Decision Trees That Remember: Gradient-Based Learning of Recurrent Decision Trees with Memory (2502.04052v1)

Abstract: Neural architectures such as Recurrent Neural Networks (RNNs), Transformers, and State-Space Models have shown great success in handling sequential data by learning temporal dependencies. Decision Trees (DTs), on the other hand, remain a widely used class of models for structured tabular data but are typically not designed to capture sequential patterns directly. Instead, DT-based approaches for time-series data often rely on feature engineering, such as manually incorporating lag features, which can be suboptimal for capturing complex temporal dependencies. To address this limitation, we introduce ReMeDe Trees, a novel recurrent DT architecture that integrates an internal memory mechanism, similar to RNNs, to learn long-term dependencies in sequential data. Our model learns hard, axis-aligned decision rules for both output generation and state updates, optimizing them efficiently via gradient descent. We provide a proof-of-concept study on synthetic benchmarks to demonstrate the effectiveness of our approach.

• The paper introduces ReMeDe Trees that incorporate internal memory to capture long-term sequential dependencies.
• It employs gradient-based training and backpropagation through time to optimize both decision paths and memory state updates.
• Experiments on synthetic benchmarks show that ReMeDe Trees achieve 100% accuracy while preserving model interpretability.

Essay on "Decision Trees That Remember: Gradient-Based Learning of Recurrent Decision Trees with Memory"

The paper "Decision Trees That Remember: Gradient-Based Learning of Recurrent Decision Trees with Memory" introduces a novel approach to incorporating recurrence in decision tree (DT) architectures, allowing them to handle sequential data with temporal dependencies. This work seeks to bridge the gap between the capabilities of neural networks, such as Recurrent Neural Networks (RNNs) and Long Short-Term Memory (LSTM) networks, which excel at learning from sequences due to their inherent memory mechanisms, and decision trees, which are traditionally limited to structured tabular data.

ReMeDe Trees: A Novel Architecture

The core innovation presented in this paper is the Recurrent Memory Decision (ReMeDe) Trees, which integrates an internal memory into the decision tree structure. This internal memory is designed to capture and utilize long-term dependencies much like an RNN, but with the interpretability and simplicity inherent to decision trees. ReMeDe Trees use axis-aligned decision rules and optimize these via gradient descent. High computational efficiency and the ability to capture complex temporal patterns distinguish this approach from traditional DTs reliant on feature engineering or fixed-size memory windows.

Methodology

Building on the foundation of Gradient-Based Decision Trees (GradTrees), ReMeDe Trees incorporate backpropagation through time to facilitate the learning of both decision paths and memory state updates. This includes:

• Memory Integration: By extending traditional DTs to consider a combined input-state space, ReMeDe Trees make pathing decisions based on both current inputs and past information stored in memory.
• Gradient-Based Training: Adjusting the classic decision process of DTs to support differentiable operations via a gradient-based framework allows the seamless integration of internal memory, paving the way for end-to-end learning of complex sequential tasks.
• Structured Experiments: Evaluation through synthetically generated benchmark datasets demonstrates that ReMeDe Trees can efficiently learn and recall sequential dependencies, contrasting with traditional DT-based models.

Experimental Results

The experiments focus on synthetic datasets designed to test the model's ability to learn patterns with explicit temporal dependencies. The results show that ReMeDe Trees achieve perfect accuracy (100%) across these synthetic benchmarks, performing comparably to established architectures like LSTMs. These results validate the proposed approach's capability to replace more elaborate and opaque models with a simpler, interpretable structure without a loss of performance.

Theoretical and Practical Implications

The introduction of ReMeDe Trees extends the applicability of decision trees to domains traditionally dominated by neural networks, particularly those involving sequential data. This model benefits from the interpretability of decision trees, offering transparent decision-making processes while operating in scenarios that demand memory of past states. Furthermore, this method holds promise for real-world applications in sectors such as finance, healthcare, and industrial processes, which often involve noisy sequential data and demand robust dynamic modeling.

Future Directions

The paper outlines several avenues for future exploration. Enhancing the hidden state updates with more sophisticated gating mechanisms, akin to those in advanced RNNs, could improve ReMeDe Trees' performance on tasks involving very long-term dependencies and various types of non-sequential datasets. Exploring integration with ensemble methods, such as GRANDE, might leverage the strengths of combining multiple models to further enhance performance. These extensions could solidify the role of ReMeDe Trees in both applied machine learning and theoretical exploration.

Overall, "Decision Trees That Remember" contributes significantly to the field by merging the strengths of decision tree interpretability and recurrent model memory capabilities, potentially setting a foundation for new paradigms in sequential data analysis and machine learning applications.