Furthermore, we propose an adapted embedding method to incorporate numerical awareness.

We investigated the effectiveness of Digit Embedding. We can see that the numbers in the (100090-100140) range are clustered together. Supplementary Materials for PERFOGRAPH: A Numerical A ware Program Graph Representation for Performance Optimization and Program Analysis We investigated with more ranges. Figure 3 shows the 2-d embedding of decimal numbers in the range [1.0, 10.0] and [20.0-31.0]. And the numbers with larger differences like (1.6478, 30.7010), (5.339, 30.5113) are far from Figure 3: Embedding of decimal numbers in the range [1.0, 10.0] and [20.0-31.0] 2 So, the above examples clearly demonstrate the effectiveness of Digit Embedding for generating the Please note that in this setup, the Digit Embedding is still applied.

The remarkable growth and significant success of machine learning have expanded its applications into programming languages and program analysis. However, a key challenge in adopting the latest machine learning methods is the representation of programming languages, which directly impacts the ability of machine learning methods to reason about programs. The absence of numerical awareness, aggregate data structure information, and improper way of presenting variables in previous representation works have limited their performances. To overcome the limitations and challenges of current program representations, we propose a graph-based program representation called PERFOGRAPH. PERFOGRAPH can capture numerical information and the aggregate data structure by introducing new nodes and edges. Furthermore, we propose an adapted embedding method to incorporate numerical awareness. These enhancements make PERFOGRAPH a highly flexible and scalable representation that effectively captures programs intricate dependencies and semantics. Consequently, it serves as a powerful tool for various applications such as program analysis, performance optimization, and parallelism discovery. Our experimental results demonstrate that PERFOGRAPH outperforms existing representations and sets new state-of-the-art results by reducing the error rate by 7.4% (AMD dataset) and 10% (NVIDIA dataset) in the well-known Device Mapping challenge. It also sets new state-of-the-art results in various performance optimization tasks like Parallelism Discovery and NUMA and Prefetchers Configuration prediction.