We propose an adaptive multi-layer (ML) filter architecture to compensate for linear impairments that occur in transmitter (Tx) and receiver (Rx) components in ultra-long-haul optical fiber transmission systems, in which large chromatic dispersion (CD) accumulates in the received signal. The architecture consists of strictly linear (SL) and widely linear (WL) filter layers, and the coefficients of the ML filters are adaptively controlled by gradient calculation with back propagation and stochastic gradient descent. Static CD compensation is performed on the received signal and its complex conjugate before the adaptive ML filters. These augmented signals are then the inputs of the first 2×1 SL filter layer of the ML filters, for compensation of in-phase (I) and quadrature (Q) impairments on the Rx side. Tx IQ impairments and polarization effects as well as Rx IQ impairments are adaptively compensated in the ML filters. By sweeping CD compensation filters before the ML filters, this architecture mitigates the computational complexity for back propagation of the ML filters especially for ultra-long-haul transmission, while mutual non-commutativity between the WL filter for IQ impairment compensation and the CD compensation filter is appropriately solved. We evaluated the proposed adaptive ML filter architecture with augmented inputs through both simulation and wavelength-division multiplexed transmission experiments of 32-Gbaud polarization-division-multiplexed 64-quadrature amplitude modulation-based probabilistic constellation shaped signals over 10,000 km of single-mode fiber (SMF). The results demonstrated that the proposed adaptive ML filter architecture effectively compensates for Tx and Rx IQ skews in ultra-long-haul SMF transmission, and that impairments can be monitored individually from the converged filter coefficients of the corresponding layers.