The performance limitations of traditional computer architectures have led to the rise of brain-inspired hardware, with optical solutions gaining popularity due to the energy efficiency, high speed, and scalability of linear operations. However, the use of optics to emulate the synaptic activity of neurons has remained a challenge since the integration of nonlinear nodes is power-hungry and, thus, hard to scale. Neuromorphic wave computing offers a new paradigm for energy-efficient information processing, building upon transient and passively nonlinear interactions between optical modes in a waveguide. Here, an implementation of this concept is presented using broadband frequency conversion by coherent higher-order soliton fission in a single-mode fiber. It is shown that phase encoding on femtosecond pulses at the input, alongside frequency selection and weighting at the system output, makes transient spectro-temporal system states interpretable and allows for the energy-efficient emulation of various digital neural networks. The experiments in a compact, fully fiber-integrated setup substantiate an anticipated enhancement in computational performance with increasing system nonlinearity. The findings suggest that broadband frequency generation, accessible on-chip and in-fiber with off-the-shelf components, may challenge the traditional approach to node-based brain-inspired hardware design, ultimately leading to energy-efficient, scalable, and dependable computing with minimal optical hardware requirements.