Distilling a Neural Network Into a Soft Decision Tree (1711.09784v1)

Abstract: Deep neural networks have proved to be a very effective way to perform classification tasks. They excel when the input data is high dimensional, the relationship between the input and the output is complicated, and the number of labeled training examples is large. But it is hard to explain why a learned network makes a particular classification decision on a particular test case. This is due to their reliance on distributed hierarchical representations. If we could take the knowledge acquired by the neural net and express the same knowledge in a model that relies on hierarchical decisions instead, explaining a particular decision would be much easier. We describe a way of using a trained neural net to create a type of soft decision tree that generalizes better than one learned directly from the training data.

• The paper introduces a distillation process that transforms neural network predictions into a soft decision tree to improve model explainability.
• The methodology employs soft sigmoid decisions, a hierarchical mixture of bigots, and specialized regularization to balance tree structure.
• Experimental results on MNIST, Connect4, and Letter datasets show that the approach maintains high accuracy while offering clearer decision paths.

Distilling a Neural Network Into a Soft Decision Tree

The paper "Distilling a Neural Network Into a Soft Decision Tree," authored by Nicholas Frosst and Geoffrey Hinton, presents a novel methodology aimed at addressing the interpretability challenges posed by deep neural networks (DNNs). While DNNs demonstrate strong classification capabilities, their decision-making processes remain opaque due to distributed hierarchical representations. This work proposes an alternative through the distillation of trained neural networks into soft decision trees to improve explainability without significantly compromising performance.

Analytical Framework

The core concept introduced in the paper is the transformation of the knowledge encoded in DNNs into interpretable models using a soft decision tree framework. Soft decision trees rely on hierarchical decisions rather than hierarchical features, allowing for more straightforward interpretability. In this context, they employ a structure where each decision point uses learned filters, and each leaf node houses a static probability distribution over potential classes.

Methodology

The training process for these soft decision trees diverges from traditional, axis-aligned decision trees. It involves:

1. Soft Decisions: Utilizing sigmoid logistic functions to enable probabilistic branching at internal nodes, thus preserving some complexity for better generalization.
2. Hierarchical Mixture of Bigots: Each leaf node ("bigot") is static post-training, embodying probability distributions that do not change dynamically.
3. Distillation Process: The neural network's predictions serve as additional soft targets for the decision tree, leveraging the network's existing generalization capabilities.
4. Regularization and Optimization: Novel penalties, particularly one encouraging balanced use of tree sub-sections, further optimize learning by adjusting the decision tree's complexity based on hierarchical depth.

Experimental Results

The authors demonstrate the efficacy of their model with several datasets:

• MNIST Dataset: The distillation process resulted in a soft decision tree with a 96.76% test accuracy, intermediate between the original neural net's 99.21% and a tree trained straight from data achieving 94.45%.
• Connect4 Dataset: A significant improvement from 78.63% to 80.60% test accuracy when employing neural network-derived soft targets, outperforming previous gradient descent-trained decision tree models.
• Letter Dataset: The approach achieved an enhanced test accuracy from 78.0% for a decision tree trained on raw data to 81.0% when distilled from an ensemble of neural nets.

Implications and Future Work

The proposed method serves the dual purpose of increasing model interpretability while maintaining high classification performance. By converting DNN outputs into soft decision trees, the authors offer a model that can explain its decisions in a way that harnesses the rigor of statistical learning without succumbing completely to the neural network's complexity.

Practical implications include improved transparency in domains where model interpretability is crucial. In theory, this method bridges a critical gap between the black-box nature of neural nets and the clarity of simpler models, thus advancing discussions about responsible AI practices.

Future developments in this domain may involve refining the soft decision tree structure, integrating more advanced regularization techniques, and extending the model to handle more complex tasks beyond classification. Exploring eclectic combinations of deep learning with classical models may become a potent avenue in the ongoing quest for interpretable AI systems.