

> $M(S) \rightarrow M'(S, D)$
- Quantify changes in memory access complexity and potential performance improvements using $O$ (Big O) notation or similar complexity measures.

### **3. Syscalls and I/O Enhancements**

The proposed framework could potentially extend the `syscall` and I/O functionalities to better support ML-driven data processing:
- **Extended Syscalls for ML**: Introduce new `syscalls` specific to ML operations, such as data batching or model loading.
- **I/O Modeling**: Adjust the I/O model to handle larger streams of data efficiently, crucial for ML processes. Propose modifications like enhanced buffer management or asynchronous I/O operations.

### **4. Formal Verification and Error Analysis**

Given the complexity of ML integrations and the critical role of fault proofing:
- Model how errors in the ML phase could propagate through the system, influencing state transitions and memory states.
- Utilize formal methods to verify the correctness of the integrated system under various operational conditions, ensuring that the modifications do not introduce new vulnerabilities.

### **5. Simulation and Evaluation Metrics**

Develop simulations that mimic real-world operational conditions to evaluate the effectiveness of the proposed modifications:
- **Simulation Setup**: Create scenarios where both traditional and ML-modified FPVMs are subjected to typical and atypical loads, measuring performance metrics like throughput, error rate, and response time.
- Define specific metrics to evaluate improvements or regressions in system behavior due to the integration, such as memory efficiency, fault detection accuracy, and computational overhead.

Will be sharing more low-level implementation details and arhcitecture has find out more on it.

> _Note: This is a High level overview of how opML's multi-phase fault-proof Mechanism can be potentially leveraged to implement fault-proof framework for Op chain or Optimistic rollups that use fault-proofs. Implementing this framework would give us possible trade-offs and performance gains compared to existing OP's canon fault-proof VM. This could potentially also be a turning point where something from ML world can actually help solving a Web3 world problem and not just another quest to find a problem for an existing solution._