Javokhir Berdikulov / Профиль

GSM++ Algorithm
The unified graph sequence model represents a conceptual framework comprising three key stages: tokenization, local encoding, and global encoding. This method enables efficient representation and analysis of complex graph structures, which is particularly critical in financial markets. Complex market systems, encompassing numerous participants and interactions, require powerful modeling tools capable of capturing nonlinear dependencies and hidden correlations.

Tokenization plays a fundamental role in transforming a graph structure into a sequential representation suitable for sequence-based models. The primary tokenization strategies include node or edge tokenization and subgraph tokenization. The choice of tokenization method significantly impacts model effectiveness, as it determines how fully the graph’s structural information is preserved and which organizational features are considered during analysis.

Node or edge tokenization treats the graph as a sequence of individual elements, disregarding their interconnections. Preserving structural information requires additional positional or structural encoding. The main drawback of this method is its high computational complexity, as the sequence length corresponds to the number of nodes or edges, complicating model training. However, it is useful when detailed information on each system element is needed—for instance, in constructing individualized asset strategies based on microscopic characteristics. In high-frequency trading, this approach allows more precise analysis of short-term market fluctuations and the detection of abnormal trading patterns.

Subgraph tokenization reduces computational costs by representing the graph as a sequence of subgraphs, enhancing the model's ability to capture local structure. This approach is particularly useful in financial applications, such as analyzing trading patterns where subgraphs correspond to clusters of correlated assets or groups of investors. Interactions between assets often have a hidden network nature, and subgraph-based analysis helps uncover persistent market patterns, critical for portfolio management, liquidity assessment, and arbitrage strategies.

Each tokenization method has advantages and limitations, so the choice depends on the task. In some cases, hybrid approaches combining both strategies achieve a better balance between data representation fidelity and computational efficiency.

Based on these ideas, the GSM++ framework authors proposed a hierarchical tokenization algorithm, based on clustering nodes by similarity (Hierarchical Affinity Clustering, HAC).

The algorithm starts by treating each graph vertex as a separate cluster. At each step, two clusters connected by the least "expensive" edge (determined by the similarity of their encodings) are merged. This process continues until the entire graph is merged into a single cluster. The result is a hierarchical tree, with the root representing the whole graph and the leaves corresponding to the original nodes.

This approach offers two key advantages. First, it organizes nodes so that similar elements are closer together, improving graph representation in models. Second, it enables multi-level graph encoding, allowing flexible structural analysis. Two tree traversal strategies are developed: depth-first search (DFS) and breadth-first search (BFS). DFS generates node sequences reflecting their hierarchical positions. BFS produces sequences where similar nodes are adjacent.

This tokenization method preserves the graph’s local structure and works efficiently with recurrent models, especially for tasks requiring global connectivity analysis.

Additionally, a hierarchical positional encoding method is used, considering the shortest paths between nodes and their positions in the cluster hierarchy. Experiments show that this encoding significantly improves graph representation quality.

Since different nodes may require different tokenization methods depending on the graph structure and task, the Mix of Tokenization (MoT) approach was proposed. It allows each node to use the most suitable encoding method by selecting optimal tokenizers and combining their representations.

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