Modern applications of neural-network-based AI solutions tend to move from datacenter backends to low-power edge devices. Environmental, computational, and power constraints are inevitable consequences of such a shift. Limiting the bit count of neural network parameters proved to be a valid technique for speeding up and increasing efficiency of the inference process. Hence, it is understandable that a similar approach is gaining momentum in the field of neural network training. In the face of growing complexity of neural network architectures, reducing resources required for preparation of new models would not only improve cost efficiency but also enable a variety of new AI applications on modern personal devices. In this work, we present a deep refinement of neural network parameters limitation with the use of the asymmetric exponent method. In addition to the previous research, we study new techniques of floating-point variables limitation, representation, and rounding. Moreover, by leveraging exponent offset, we present floating-point precision adjustments without an increase in variables’ bit count. The proposed method allowed us to train LeNet, AlexNet and ResNet-18 convolutional neural networks with a custom 8-bit floating-point representation achieving minimal or no results degradation in comparison to baseline 32-bit floating-point variables.