List of Publications

Solving Hamiltonian Systems Based on a Data-driven Deep Learning Algorithm
Social Science Research Network (SSRN) 2024

Uniform Autoencoder with Latent Flow Matching: Learning Robust Representations via Bounded Spaces

Tayfun Ünal1,2,*, Ünver Çiftçi2,*
1Kırklareli University
2Tekirdağ Namık Kemal University
Social Science Research Network (SSRN), 2026
Paper (Prepr.) Code

Proposed Model

Sixth research result visualization

Schematic representation of the Uniform Autoencoder (UAE). The encoder fθ maps inputs to a uniform latent space z via geometric expansion, while the decoder gφ reconstructs the data. The dashed frame illustrates the subsequent generative inference stage, where a Latent Flow Matching (LFM) module transforms source noise z0 into the target latent manifold ẑ based on the fixed representations, enabling high-fidelity data synthesis via the frozen decoder.

Abstract

This paper introduces the Uniform Autoencoder (UAE), a generative framework designed to learn effective representations in low-dimensional latent spaces while preserving the geometric structure of the data. Unlike traditional Variational Autoencoders (VAEs) that impose an unbounded Gaussian prior often leading to posterior collapse or topological mismatch, UAE enforces a uniform distribution within a bounded latent space. By integrating a reconstruction objective with a geometric expansion objective, the model effectively captures the intrinsic data manifold. To enable high-fidelity data generation from this bounded space, we employ Latent Flow Matching (LFM) as a post-hoc sampling mechanism to model the empirical distribution of the fixed latent representations. We evaluate the proposed framework on a diverse set of benchmarks, including synthetic manifolds (Moon, Spiral, Swiss Roll) and high-dimensional datasets (Digits, MNIST, CIFAR-10, CelebA). Our experiments demonstrate that UAE outperforms standard baselines in preserving data topology. Furthermore, the model exhibits strong discriminative capacity, achieving 93% accuracy on downstream classification tasks for Digits and MNIST, validating the effectiveness of uniform latent priors in separating distinct data classes. The proposed method offers a robust alternative for representation learning, balancing generative capability with high-quality feature extraction. Our implementation is available at https://tayfununal.github.io/Article-3/.

Original Datasets

Visualizations of the diverse datasets used in our experiments.

Dataset-Wise Visualization of Results

Visualizations of the results obtained across different datasets.

SwissRoll and Spiral dataset animation

2D latent space transitions for the Swiss Roll and Spiral datasets on the test set during training.

BibTeX

@article{Unal2026uae,
        title={Uniform Autoencoder with Latent Flow Matching: Learning Robust Representations via Bounded Spaces},
        author={Tayfun Ünal, and Ünver Çiftçi},
        journal={Social Science Research Network (SSRN)},
        year={2026},
        url={https://papers.ssrn.com/sol3/papers.cfm?abstract_id=6174263}
        }
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