signal processing software developers

Abstract: Lightweight representation bridges make pretrained, task-adapted EEG foundation models executable on other biosignal modalities without retraining their backbones. However, selecting a single bridge pathway globally assigns every instance to the same transfer route and ignores complementary errors across routes. We therefore formulate multi-bridge transfer as an instance-level algorithm-selection problem and introduce BridgeRouter, a gain-aware router over a portfolio of frozen cross-modal pathways. A validation-selected Single Best Solver (SBS) serves as a protected default route. During training, task labels are used to compute the reduction in negative log-likelihood provided by each alternative route relative to the SBS, and a lightweight MLP predicts these route-specific gains from a target-modality representation extracted by a frozen encoder. At inference, BridgeRouter observes only the target modality, requires neither EEG, task labels, nor predictions from all candidate routes, and executes exactly one bridge pathway: the route with the largest predicted gain when that gain exceeds a validation-calibrated threshold, and the SBS otherwise. We evaluate seven EEG foundation-model bridge pathways for EMG-based freezing-of-gait detection on FOG and ECG-based sleep classification on ISRUC. Across five seeds, BridgeRouter achieves $81.38\pm1.11\%$ balanced accuracy on FOG, improving over the BIOT SBS by $11.49$ percentage points, and $62.92\pm2.17\%$ on ISRUC, improving over the CBraMod SBS by $3.83$ points. Per-instance bridge oracles reach $99.96\%$ and $78.61\%$, respectively, revealing substantial remaining portfolio headroom. These results show that anchor-relative gain prediction can convert complementary cross-modal bridge behavior into deployable instance-level routing improvements while retaining single-route inference.

Abstract: Coded diffraction patterns (CDPs) provide a structured and physically relevant model for phase retrieval, but the dependence among Fourier measurements generated by a common mask makes sharp stability analysis challenging. For a fixed unit-norm signal $\boldsymbol{x}_\star \in \mathbb{C}^n$, let $\boldsymbol{X}_\star=\boldsymbol{x}_\star\boldsymbol{x}_\star^*$, and let $\mathcal A$ be the lifted CDP measurement operator. We prove that, with $L=O(\log n)$ random masks, the following uniform lower isometry holds with high probability: $\|\boldsymbol{X}-\boldsymbol{X}_\star\|_F \lesssim \log^2(2n) \frac{\|\mathcal A(\boldsymbol{X}-\boldsymbol{X}_\star)\|_2}{\sqrt{nL}}, \boldsymbol{X}\succeq\boldsymbol{0},$ from which we derive two consequences. First, for $\boldsymbol{y}=\mathcal A(\boldsymbol{X}_\star)+\boldsymbol{e}$, PhaseLift-type convex programs achieve the Gaussian-type stable recovery bound $\|\widehat{\boldsymbol{X}}-\boldsymbol{X}_\star\|_F \lesssim \frac{\log^2(2n)}{\sqrt{nL}}\|\boldsymbol{e}\|_2.$ Second, in the noiseless case, the nonconvex factorized loss has a benign landscape when the factor width satisfies $r = O(\log^5(2n))$: every second-order critical point $\boldsymbol{V}\in\mathbb C^{n\times r}$ satisfies $\boldsymbol{V}\boldsymbol{V}^*=\boldsymbol{X}_\star$. The key ingredient is a uniform operator-norm bound over row subsets of the dependent CDP measurement matrix, which permits the removal of a controlled set of adaptively selected rows while preserving tangent injectivity.

Abstract: Multi-user multiple-input multiple-output (MU-MIMO) is a key technology that improves wireless capacity through multiple antennas. In MU-MIMO downlink precoding, vector perturbation (VP) is a representative nonlinear method that achieves high performance. However, its search for the integer perturbation vector reduces to a closest vector problem, whose complexity grows rapidly as the number of users increases. We propose a method that relaxes the discrete structure of the integer perturbation into a continuous mixture of $t$-distributions, enabling efficient search via gradient-based Hamiltonian Monte Carlo (HMC). Complexity analysis and numerical experiments demonstrate the effectiveness of the proposed method. Its search complexity scales as O(N^2) in the number of users N. At a symbol error rate of 10^-3, it performs within 2.4 dB of a hypersphere approximation benchmark, which approximates the performance limit of VP. This paper reframes the VP perturbation search as a probabilistic inference problem, providing a general formulation for handling high-dimensional discrete search in a continuous space.