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We analyze the performance of Convolutional Autoencoders in generating reduced-order representations of 2D Rayleigh-Bénard flows across a wide range of Rayleigh numbers ($10^6 \leq Ra \leq 2.5 \times 10^8$), aiming to identify the smallest possible representations that still capture all relevant flow physics. We introduce a novel metric based on the Kolmogorov scale to determine the minimum number of dimensions required to compress data down to the dissipation scale, offering an alternative to the Mean Squared Error (MSE) typically employed in such neural network methods. Our architecture is compared to two regularized variants as well as to linear methods. This study provides a framework for identifying minimal representations of increasingly turbulent flows. Additionally, we demonstrate how the number of dimensions scales with $Ra$, revealing a change in slope that deviates from the expected scaling of conventional degrees of freedom.