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Tu Pham

Publications and source records attributed to Tu Pham.

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DGNNFlow: A Streaming Dataflow Architecture for Real-Time Edge-based Dynamic GNN Inference in HL-LHC Trigger Systems

Dynamic GNN inference exhibits strong capability to model interactions over time, such as complex particle collision events in High Energy Physics (HEP) experiments at High Luminosity Large Hadron Collider (HL-LHC). With much larger scale of collision data captured in future HEP experiments to help unlocking physics discoveries and limitation in both offline compute capacity and storage, revamped trigger systems require FPGAs to run ultra-low-latency Machine Learning models with low power consumption for online filtering of useful events. Many state-of-the-art GNN accelerators relied on static graph structures, but this assumption breaks down in HL-LHC trigger systems and other edge-based dynamic GNN applications where edge embeddings can change in-place based on neighbor node embeddings during runtime. We propose DGNNFlow, a novel streaming dataflow architecture for real-time edge-based dynamic GNN inference applications (including but not limited to HL-LHC trigger systems) along with three key contributions. First, we introduce hardware enhancement for edge embedding dynamic computation. Second, we alleviate data dependencies in edge-based dynamic GNN dataflow with Node Embedding Broadcast. Third, we provide input dynamic graph construction for complete support of graphs without pre-defined edge embeddings. We deploy DGNNFlow using AMD Alveo U50 FPGA to evaluate performance at 200 MHz clock frequency. DGNNFlow achieved 2.59x-4.36x and 1.30x-2.14x speedup compared to NVIDIA RTX A6000 GPU (batch sizes 1 and 2) with 3.59x-3.70x less power consumption, achieved 2.29x-3.54x speedup with 1.93x-2.12x less power consumption compared to Intel Xeon Gold 6226R CPU. Our implementation is available on GitHub.

cs.DC

Enumeration of Golomb Rulers and Acyclic Orientations of Mixed Graphs

A \emph{Golomb ruler} is a sequence of distinct integers (the \emph{markings} of the ruler) whose pairwise differences are distinct. Golomb rulers can be traced back to additive number theory in the 1930s and have attracted recent research activities on existence problems, such as the search for \emph{optimal} Golomb rulers (those of minimal length given a fixed number of markings). Our goal is to enumerate Golomb rulers in a systematic way: we study [g_m(t) := # {\x \in \Z^{m+1} : \, 0 = x_0 < x_1 < ... < x_{m-1} < x_m = t, \text{all} x_j - x_k \text{distinct}},] the number of Golomb rulers with $m+1$ markings and length $t$. Our main result is that $g_m(t)$ is a quasipolynomial in $t$ which satisfies a combinatorial reciprocity theorem: $(-1)^{m-1} g_m(-t)$ equals the number of rulers $\x$ of length $t$ with $m+1$ markings, each counted with its \emph{Golomb multiplicity}, which measures how many combinatorially different Golomb rulers are in a small neighborhood of $\x$. Our reciprocity theorem can be interpreted in terms of certain mixed graphs associated to Golomb rulers; in this language, it is reminiscent of Stanley's reciprocity theorem for chromatic polynomials. Thus in the second part of the paper we develop an analogue of Stanley's theorem to mixed graphs, which connects their chromatic polynomials to acyclic orientations.

math.CO