Konstantinos Fotopoulos

Konstantinos Fotopoulos, Petros Maragos, Panagiotis Misiakos

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.

Konstantinos Fotopoulos, Petros Maragos

We investigate deep morphological neural networks (DMNNs). We demonstrate that despite their inherent non-linearity, "linear" activations are essential for DMNNs. To preserve their inherent sparsity, we propose architectures that constraint the parameters of the "linear" activations: For the first (resp. second) architecture, we work under the constraint that the majority of parameters (resp. learnable parameters) should be part of morphological operations. We improve the generalization ability of our networks via residual connections and weight dropout. Our proposed networks can be successfully trained, and are more prunable than linear networks. To the best of our knowledge, we are the first to successfully train DMNNs under such constraints. Finally, we propose a hybrid network architecture combining linear and morphological layers, showing empirically that the inclusion of morphological layers significantly accelerates the convergence of gradient descent with large batches.

Konstantinos Fotopoulos, Christos Garoufis, Petros Maragos

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.