Autoencoders (AEs) have emerged as powerful tools for non-linear dimensionality reduction, often surpassing traditional linear methods such as Proper Orthogonal Decomposition (POD) in scenarios characterized by slowly decaying Kolmogorov n-widths. In the realm of Reduced-Order Modelling (ROM), these models are increasingly utilized to learn low-dimensional representations of solution manifolds associated with parametric Partial Differential Equations (PDEs). However, the high expressivity of AEs presents a challenge: although trained networks typically minimize reconstruction error, they often struggle to capture the essential properties necessary for building accurate ROM. To overcome this issue, it is crucial to introduce bias during training, ensuring the model learns a pair of encoder (E) and decoder (D) that maintains representation consistency—specifically, constraining the composition of the encoder and decoder to be equal to the identity map (E ◦ D = id) within the local coordinates of the chart formed by the encoder and the solution manifold. Recent work by [1] and [2] has tackled this challenge in fully connected AEs by proposing representation-consistent architectures. This study builds upon that concept by extending representation consistency into the convolutional domain. We introduce a novel class of symmetric Convolutional Autoencoders (CAEs) designed to embody the primary properties of manifold parametrization mappings. When integrated into a ROM framework, this architecture demonstrates significantly improved predictive capabilities. Numerical experiments indicate that, in comparison to standard CAEs, our proposed approach achieves reduced reconstruction errors and generates more accurate latent-space trajectories. [1] Samuel E. Otto, Gregory R. Macchio, and Clarence W. Rowley, Learning nonlinear projections for reduced-order modeling of dynamical systems using constrained autoencoders, Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 11, 113130, 2023. [2] Simone Brivio, Nicola Rares Franco, LDeep Symmetric Autoencoders from the Eckart-Young-Schmidt Perspective, arXiv:2506.11641