Fig. 1: Key features of the Krakencoder architecture.

a, Autoencoder path_ii: connectivity flavor i to connectivity flavor i. This path begins by stacking the upper triangular portion of each subject’s connectivity matrix into input \({X}_{i}\in {{\mathbb{R}}}^{{n}_{{\rm{edges}}}\times {n}_{{\rm{subj}}}}\). A precomputed, fixed PCA transformation normalizes the data and reduces dimensionality to \({X}_{i}^{{\prime} }\in {{\mathbb{R}}}^{256\times {n}_{{\rm{subj}}}}\), equalizing the size of disparate input flavors. A single fully connected layer Encoder_i, followed by L² normalization, transforms \({X}_{i}^{{\prime} }\) into a latent hypersphere surface \({z}_{i}\in {{\mathbb{R}}}^{128\times {n}_{{\rm{subj}}}}\). Batch-wise encoding loss L_z(z_i) controls inter-subject separation in latent space. A single fully connected layer Decoder_i transforms z_i to \({\hat{X}}_{i}^{{\prime} }\), and batch-wise reconstruction loss \({L}_{r}({X}_{i}^{{\prime} },{\hat{X}}_{i}^{{\prime} })\) and L_z(z_i) are backpropagated to optimize Encoder_i and Decoder_i. b, Transcoder path_ij: connectivity flavor i to connectivity flavor j. This path converting input flavor i to output flavor j begins the same as path_ii, transforming \({X}_{i}\to {X}_{i}^{{\prime} }\to {z}_{i}\), then Decoder_j transforms \({z}_{i}\to {\hat{X}}_{j}^{{\prime} }\), and reconstruction loss \({L}_{r}({X}_{j}^{{\prime} },{\hat{X}}_{j}^{{\prime} })\) is backpropagated to optimize Encoder_i and Decoder_j. c, Cross-path latent-space similarity optimization. The latent similarity loss L_z.sim(z_i, z_j, z_k, …) provides explicit control to ensure that the latent representations of each subject are consistent across connectivity flavors. See Extended Data Table 1 for details about the loss terms. d, Multimodality fusion predictions from averaged latent space vectors. For these predictions we average the encoded latent vector from all input flavors (as in the fusion model), or a subset of input flavors (as in the fusionSC model, which averages latent vectors from only the SC inputs), and then decode this average vector to all output flavors. The fusion-parc model demonstrates cross-parcellation prediction, by averaging inputs from only the other parcellations.