arXiv subjects

Konstantinos Fotopoulos

Publications and source records attributed to Konstantinos Fotopoulos.

3 recordsLinked to original sources

arXiv2026

Training Deep Morphological Neural Networks as Universal Approximators

We investigate deep morphological neural networks (DMNNs), studying how changes in algebraic structure affect the expressivity and trainability of deep architectures. We show that despite the inherent non-linearity of morphological operations, existing deep morphological architectures fail to be universal approximators and exhibit optimization limitations related to sparse and uninformative gradients. To address these issues, we introduce architectures incorporating constrained "linear" activations between morphological layers and averaging max-plus and min-plus neurons. Only O(N) parameters (or learnable parameters) per layer of size N belong to the activations, with the remaining parameters constrained to morphological operations. We prove universal approximation results for the proposed architectures without requiring substantially larger parameter counts than comparable linear networks. Residual connections and weight dropout further improve generalization. Our experiments show that our networks are trainable and compact, despite the imposed architectural restrictions.

cs.LG↗

arXiv2025

TropNNC: Structured Neural Network Compression Using Tropical Geometry

We present TropNNC, a framework for compressing neural networks with linear and convolutional layers and ReLU activations using tropical geometry. By representing a network's output as a tropical rational function, TropNNC enables structured compression via reduction of the corresponding tropical polynomials. Our method refines the geometric approximation of previous work by adaptively selecting the weights of retained neurons. Key contributions include the first application of tropical geometry to convolutional layers and the tightest known theoretical compression bound. TropNNC requires only access to network weights - no training data - and achieves competitive performance on MNIST, CIFAR, and ImageNet, matching strong baselines such as ThiNet and CUP.

cs.CV↗

arXiv2025

Sparse Hybrid Linear-Morphological Networks

We investigate hybrid linear-morphological networks. Recent studies highlight the inherent affinity of morphological layers to pruning, but also their difficulty in training. We propose a hybrid network structure, wherein morphological layers are inserted between the linear layers of the network, in place of activation functions. We experiment with the following morphological layers: 1) maxout pooling layers (as a special case of a morphological layer), 2) fully connected dense morphological layers, and 3) a novel, sparsely initialized variant of (2). We conduct experiments on the Magna-Tag-A-Tune (music auto-tagging) and CIFAR-10 (image classification) datasets, replacing the linear classification heads of state-of-the-art convolutional network architectures with our proposed network structure for the various morphological layers. We demonstrate that these networks induce sparsity to their linear layers, making them more prunable under L1 unstructured pruning. We also show that on MTAT our proposed sparsely initialized layer achieves slightly better performance than ReLU, maxout, and densely initialized max-plus layers, and exhibits faster initial convergence.

cs.LG↗