The paper introduces a robust gradient-based liquid neural network (GLNN) framework for millimeter-wave (mmWave) multiple-input multiple-output (MIMO) communication. The GLNN combines manifold learning techniques and liquid neural networks (LNNs) with gradient-based learning to address the challenges of dynamic and noisy mmWave channels. The LNN, inspired by the nervous system of Caenorhabditis elegans, uses ordinary differential equations (ODEs) to process noisy and dynamic data efficiently. The GLNN extracts high-order channel feature information from gradients of the optimization objective function and employs residual connections to reduce training complexity. Additionally, manifold learning is used to compress the search space, enhancing robustness to channel estimation errors (CEE). Simulation results demonstrate that the GLNN achieves 4.15% higher spectral efficiency (SE) compared to typical iterative algorithms and reduces time consumption to only 1.61% of conventional methods. The GLNN's performance is validated through various scenarios, including varying transmit power, CEE levels, and dynamic environments, showcasing its adaptability and robustness.The paper introduces a robust gradient-based liquid neural network (GLNN) framework for millimeter-wave (mmWave) multiple-input multiple-output (MIMO) communication. The GLNN combines manifold learning techniques and liquid neural networks (LNNs) with gradient-based learning to address the challenges of dynamic and noisy mmWave channels. The LNN, inspired by the nervous system of Caenorhabditis elegans, uses ordinary differential equations (ODEs) to process noisy and dynamic data efficiently. The GLNN extracts high-order channel feature information from gradients of the optimization objective function and employs residual connections to reduce training complexity. Additionally, manifold learning is used to compress the search space, enhancing robustness to channel estimation errors (CEE). Simulation results demonstrate that the GLNN achieves 4.15% higher spectral efficiency (SE) compared to typical iterative algorithms and reduces time consumption to only 1.61% of conventional methods. The GLNN's performance is validated through various scenarios, including varying transmit power, CEE levels, and dynamic environments, showcasing its adaptability and robustness.