Neural Algorithmic Reasoning for Transformers: The TransNAR Framework

In the TransNAR model, cross-attention with "glue" weights plays a crucial role in combining the language understanding capabilities of the Transformer with the robust algorithmic reasoning abilities of the pre-trained graph neural network-based NAR.

The process begins with the Transformer utilizing the NAR as a high-dimensional tool to modulate its token embeddings. The NAR module is a graph neural network pre-trained to execute various algorithmic computations on graph-based inputs. Throughout its forward pass, the Transformer can access the embeddings computed by the NAR by utilizing cross-attention with learnable "glue" weights.

The significance of using cross-attention with "glue" weights lies in the synergy it creates between the Transformer and NAR modules. By attending to the embeddings computed by the NAR, the Transformer can augment its understanding with robust algorithmic reasoning capabilities from the pre-trained NAR module. This integration enhances the reasoning abilities of the language model, particularly for out-of-distribution algorithmic tasks.

By combining the language understanding of Transformers with the robust algorithmic reasoning of NARs, TransNAR achieves significant improvements over the baseline Transformer model. It outperforms the baseline overall and on most individual algorithms, both in-distribution and out-of-distribution. This demonstrates the effectiveness of using cross-attention with "glue" weights to integrate the two modules and leverage their respective strengths in solving algorithmic tasks specified in natural language.

Neural algorithmic reasoners (NARs) face several primary challenges when dealing with natural language inputs. These challenges stem from the inherent complexity and variability of natural language, which is vastly different from the structured and well-defined inputs that NARs typically handle3. Some of the main challenges include:

1. Input formatting: NARs require rigidly structured input formatting, which is not directly applicable to problems posed in noisy forms like natural language. Mapping natural language inputs to the required algorithmic input space for NARs is a significant challenge.

2. Ambiguity: Natural language is often ambiguous, with words and phrases having multiple meanings depending on the context. This ambiguity makes it difficult for NARs to accurately interpret and process natural language inputs.

3. Language differences: Human language is diverse, with thousands of languages spoken around the world, each with its own grammar, vocabulary, and cultural nuances3. NARs need to be able to handle this diversity and understand different languages to effectively reason with natural language inputs3.

4. Data scarcity: NARs rely on large amounts of data for training. However, obtaining high-quality and diverse training data for natural language inputs can be challenging, especially for low-resource languages or specific domains3.

5. Generalization: NARs need to be able to generalize well beyond their training distribution to effectively handle natural language inputs. This includes generalizing to unseen inputs, out-of-distribution data, and real-world scenarios that may differ from the training data.

These challenges highlight the need for developing methods that can handle algorithmic reasoning in natural language while maintaining strong generalization capabilities. Approaches like TransNAR, which combines the language understanding capabilities of Transformers with the robust algorithmic reasoning abilities of pre-trained GNN-based NARs, aim to address these challenges and enhance the reasoning capabilities of language models for natural language inputs3.