Hluboké neuronové sítě s biologicky inspirovanou lokální konektivitou a topografickou organizací

Rechtorík, Filip

Convolutional neural networks achieve strong computer vision performance, but their rigid weight sharing and channel-based feature organization are poorly aligned with the topographic organization of biological visual cortex. This thesis investigates whether cortical-like topographic organization can emerge from architectural constraints, rather than being directly imposed through a similarity loss. We introduce LocalLinear, a generalization of locally connected layers that maps between two-dimensional neuronal sheets of arbitrary sizes and densities, replacing convolutional weight sharing with localized, neuron-specific connectivity. To structure the resulting connections, weights are generated by hypernetworks conditioned on neuronal descriptors and spatial offsets. To make these models trainable, we implement a custom CUDA kernel and memory- efficient hypernetwork backpropagation. The best-performing hypernetwork-based variant achieves image classification performance comparable to FLOP-matched convolutional baselines, while sinusoidal implicit representations produce the clearest smooth orientation preference maps. Together, these results suggest a path toward deep visual models whose neuronal structure can be represented as a function over continuous space.

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