Worth of knowledge in deep learning (2307.00712v1)

Abstract: Knowledge constitutes the accumulated understanding and experience that humans use to gain insight into the world. In deep learning, prior knowledge is essential for mitigating shortcomings of data-driven models, such as data dependence, generalization ability, and compliance with constraints. To enable efficient evaluation of the worth of knowledge, we present a framework inspired by interpretable machine learning. Through quantitative experiments, we assess the influence of data volume and estimation range on the worth of knowledge. Our findings elucidate the complex relationship between data and knowledge, including dependence, synergistic, and substitution effects. Our model-agnostic framework can be applied to a variety of common network architectures, providing a comprehensive understanding of the role of prior knowledge in deep learning models. It can also be used to improve the performance of informed machine learning, as well as distinguish improper prior knowledge.

• The paper proposes a novel Shapley-value framework to measure the contribution of prior knowledge in deep learning models.
• It uncovers complex interactions between data and rules, showing how data volume can reduce local importance while enhancing global impact in different distributions.
• The framework optimizes model training by identifying and adjusting for improper rules, improving overall predictive accuracy.

Evaluating the Worth of Knowledge in Deep Learning

This paper introduces a novel framework to assess the value of prior knowledge within deep learning systems, addressing complex relationships between data and integrated rules. The work leverages the Shapley value theory, a method rooted in game theory, to propose new quantitative measures of rule importance (RI) and full importance (FI). This theoretical framework aims to provide insights into the role of knowledge in informed machine learning models, fundamentally exploring how prior data and rules interact to enhance or diminish a model's predictive capabilities.

Core Contributions

The paper explores three fundamental questions regarding informed machine learning:

1. Evaluating the Worth of Knowledge: The authors propose a method inspired by Shapley values to quantitatively measure the impact of prior knowledge integrated into machine learning models. This approach calculates the contribution of each rule based on marginal contributions to machine learning models.
2. Relationship between Data and Rules: Through comprehensive experiments, the paper uncovers various complex interactions between data and prior rules, including dependence, synergy, and substitution effects. The authors provide empirical evidence of how increasing data volumes impact rule importance differently, depending on whether models are dealing with in-distribution or out-of-distribution scenarios.
3. Optimizing the Use of Prior Rules: The proposed framework can adjust regularization parameters during training to enhance model performance and to identify unsuitable prior rules that negatively affect the training process.

Experimental Evaluation

The paper's experimental section is thorough, using canonical physical processes modeled by explicit governing equations to test their framework. Key findings illustrate how rule importance changes depending on data volume. For instance, in in-distribution predictions, an increase in data volume led to a decreased RI, elucidating conditions under which rules have diminishing returns. Conversely, in out-distribution predictions, larger data volumes enhanced global rule importance but reduced local rule importance—highlighting the nuanced role of different rule types in various predictive contexts.

An additional dimension explored is rule interactions. The authors explore dependence, synergy, and substitution effects among rules, shedding light on the inner workings of integrated rule sets. For instance, some rules only exhibited high importance when reliant on other rules, which has practical implications for constructing robust machine learning models that can efficiently integrate domain knowledge.

Practical Implications

The ability to quantitatively assess the worth of knowledge in machine learning systems carries significant implications both theoretically and practically. Practically, the developed framework can guide the construction of more reliable and accurate informed machine learning models by optimizing the inclusion and weighting of prior knowledge. This is especially pivotal in domains where machine learning models must incorporate complex physical laws or expert knowledge.

Furthermore, the framework's ability to identify improper rules has substantial benefits. In real-world applications, erroneous rule inclusion can be detrimental to a model's performance. By flagging these adverse rules through their negative RI scores, model builders can refine algorithms, thus improving robustness and accuracy.

The insights provided also offer a foundation for future research to pivot on. The framework opens avenues for further studies into the computational efficiency of calculating rule importance and applying similar methodologies to balance interpretability with predictive performance in fields such as physics-informed machine learning.

Conclusion and Future Work

The paper presents a significant advancement in understanding and evaluating the collaboration between data and knowledge in deep learning systems. Its contributions forge an important path toward more interpretable, secure, and reliable machine learning models. Future efforts could focus on increasing computational efficiency for large-scale models and exploring the incorporation of mathematical and physical rules, such as invariants and logic rules.

As the field continues to evolve, methods to quantify and optimize the worth of incorporated knowledge will become critical in developing models that are not only accurate but also robust and interpretable. The approach offers both an academic and practical toolset for researchers and practitioners striving to balance deep learning's powerful data-driven methods with the nuanced integration of human knowledge.