Biyolojik olarak makul kredi tahsisi için normatif bir ilke olarak determinant maksimizasyon kriteri

We demonstrate that the determinant maximization (Det-Max) criterion arises as a normative principle to construct biologically-plausible learning algorithms for both unsupervised and supervised methods. The importance of determinant maximization lies in its central role within structured matrix factorization frameworks, enabling the extraction of hidden information from input data. We apply this criterion to formulate principled optimization problems that address specific issues in an online setting, leading to the development of neural networks with local learning updates. Our primary objectives involve solving two central problems in signal processing and machine learning: blind source separation and supervised learning. For blind source separation, we propose two normative biologically-plausible methods that incorporate the determinant maximization criterion and assume the source vectors are sufficiently scattered in their domains. The first method employs a cascade of two weighted similarity matching constraints. Each constraint aims to equalize the generalized inner products among output vectors and their corresponding input vectors. We prove that a batched optimization problem based on weighted similarity matching achieves the same global optimum as the determinant maximization optimization, resulting in perfect separation. The corresponding online optimization can be realized by a two-layered neural network with piece-wise linear activations and local Hebbian learning. The second method we propose involves maximizing correlative mutual information from input vectors to output vectors. This approach relies solely on second-order statistics of the inputs and outputs, eliminating the need for computationally expensive higher-order statistics or joint probability density function estimates. This novel framework serves as a unified approach for developing biologically-plausible neural networks for various unsupervised data decomposition methods, aiming to obtain structured latent representations. Furthermore, we demonstrate that augmenting the correlative information maximization objective with mean squared error for fitting to labeled data provides an alternative normative approach to explain signal propagation in supervised biological neural networks. The coordinate descent optimization of this novel objective establishes a neural network structure that mimics biologically realistic networks of multi-compartment pyramidal neurons with dendritic processing and lateral inhibitory neurons. Importantly, our approach naturally resolves the weight transport problem associated with the backpropagation algorithm, which has been a significant critique of training conventional neural networks from a biologically-plausible perspective. We achieve this by leveraging two alternative forms of correlative information measures. In brief, this thesis proposes several normative methods for establishing biologically-plausible neural networks for various tasks. We provide diverse numerical experiments to showcase the effectiveness of each proposed method in comparison to recent approaches.