What Can Neural Networks Reason About? (1905.13211v4)

Abstract: Neural networks have succeeded in many reasoning tasks. Empirically, these tasks require specialized network structures, e.g., Graph Neural Networks (GNNs) perform well on many such tasks, but less structured networks fail. Theoretically, there is limited understanding of why and when a network structure generalizes better than others, although they have equal expressive power. In this paper, we develop a framework to characterize which reasoning tasks a network can learn well, by studying how well its computation structure aligns with the algorithmic structure of the relevant reasoning process. We formally define this algorithmic alignment and derive a sample complexity bound that decreases with better alignment. This framework offers an explanation for the empirical success of popular reasoning models, and suggests their limitations. As an example, we unify seemingly different reasoning tasks, such as intuitive physics, visual question answering, and shortest paths, via the lens of a powerful algorithmic paradigm, dynamic programming (DP). We show that GNNs align with DP and thus are expected to solve these tasks. On several reasoning tasks, our theory is supported by empirical results.

• The paper introduces an algorithmic alignment metric to quantitatively evaluate how neural network architectures replicate reasoning algorithms with improved sample efficiency.
• The study empirically demonstrates that Graph Neural Networks naturally align with dynamic programming, outperforming Deep Sets and MLPs in tasks like shortest path computation and relational reasoning.
• The findings suggest that designing neural networks with proper algorithmic alignment can lead to more sample-efficient models and innovative reasoning architectures.

Analyzing the Theoretical Capacities of Neural Networks in Reasoning Tasks

The paper "What Can Neural Networks Reason About?" by Xu et al., provides a comprehensive theoretical framework for understanding the ability of various neural network architectures to perform reasoning tasks. Despite the empirical success of network structures like Graph Neural Networks (GNNs) in solving reasoning-based problems, from visual and text-based question answering to intuitive physics, the underlying reasons for this success remain inadequately explored. This research introduces a model to assess how well the computational framework of a neural network aligns with the algorithmic processes inherent to a reasoning task, potentially illuminating the path to better models and a deeper theoretical understanding.

Framework Development and Theoretical Insights

The authors propose a metric for "algorithmic alignment," which essentially evaluates the degree to which a neural network's architecture can efficiently replicate a task's underlying reasoning algorithm. This evaluation is predicated on the notion that better alignment equates to improved sample complexity, meaning networks that can represent an algorithm efficiently require fewer samples to generalize effectively. The framework is therefore both a measure of potential neural network efficacy and a diagnostic tool for understanding the structural limitations of network architectures.

Xu et al. show that GNNs exhibit a natural alignment with dynamic programming (DP), a common algorithmic pattern used in reasoning tasks. This alignment explains why GNNs effectively handle tasks like shortest path computation, intuitive physics prediction, and visual question answering, which can all be reformulated as instances of DP. The paper provides empirical evidence supporting this alignment through experiments on a range of reasoning tasks that reveal GNNs' superior ability to generalize compared to other architectures like Deep Sets and simple MLPs.

Empirical Validation and Results

The paper validates its theoretical insights with extensive experiments across four complex tasks: computing summary statistics, relational argmax tasks, tasks representable by dynamic programming, and solving an NP-hard subset sum problem. GNNs outperform Deep Sets and MLPs in problems where the tasks are naturally expressible through relations and dynamic programming structures. Specifically, the results highlight GNNs' ability to handle multi-step relational reasoning efficiently, supporting the hypothesis of better sample complexity with better alignment.

A notable experiment in the paper involves comparing network performance on the shortest paths task. The researchers found that GNNs—especially those with multiple iterations—closely align with the BeLLMan-Ford algorithm, a classic DP approach, leading to superior performance over MLPs. These findings underpin the theoretical propositions regarding algorithmic alignment, offering a quantitative framework to predict and analyze the generalization ability of neural networks on reasoning tasks.

Implications and Future Speculations

The insights from this paper suggest profound implications for the design of neural networks intended for reasoning tasks. By adopting structures that align well with specific algorithmic processes, researchers can develop more sample-efficient and effective neural networks. The theory supports not only current architectures like GNNs and their use in relational reasoning but also paves the way for innovative models capable of learning from complex reasoning paradigms beyond those captured by current methods.

Looking ahead, this work opens several avenues for further research, such as exploring neural networks that can leverage algorithmic alignment for tasks that lie beyond the capabilities of existing models, including those involving approximation algorithms or unknown task structures. Additionally, integrating insights on architectural design with neural architecture search might facilitate the discovery of new, more effective reasoning models. In essence, this paper lays the foundational groundwork for enhancing our understanding and design of neural networks to align more precisely with the intricate structure of reasoning algorithms.