Manifold-Constrained Residual Adaptation with Frame-Adaptive Layer Aggregation for Speaker Verification

Large self-supervised speech models provide powerful representations for speaker verification, but full fine-tuning is expensive. Most conventional adapters insert small trainable modules to modify the output of each layer, while keeping the original residual connections unchanged. Building on our preliminary study of manifold-constrained Hyper-Connections in speaker encoders, we explore parameter-efficient adaptation of both residual paths and feature selection across layers. We first propose a Manifold-Constrained Residual Adapter (MCRA), which splits the hidden dimensions of each Transformer residual state into N groups and uses a small Sinkhorn-normalized matrix to exchange information among them. A learnable gate controls the balance between the original and mixed residual paths. The gate adds only one scalar parameter at each residual connection and initially favors the original path, allowing gradual adaptation. We further propose Frame-Adaptive Layer Aggregation (FALA), an attention-based aggregation method that uses a single learned query shared across all utterances to compute layer weights separately for each speech frame. Because the layer representations depend on the input, the resulting weights vary across both utterances and frames, unlike the fixed weights of a conventional layer-weighted sum. Compared with a frozen WavLM baseline using a fixed layer-weighted sum, our method achieves relative EER reductions of 22.4% on VoxCeleb1-O and 2.9% on CN-Celeb, with trainable adaptation parameters equivalent to only 0.0009% and 0.0016% of the WavLM-Large parameters, respectively.