Muhammad Numan Yousaf | Search arXiv

arXiv2026

When Does Unsupervised Learning Succeed or Fail? A PoS Perspective on Reconstruction-Based Anomaly Detection

Reconstruction-based unsupervised learning can fail in two opposing ways: a model may reconstruct anomalies too accurately or discard valid nominal variation. Using the Pursuit of Subspaces hypothesis, we characterize these failures through the meet, union, and join geometries induced by the nominal components. Excess learned range produces join blindness, while insufficient capacity produces meet preference and loss of nominal fidelity. We show that the compact nominal union is optimal among nominal faithful ranges and generally requires a nonlinear reconstruction map. Based on this geometry, we introduce Dynamic Push and Pull, which learns from controlled perturbations without anomaly labels, and nested manifold carving, which applies the same principle recursively in latent space. Experiments confirm the predicted changes in latent geometry across every tested Push and Pull configuration. The proposed methods improve reconstruction-based anomaly detection across standard benchmarks and unseen image degradations, while also improving pretrained ECG representations for downstream classification. These results connect reconstruction failures to identifiable geometric conditions and provide practical mechanisms for learning compact representations.

cs.LG↗

arXiv2025

Multiscale Tensor Summation Factorization as a New Neural Network Layer (MTS Layer) for Multidimensional Data Processing

Multilayer perceptrons (MLP), or fully connected artificial neural networks, are known for performing vector-matrix multiplications using learnable weight matrices; however, their practical application in many machine learning tasks, especially in computer vision, can be limited due to the high dimensionality of input-output pairs at each layer. To improve efficiency, convolutional operators have been utilized to facilitate weight sharing and local connections, yet they are constrained by limited receptive fields. In this paper, we introduce Multiscale Tensor Summation (MTS) Factorization, a novel neural network operator that implements tensor summation at multiple scales, where each tensor to be summed is obtained through Tucker-decomposition-like mode products. Unlike other tensor decomposition methods in the literature, MTS is not introduced as a network compression tool; instead, as a new backbone neural layer. MTS not only reduces the number of parameters required while enhancing the efficiency of weight optimization compared to traditional dense layers (i.e., unfactorized weight matrices in MLP layers), but it also demonstrates clear advantages over convolutional layers. The proof-of-concept experimental comparison of the proposed MTS networks with MLPs and Convolutional Neural Networks (CNNs) demonstrates their effectiveness across various tasks, such as classification, compression, and signal restoration. Additionally, when integrated with modern non-linear units such as the multi-head gate (MHG), also introduced in this study, the corresponding neural network, MTSNet, demonstrates a more favorable complexity-performance tradeoff compared to state-of-the-art transformers in various computer vision applications. The software implementation of the MTS layer and the corresponding MTS-based networks, MTSNets, is shared at https://github.com/mehmetyamac/MTSNet.

cs.LG↗