τ -Diag2Diag: A Causal 5D Generalization of Diag2Diag with Learned Delay Spectra

τ -Diag2Diag extends the Princeton Diag2Diag framework (Jalalvand et al., Nature Commu-nications 2025) by introducing a physically interpretable five-dimensional causal delay-field.Instead of relying on implicit memory in recurrent or transformer layers, τ -Diag2Diag learns ex-plicit Sum-of-Exponentials (SOE) delay kernels κτ,j→A(t) that represent the causal influence andmemory depth of each diagnostic channel. This yields both superior reconstruction accuracy anda direct mapping between diagnostics and their characteristic delay timescales.