Graph Compression

Creates a smaller, approximate representation by grouping nodes based on attributes (attribute summarization) or connectivity patterns (structural summarization). Unlike lossless compression, it accepts a controlled loss of detail for greater size reduction.

• Application: Ideal for agentic memory when storing episodic traces; fine-grained interaction details can be summarized into salient events.
• Output: A summary graph where supernodes may have aggregate attributes (e.g., 'total_interaction_count'), preserving the essential narrative or relational topology.

Many real-world graphs (social, citation, knowledge) follow a power-law degree distribution, where a few nodes (hubs) have very high degree. Compression schemes like BV-Byte exploit this by using different, efficient encodings for the neighbor lists of high-degree and low-degree nodes.

• Technique: Hub lists are compressed with delta encoding, while small-degree lists might be stored in full.
• Benefit: Achieves superior compression ratios by tailoring the algorithm to the specific, non-uniform graph structure.

The K²-tree is a succinct data structure that represents the adjacency matrix of a graph as a compact binary tree. It is particularly effective for very large, sparse graphs with clustering (locality).

• Mechanism: Recursively subdivides the adjacency matrix. Each subdivision is represented by a bit: '1' if the quadrant contains an edge, '0' otherwise.
• Advantage: Supports efficient neighbor and reverse neighbor queries directly on the compressed representation, which is critical for traversal in agentic reasoning over compressed knowledge bases.

Knowledge distillation is a model compression technique where a smaller 'student' model is trained to mimic a larger 'teacher' model. In a graph context, this can apply to compressing a large GNN into a smaller, faster one that approximates its predictions. The student learns from both the ground-truth labels and the softened output distributions (logits) of the teacher.

• Key Use: Deploying graph-based models on resource-constrained edge devices.
• Process: Transfer relational inductive bias from a complex to a simple model.

Quantization reduces the numerical precision of a model's parameters and activations (e.g., from 32-bit floats to 8-bit integers). For graph models, this applies to the weights of GNN layers and the stored node/edge embeddings. Post-training quantization (PTQ) and quantization-aware training (QAT) are two primary approaches, drastically reducing memory footprint and accelerating inference on supported hardware.

• Key Use: Deploying graph embedding models and GNNs in production.
• Result: 4x memory reduction for FP32 to INT8 conversion.

Pruning removes less important weights or neurons from a neural network. For Graph Neural Networks, this can involve weight pruning (removing individual parameters) or structural pruning (removing entire neurons, channels, or even graph edges). Iterative magnitude pruning is a common method, gradually sparsifying the model during training to maintain performance.

• Key Use: Creating sparse, efficient GNNs for faster inference.
• Outcome: A smaller, faster model with minimal accuracy loss.

A Bloom filter is a probabilistic, memory-efficient data structure for set membership queries. In graph systems, it can compress very large edge lists or node ID sets for fast preliminary checks, accepting a controllable false positive rate. It is often used in distributed graph databases to reduce network calls for 'non-existent' queries.

• Key Use: Approximate edge existence checks in massive graphs.
• Trade-off: Extremely compact memory use vs. possible false positives.