Prox-Friendly Log-Magnitude Prior on Complex-Valued Signal

Sparse training reduces the memory and computational costs of deep neural networks. However, sparse optimization methods, e.g., those adding an $\ell_1$ penalty, often control sparsity only indirectly through a regularization parameter $λ$, whose mapping to the final sparsity rate is non-trivial. In our experiments, we found this parameter sensitivity to be particularly pronounced for Bregman-based optimizers. Specifically, the two variants LinBreg and AdaBreg reach the same sparsity at $λ$ values that differ by up to two orders of magnitude, requiring expensive trial-and-error sweeps to achieve a user-specified sparsity. To address this, we propose an adaptive regularization scheme that updates $λ$ based on the difference between the model's current sparsity and the target sparsity. We analyze the resulting algorithm and evaluate it on automatic speaker verification with ECAPA-TDNN and ResNet34 on VoxCeleb and CNCeleb. The proposed method reliably achieves sparsity targets ranging between 75% and 99%. It also converges faster than the oracle-tuned non-adaptive baseline during early training and matches or surpasses its final performance in equal error rate. We further show that the adaptive scheme inherits key properties from its non-adaptive counterpart, including improved out-of-distribution robustness over the dense baselines.

Audio spotforming is a technique for extracting target speech from noisy mixtures by utilizing multiple microphone arrays. Conventional methods estimate a shared target speech component from linearly separated signals obtained by each array using low-rank approximations and apply post filtering (PF) based on this estimated low-rank representation. However, owing to the mismatch between low-rank models and the complex structure of speech signals, directly relying on low-rank approximations for PF can degrade the speech extraction performance. In this study, we leverage the observation that non-target components located in the target speech direction from the perspective of one array can be spatially separated when viewed from other arrays. This insight motivates a new spotforming method for efficient post-filter estimation using non-target estimates across arrays instead of relying on low-rank approximations. Experiments demonstrate that the proposed method outperforms conventional spotforming methods.

We propose a unified fractional regularization framework for sparse signal recovery based on the $\ell_1/\ell_p^q$ model. This model generalizes several widely used sparsity-promoting regularizers and provides additional flexibility through the parameters $p$ and $q$. Our main theoretical contribution is the characterization of the equivalence between the first-order stationary points of the $\ell_1/\ell_p^q$ formulation and the subtractive $\ell_1-α\ell_p$ model, thereby offering a unified perspective on these nonconvex regularizers. In addition, we establish a new sufficient recovery condition under the Restricted Isometry Property (RIP), which shows that the proposed framework can provide relaxed recovery guarantees and improved robustness. To solve the resulting nonconvex problem, we develop a majorization--minimization (MM) algorithm and prove its convergence by using the Kurdyka--Łojasiewicz (KL) property. Numerical experiments on sparse recovery problems with different sensing matrices and MRI reconstruction demonstrate that the proposed approach outperforms existing methods in recovery accuracy.