Machine learning may include training and drawing inference from artificial neural networks, processes which may include performing convolution and matrix multiplication operations. Convolution and matrix multiplication operations are performed using vectors of block floating-point (BFP) values that may include outliers. BFP format stores floating-point values using a plurality of mantissas of a fixed bit width and a shared exponent. Elements are outliers when they are too large to be represented precisely with the fixed bit width mantissa and shared exponent. Outlier values are split into two mantissas. One mantissa is stored in the vector with non-outliers, while the other mantissa is stored outside the vector. Operations, such as a dot product, may be performed on the vectors in part by combining the in-vector mantissa and exponent of an outlier value with the out-of-vector mantissa and exponent.