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diff --git a/chapters/05-conclusion.tex b/chapters/05-conclusion.tex index d90f15c..271c45a 100644 --- a/chapters/05-conclusion.tex +++ b/chapters/05-conclusion.tex @@ -1,4 +1,40 @@ -\chapter{Conclusion} +\chapter{Conclusion and Future Work} \label{ch:conclusion} -% This chapter provides concluding remarks and potentially directions for future work. +In this thesis, we introduced \textbf{VEIN}, a novel framework for neural network verification with +a particular focus on network equivalence checking. The key achievements of this work include: +\begin{itemize} + \item The formalization and implementation of an ONNX-to-IN translation pipeline. + \item The design of interaction rules implementing symbolic constant folding, constant + propagation, and identity elimination. + \item A soundness proof of the reduction engine, demonstrating that each graph rewriting step + preserves the semantic of the original neural network. + \item An experimental evaluation verifying the effectiveness of VEIN on multiple benchmarks + across strict, epsilon, and argmax equivalence metrics. +\end{itemize} + +While the current version of VEIN establishes a solid foundation for IN-based verification, several +limitations remain to be addressed in future research. The future roadmap focuses on performance +optimizations, modeling expressiveness and advanced interaction rules. + +\paragraph{Custom Reduction Engine} +The current reduction engine relies on a modified version of the INPLA interpreter. While +practical, it is prone to high memory overhead. A core objective of future work is to replace +INPLA with a custom reduction engine written in Rust. Implementing the engine in Rust will provide: +memory safety without garbage collection, high-performance concurrency and flexibility. + +\paragraph{Complex Agent Attributes} +Currently, interaction net agents in VEIN are limited to simple scalar attributes. This restriction +prevents the direct translation of complex operations into single agents. Future work will extend +the framework to support complex attributes, such as tensors and boundary intervals. + +\paragraph{Advanced Interaction Rules and Symbolic ReLU Pruning} +The interaction rules implemented in VEIN are currently limited to constant folding of linear +operations. Non-linear activation functions, specifically ReLUs, are passed through without +modification unless their inputs are concrete constants. To improve simplification efficiency, we +plan to implement range analysis and interval arithmetic directly within the IN, substantially +reducing the number of split constraints faced by the SMT solver. + +\paragraph{Integration with Specialized Solvers} +The current evaluation of VEIN targets the Z3 solver, the intermediate SMT-LIB representation can be +adapted to other backends like Marabou~\cite{katz2019marabou}. |