As machine learning spreads into more and more application areas, micro controllers and low power CPUs are increasingly being used to perform inference with machine learning models. The capability to deploy onto these limited hardware targets is enabling machine learning models to be used across a diverse range of new domains. Optimising the inference process on these targets poses different challenges from either desktop CPU or GPU implementations, where the small amounts of RAM available on these targets sets limits on size of models which can be executed. Analysis of the memory use patterns of eleven machine learning models was performed. Memory load and store patterns were observed using a modified version of the Valgrind debugging tool, identifying memory areas holding values necessary for the calculation as inference progressed. These analyses identified opportunities optimise the memory use of these models by overlapping the input and output buffers of individual tensor operations. Three methods are presented which can calculate the safe overlap of input and output buffers for tensor operations. Ranging from a computationally expensive approach with the ability to operate on compiled layer operations, to a versatile analytical solution which requires access to the original source code of the layer. The diagonal memory optimisation technique is described and shown to achieve memory savings of up to 34.5% when applied to eleven common models. Micro-controller targets are identified where it is only possible to deploy some models if diagonal memory optimisation is used.