We introduce the Learning Hyperplane Tree (LHT), a novel oblique decision tree model designed for expressive and interpretable classification. LHT fundamentally distinguishes itself through a non-iterative, statistically-driven approach to constructing splitting hyperplanes. Unlike methods that rely on iterative optimization or heuristics, LHT directly computes the hyperplane parameters, which are derived from feature weights based on the differences in feature expectations between classes within each node. This deterministic mechanism enables a direct and well-defined hyperplane construction process. Predictions leverage a unique piecewise linear membership function within leaf nodes, obtained via local least-squares fitting. We formally analyze the convergence of the LHT splitting process, ensuring that each split yields meaningful, non-empty partitions. Furthermore, we establish that the time complexity for building an LHT up to depth $d$ is $O(mnd)$, demonstrating the practical feasibility of constructing trees with powerful oblique splits using this methodology. The explicit feature weighting at each split provides inherent interpretability. Experimental results on benchmark datasets demonstrate LHT's competitive accuracy, positioning it as a practical, theoretically grounded, and interpretable alternative in the landscape of tree-based models. The implementation of the proposed method is available at https://github.com/Hongyi-Li-sz/LHT_model.

This paper introduces a novel tree-based model, Learning Hyperplane Tree (LHT), which outperforms state-of-the-art (SOTA) tree models for classification tasks on several public datasets. The structure of LHT is simple and efficient: it partitions the data using several hyperplanes to progressively distinguish between target and non-target class samples. Although the separation is not perfect at each stage, LHT effectively improves the distinction through successive partitions. During testing, a sample is classified by evaluating the hyperplanes defined in the branching blocks and traversing down the tree until it reaches the corresponding leaf block. The class of the test sample is then determined using the piecewise linear membership function defined in the leaf blocks, which is derived through least-squares fitting and fuzzy logic. LHT is highly transparent and interpretable--at each branching block, the contribution of each feature to the classification can be clearly observed.

Temperature scaling is a popular technique for tuning the sharpness of a model distribution. It is used extensively for sampling likely generations and calibrating model uncertainty, and even features as a controllable parameter to many large language models in deployment. However, autoregressive models rely on myopic temperature scaling that greedily optimizes the next token. To address this, we propose Long Horizon Temperature Scaling (LHTS), a novel approach for sampling from temperature-scaled joint distributions. LHTS is compatible with all likelihood-based models, and optimizes for the long horizon likelihood of samples. We derive a temperature-dependent LHTS objective, and show that finetuning a model on a range of temperatures produces a single model capable of generation with a controllable long horizon temperature parameter. We experiment with LHTS on image diffusion models and character/language autoregressive models, demonstrating advantages over myopic temperature scaling in likelihood and sample quality, and showing improvements in accuracy on a multiple choice analogy task by $10\%$.