End-to-End Differentiable Proving (1705.11040v2)

Abstract: We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the backward chaining algorithm as used in Prolog. Specifically, we replace symbolic unification with a differentiable computation on vector representations of symbols using a radial basis function kernel, thereby combining symbolic reasoning with learning subsymbolic vector representations. By using gradient descent, the resulting neural network can be trained to infer facts from a given incomplete knowledge base. It learns to (i) place representations of similar symbols in close proximity in a vector space, (ii) make use of such similarities to prove queries, (iii) induce logical rules, and (iv) use provided and induced logical rules for multi-hop reasoning. We demonstrate that this architecture outperforms ComplEx, a state-of-the-art neural link prediction model, on three out of four benchmark knowledge bases while at the same time inducing interpretable function-free first-order logic rules.

• The paper replaces traditional symbolic unification with a differentiable computation using an RBF kernel, enhancing learning and inference over incomplete knowledge bases.
• It recursively constructs neural networks modeled on Prolog’s backward chaining, enabling multi-hop reasoning while preserving rule interpretability.
• The approach induces human-readable logic rules and outperforms benchmarks on tasks like transitive reasoning, demonstrating its practical impact in AI.

Insightful Overview of "End-to-End Differentiable Proving"

The paper "End-to-End Differentiable Proving" by Tim Rocktäschel and Sebastian Riedel presents a novel approach to integrating neural networks with logical reasoning for automated knowledge base completion. The proposed framework, termed Neural Theorem Provers (NTPs), enables end-to-end differentiable proving by leveraging subsymbolic vector representations of symbols, akin to Prolog's backward chaining algorithm. This integration facilitates multi-hop reasoning while retaining the interpretability and flexibility of symbolic systems.

Summary of Core Contributions

1. Differentiable Unification: The core innovation in NTPs is the replacement of symbolic unification with differentiable computations using a radial basis function (RBF) kernel. This allows the model to soften rigid symbol matching into a continuous similarity measure, which is crucial for learning and generalizing from incomplete knowledge bases (KBs).
2. Neural Network Construction: By recursively constructing neural networks based on Prolog’s backward chaining, NTPs blend symbolic reasoning's recursive structure with the ability to learn dense representations. This construction retains the interpretability of symbolic rules while enabling learning through gradient descent.
3. Multi-hop Reasoning: Beyond single-step inferences typical of many link prediction models, NTPs are designed for multi-hop reasoning, allowing them to infer more complex relational patterns from KBs.
4. Rule Induction: NTPs are capable of inducing function-free first-order logic rules, which can be decoded to human-readable forms. This feature demonstrates the model's interpretive power, allowing for insights into the learned logical structures.
5. Empirical Results: The architecture outperforms existing models like ComplEx on several benchmark datasets, notably on transitive reasoning tasks, highlighting its potential in settings where relational complexity goes beyond triples.

Results and Implications

Across benchmark datasets including "Countries", "Kinship", "Nations", and "UMLS", NTPs demonstrated superior performance in settings that require complex reasoning, evidenced by metrics such as AUC-PR and Mean Reciprocal Rank (MRR). These results suggest significant practical implications for AI systems requiring deeper logical inference capabilities, particularly in domains where interpretability of learned knowledge is critical.

In future developments, potential areas of exploration include scaling NTPs for larger KBs and integrating more sophisticated symbolic reasoning algorithms. Additionally, the end-to-end differentiability of NTPs opens possibilities for merging them with other neural-symbolic learning paradigms, potentially enhancing tasks like automated theorem proving or relational understanding in natural language processing.

Conclusion

The integration of differentiable proving with neural networks posited by this paper represents a significant step in combining logical reasoning with machine learning. By endowing neural models with recursive, interpretable reasoning capabilities, NTPs bridge a gap in AI, offering tools capable of reasoning about, and learning from, complex relational data. As the field progresses, such frameworks are poised to play a transformative role in the development of AI systems that require both robust inference and interpretability.