  This paper investigates the possibility of approximating multiple
mathematical operations in latent space for expression derivation. To this end,
we introduce different multi-operational representation paradigms, modelling
mathematical operations as explicit geometric transformations. By leveraging a
symbolic engine, we construct a large-scale dataset comprising 1.7M derivation
steps stemming from 61K premises and 6 operators, analysing the properties of
each paradigm when instantiated with state-of-the-art neural encoders.
Specifically, we investigate how different encoding mechanisms can approximate
expression manipulation in latent space, exploring the trade-off between
learning different operators and specialising within single operations, as well
as the ability to support multi-step derivations and out-of-distribution
generalisation. Our empirical analysis reveals that the multi-operational
paradigm is crucial for disentangling different operators, while discriminating
the conclusions for a single operation is achievable in the original expression
encoder. Moreover, we show that architectural choices can heavily affect the
training dynamics, structural organisation, and generalisation of the latent
space, resulting in significant variations across paradigms and classes of
encoders.
