We present a spectral convolutional autoencoder framework to infer an integer, observation-conditioned estimate for the inertial-manifold dimension in the Kuramoto-Sivashinsky equation. Training on trajectory segments of temporal horizon $\tau$, we analyze reconstruction-error scaling with latent dimension $d$ through a local log-slope diagnostic $\gamma (d,\tau )$ and identify a robust horizon-induced change-point: once $\tau$ exceeds a mixing scale, the scaling gain localizes at a unique integer $d^{*}\left(L\right)$ and remains stable for larger horizons. Across $L=\{22,44,58,66,88,96\}$, the extracted $d^{*}$ is extensive and is well described by a linear law, $d^{*}\approx 0.366L$. Moreover, $d^{*}$ is largely insensitive to temporal-frequency truncation provided the energy-dominant low-frequency band is retained, indicating bandwidth sufficiency for stable dimension identification under the present observation scheme.

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• Dissipative dynamics
• Pattern formation
• Spatiotemporal chaos
• Chaotic systems
• Convolutional neural networks
• Dimensionality reduction