The Tree Ensemble Layer: Differentiability meets Conditional Computation (2002.07772v2)

Abstract: Neural networks and tree ensembles are state-of-the-art learners, each with its unique statistical and computational advantages. We aim to combine these advantages by introducing a new layer for neural networks, composed of an ensemble of differentiable decision trees (a.k.a. soft trees). While differentiable trees demonstrate promising results in the literature, they are typically slow in training and inference as they do not support conditional computation. We mitigate this issue by introducing a new sparse activation function for sample routing, and implement true conditional computation by developing specialized forward and backward propagation algorithms that exploit sparsity. Our efficient algorithms pave the way for jointly training over deep and wide tree ensembles using first-order methods (e.g., SGD). Experiments on 23 classification datasets indicate over 10x speed-ups compared to the differentiable trees used in the literature and over 20x reduction in the number of parameters compared to gradient boosted trees, while maintaining competitive performance. Moreover, experiments on CIFAR, MNIST, and Fashion MNIST indicate that replacing dense layers in CNNs with our tree layer reduces the test loss by 7-53% and the number of parameters by 8x. We provide an open-source TensorFlow implementation with a Keras API.

• The paper introduces the Tree Ensemble Layer, which integrates differentiable decision trees with neural networks through joint gradient-based optimization.
• It implements a novel cubic smooth-step activation function to enable conditional computation and efficient sparsity-based backpropagation.
• Experiments on 23 datasets demonstrate significantly faster training and reduced model size, achieving up to a tenfold speed boost and an eightfold parameter reduction.

The Tree Ensemble Layer: Differentiability Meets Conditional Computation

The paper introduces a novel architectural component for machine learning models called the Tree Ensemble Layer (TEL), which endeavors to unite the statistical strengths of neural networks and decision tree ensembles. TEL integrates an ensemble of differentiable decision trees—termed soft trees—into neural network frameworks, thus enabling the joint training of these models using gradient-based optimization techniques like stochastic gradient descent (SGD).

Core Contributions

The paper presents multiple contributions to the integration and efficiency of soft decision tree ensembles in neural network architectures:

1. Differentiable Activation Function: The authors propose a new cubic smooth-step activation function for tree node routing that ensures differentiability while allowing nodes to output exact zeros and ones. This characteristic facilitates the implementation of conditional computation, where only a subset of the model architecture is activated depending on the input data.
2. Optimization Algorithms: Specialized forward and backward propagation algorithms are presented, which are optimized to exploit the sparsity introduced by the aforementioned activation function. These algorithms allow for the efficient training of large ensemble models by reducing the computational complexity associated with gradient calculations.
3. Conditional Computation: The implementation leverages conditional computation, which allows samples to utilize only a portion of the model's architecture, increasing computational efficiency during both training and inference.
4. Joint Training Capability: Unlike traditional tree training, which is generally staged or greedily optimized, TEL enables the simultaneous optimization of all tree ensemble parameters. This is facilitated through first-order optimization methods.
5. Open-Source Implementation: The authors have offered an open-source TensorFlow implementation of TEL, making it accessible to the broader research community and enabling further improvements over existing methodologies for integrating tree-based and neural network models.

Performance Analysis and Implications

Experiments conducted across 23 classification datasets demonstrate that TEL significantly accelerates training processes—achieving over ten times faster training compared to typical differentiable trees and reducing parameter count by over 20 times relative to gradient-boosted decision trees (GBDT). Moreover, when integrated into convolutional neural networks (CNNs), replacing dense layers, TEL yields a reduction in test loss by 7-53% and reduces the number of parameters by eightfold.

Theoretical and Practical Implications

The implications of this research extend both theoretically and practically within the field:

• Theoretical Advancements: The work contributes to our understanding of integrating differentiable trees within gradient-descent frameworks, highlighting the potential for new learning paradigms combining structured tree-based decisions and deep learning models.
• Practical Applications: The increase in computational efficiency and model compactness offered by TEL harbors significant potential for deployment in resource-constrained environments and applications requiring model explainability—traits inherited from decision trees.
• Future Scope: Future work might explore further optimizing the TEL architecture by leveraging sparse feature sets or integrating it with other forms of deep learning layers and architectures to enhance automatic feature extraction.

In sum, the TEL represents a substantive stride toward the amalgamation of decision tree and neural network methodologies, setting a precedent for future research focused on hybrid model architectures that harness the best aspects of both paradigms.