arXiv subjects

Qipeng Zhan

Publications and source records attributed to Qipeng Zhan.

5 recordsLinked to original sources

arXiv2026

Invertible Logits Transformation for Accuracy-Preserving Post-Hoc Uncertainty Calibration

Post-hoc calibration aligns a classifier's predicted confidences with its empirical accuracy without retraining. An ideal calibrator should correct nonlinear miscalibration, scale gracefully to large label spaces, and preserve the original predictions; existing methods typically violate at least one of these properties---temperature scaling lacks expressivity, more flexible parametric alternatives introduce parameters that grow with the number of classes $C$, and other expressive methods do not preserve the rank ordering of class scores and may alter the predicted class. We propose \textbf{Invertible Logits Transformation (InvLT)}, which applies a learned scalar MLP $f:\mathbb{R}\to\mathbb{R}$ element-wise to the pre-softmax logits. Sharing $f$ across all logit dimensions makes the parameter count independent of $C$. Monotonicity of $f$---and hence preservation of the argmax prediction---is softly encouraged via a paired inverse network rather than enforced through the numerical integration required by prior monotone calibrators; this avoids their computational overhead while empirically preserving the original classification accuracy in every setting we evaluate. Across standard image classification benchmarks and a range of architectures, InvLT consistently outperforms a broad set of post-hoc baselines on standard calibration metrics.

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arXiv2026

Generative Cross-Entropy: A Strictly Proper Loss for Data-Efficient Classification

Cross-entropy (CE) is the default training loss for supervised classification, but its sample efficiency is limited when labels are scarce. Existing remedies primarily act on the data side, via augmentation, synthesis, or transfer from pretrained models; the training objective itself is rarely revisited. We revisit it here. Drawing on the classical observation that generative classifiers reach their asymptotic error with fewer samples than discriminative ones, we propose Generative Cross-Entropy (GenCE), a drop-in replacement for CE that introduces a generative learning principle into a standard discriminative network without altering the architecture or fitting a separate density model. GenCE follows from a Bayesian rewrite of the class-conditional likelihood and, in the mini-batch approximation, reduces to normalizing each sample's softmax score against the model's predictions on the batch, coupling the training signal across examples sharing a class. We extend the proper-scoring-rule framework to such non-local losses and prove that GenCE is strictly proper under a mild completeness condition: its population risk is uniquely minimized at the true posterior. Across three datasets, on two architectures and in both balanced small-data and class-imbalanced regimes, GenCE outperforms CE and other widely used losses, while also producing better-calibrated probabilities and stronger out-of-distribution detection.

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arXiv2026

Bi-Lipschitz Autoencoder With Injectivity Guarantee

Autoencoders are widely used for dimensionality reduction, based on the assumption that high-dimensional data lies on low-dimensional manifolds. Regularized autoencoders aim to preserve manifold geometry during dimensionality reduction, but existing approaches often suffer from non-injective mappings and overly rigid constraints that limit their effectiveness and robustness. In this work, we identify encoder non-injectivity as a core bottleneck that leads to poor convergence and distorted latent representations. To ensure robustness across data distributions, we formalize the concept of admissible regularization and provide sufficient conditions for its satisfaction. In this work, we propose the Bi-Lipschitz Autoencoder (BLAE), which introduces two key innovations: (1) an injective regularization scheme based on a separation criterion to eliminate pathological local minima, and (2) a bi-Lipschitz relaxation that preserves geometry and exhibits robustness to data distribution drift. Empirical results on diverse datasets show that BLAE consistently outperforms existing methods in preserving manifold structure while remaining resilient to sampling sparsity and distribution shifts. Code is available at https://github.com/qipengz/BLAE.

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arXiv2026

PCAE: Learning Ordered Representations in Latent Space for Intrinsic Dimension Estimation via Principal Component Autoencoder

Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA). Prior studies have demonstrated that linear autoencoders (LAEs) can recover the ordered, axis-aligned principal components of PCA by incorporating non-uniform $\ell_2$ regularization or by adjusting the loss function. However, these approaches become insufficient in the nonlinear setting, as the remaining variance cannot be properly captured independently of the nonlinear mapping. In this work, we propose a novel autoencoder framework that integrates non-uniform variance regularization with an isometric constraint. This design serves as a natural generalization of PCA, enabling the model to preserve key advantages, such as ordered representations and variance retention, while remaining effective for nonlinear dimensionality reduction tasks.

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arXiv2025

Multi-Scale Geometric Autoencoder

Autoencoders have emerged as powerful models for visualization and dimensionality reduction based on the fundamental assumption that high-dimensional data is generated from a low-dimensional manifold. A critical challenge in autoencoder design is to preserve the geometric structure of data in the latent space, with existing approaches typically focusing on either global or local geometric properties separately. Global approaches often encounter errors in distance approximation that accumulate, while local methods frequently converge to suboptimal solutions that distort large-scale relationships. We propose Multi-Scale Geometric Autoencoder (MAE), which introduces an asymmetric architecture that simultaneously preserves both scales of the geometric structure by applying global distance constraints to the encoder and local geometric constraints to the decoder. Through theoretical analysis, we establish that this asymmetric design aligns naturally with the distinct roles of the encoder and decoder components. Our comprehensive experiments on both synthetic manifolds and real-world datasets demonstrate that MAE consistently outperforms existing methods across various evaluation metrics.

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