From Parallelism to Specialisation: SSA-Guided Multi-Branch Implicit Neural Representations

Although Multi-branch Implicit Neural Representations (INRs) increase the modelling capacity of the network, the parallel paths are not inherently guided to learn distinct components of the target signal. To address this limitation, we introduce a Singular Spectrum Analysis (SSA) guided multi-branch INR, which provides each branch with a specific signal component as the branch-specific target. For a two-dimensional signal, for example, an image, a separable two-dimensional SSA decomposes the target signal into 4 distinct components, which separately represent structure, horizontal-detail, vertical-detail, and joint-detail, to provide each branch with a designated target to achieve. Gated contributions of each branch are then additively combined to obtain the final signal reconstruction. In addition, we introduce a Particle Swarm Optimisation (PSO)-initialised, learnable coordinate scaling at the input to each branch to enable it to model the target effectively. Branch-wise pretraining against the respective SSA component ensures that all the parallel branches are properly supervised to attain the respective target. Experiments on Kodak images demonstrate that the proposed algorithm shows the best overall peak signal-to-noise ratio (PSNR) performance among state-of-the-art (SOTA) algorithms including COSMO-RC, INCODE, FR-INR, and SIREN. Moreover, ablation studies against unguided parallel INRs show that the guided model consistently outperforms the unguided baseline. Spatial alignment matrices, training dynamics, and Fourier-domain analysis suggest that the learned branches retain distinct and coherent roles. The same specialisation principle extends to any n-dimensional signal, including audio, which is a one-dimensional signal. Further ablations demonstrate that the main source of the improvement is branch specialisation, indicating that specialisation and explicit branch-wise task allocation are more important than branch parallelisation alone. The complete source code and implementation will be made publicly available upon acceptance.