This paper presents a new neural network (NN) algorithm for real-time retrievals of low amounts of precipitable water vapor (PWV) and integrated liquid water from millimeter-wave ground-based observations. Measurements are collected by the 183.3-GHz G-band vapor radiometer (GVR) operating at the Atmospheric Radiation Measurement (ARM) Program Climate Research Facility, Barrow, AK. The NN provides the means to explore the nonlinear regime of the measurements and investigate the physical boundaries of the operability of the instrument. A methodology to compute individual error bars associated with the NN output is developed, and a detailed error analysis of the network output is provided. Through the error analysis, it is possible to isolate several components contributing to the overall retrieval errors and to analyze the dependence of the errors on the inputs. The network outputs and associated errors are then compared with results from a physical retrieval and with the ARM two-channel microwave radiometer (MWR) statistical retrieval. When the NN is trained with a seasonal training data set, the retrievals of water vapor yield results that are comparable to those obtained from a traditional physical retrieval, with a retrieval error percentage of ~5% when the PWV is between 2 and 10 mm, but with the advantages that the NN algorithm does not require vertical profiles of temperature and humidity as input and is significantly faster computationally. Liquid water path (LWP) retrievals from the NN have a significantly improved clear-sky bias (mean of ~2.4 g/m2) and a retrieval error varying from 1 to about 10 g/m2 when the PWV amount is between 1 and 10 mm. As an independent validation of the LWP retrieval, the longwave downwelling surface flux was computed and compared with observations. The comparison shows a significant improvement with respect to the MWR statistical retrievals, particularly for LWP amounts of less than 60 g/m2. This p- - aper shows that the GVR alone can provide overall improved PWV and LWP retrievals when the PWV amount is less than 10 mm, and, when combined with the MWR, can provide improved retrievals over the whole water-vapor range.