SoftMax converts unconstrained logits into a multinomial distribution. Analogously, Sinkhorn-Knopp iterations convert an unconstrained square matrix into a doubly stochastic approximation to a permutation matrix.
A differentiable network that proposes a soft permutation in response to input features is a powerful tool for optimal transport, applicable to diverse text and graph matching tasks. It enables us to featurize complex data artifacts into sets of embeddings, rather than single, fixed-length vectors, and learn to compare a `query' set against a `document' set, suitable for scoring tasks in retrieval and textual entailment.
Warming up from set-of-vector retrieval as a modified form of ColBERT, we discuss vector subset retrieval and efficient indexing, then proceed to matching problems in graphs with rich node and edge features, even if Sinkhorn-Knopp iterations may not directly apply to all of them.
Knowledge graphs (KGs) have entities (Einstein, relativity) for nodes and relations (discovered) for edges. Nodes and edges have canonical IDs, but are also known by numerous textual aliases in various languages. Aligning KGs from various languages, i.e., inferring that two entities or relations are one and the same, can help maintain a "super-KG" like
WikiData. We will describe a formulation where KG alignment is in synergy with inference of missing edges, using vector set similarity at its heart.
While hallucination by large language models (LLMs) is generally regarded as a nuisance, we have found that allowing an LLM to hallucinate a relational schema (tables, columns, foreign keys) from a natural language question, then aligning the hallucinated schema graph to the actual schema graph of the target database can improve schema retrieval, and thereby, text to SQL generation.
Moving on to classical combinatorial graph problems, such as subgraph isomorphism, graph edit distance, and maximal clique, we build new network gadgets around graph neural networks (GNNs) and Sinkhorn-Knopps networks, leading to a series of related solutions to these problems. GNNs can help bypass intractable quadratic assignment problems and replace them with transportation as approximations, induced by contextual node or edge embeddings.
We conclude with a few remarks on the ongoing evolution of architectures where text and graph encoders and decoders must interact to solve retrieval and generation tasks.
Relevant Paper
- Joint Completion and Alignment of
Multilingual Knowledge Graphs.
With Harkanwar Singh, Shubham Lohiya, Prachi Jain and Mausam.
EMNLP 2022.
- Graph Edit Distance with General Costs Using Neural Set Divergence.
With Eeshaan Jain, Indradyumna Roy, Saswat Meher and Abir De.
NeurIPS 2024.
- CRUSH4SQL:
Collective Retrieval Using Schema Hallucination For Text2SQL.
With Mayank Kothyari, Dhruva Dhingra, and Sunita Sarawagi.
EMNLP 2023.
- Locality Sensitive
Hashing in Fourier Frequency Domain For Soft Set Containment Search.
With Indradyumna Roy, Rishi Agarwal, Anirban Dasgupta,
and Abir De. NeurIPS 2023.
- Maximum Common
Subgraph Guided Graph Retrieval: Late and Early Interaction Networks.
With Indradyumna Roy and Abir De.
NeurIPS 2022.
- Interpretable
Neural Subgraph Matching for Graph Retrieval.
With Indradyumna Roy, Venkata Sai Velugoti and Abir De. AAAI 2022.