M. Rostami

M. Rostami, H. Moradian, S. S. Kia

This paper proposes a set of novel optimization algorithms for solving a class of convex optimization problems with time-varying streaming cost function. We develop an approach to track the optimal solution with a bounded error. Unlike the existing results, our algorithm is executed only by using the first-order derivatives of the cost function which makes it computationally efficient for optimization with time-varying cost function. We compare our algorithms to the gradient descent algorithm and show why gradient descent is not an effective solution for optimization problems with time-varying cost. Several examples including solving a model predictive control problem cast as a convex optimization problem with a streaming time-varying cost function demonstrate our results.

Marjan Beheshti, Majid Rostami, Bo Chen

Audio deepfake detection systems often fail to generalize across domains because they rely on features tied to specific attacks or recording conditions. Self-supervised speech models offer rich multi-layer representations, yet existing approaches either use a single layer or fuse all layers indiscriminately, and only reveal layer importance after training. We propose a model-agnostic, two-stage methodology that identifies informative depth zones before any task-specific model is trained. In the first stage, lightweight XGBoost probes evaluate each transformer layer's cross-domain discriminative power, producing a layer ranking. In the second stage, a compact neural classifier fuses only the selected layers through per-layer attention pooling and a shared bottleneck projection, while the backbone remains frozen. Applied across three backbones, the probing reveals two key findings. First, informative layers cluster in depth zones rather than at uniquely optimal positions: within-zone substitutions fall within multi-seed noise, while zone violations degrade performance by up to 5x. Second, the probing produces backbone-specific selections rather than a fixed layer recipe. On XLS-R-300M, four probing-selected layers with 1.34M trainable parameters achieve 4.94 +/- 0.32% equal error rate on In-The-Wild and 5.07% cross-domain average over four shared datasets, a 28% relative improvement over the best prior frozen-backbone result (Xiao and Vu, 2025) using all 25 layers with identical training data.

M. Rostami, S. S. Kia

In this article, we consider the problem of unconstrained time-varying convex optimization, where the cost function changes with time. We provide an in-depth technical analysis of the problem and argue why freezing the cost at each time step and taking finite steps toward the minimizer is not the best tracking solution for this problem. We propose a set of algorithms that by taking into account the temporal variation of the cost aim to reduce the tracking error of the time-varying minimizer of the problem. The main contribution of our work is that our proposed algorithms only require the first-order derivatives of the cost function with respect to the decision variable. This approach significantly reduces computational cost compared to the existing algorithms, which use the inverse of the Hessian of the cost. Specifically, the proposed algorithms reduce the computational cost from $O(n^3)$ to $O(n)$ per timestep, where $n$ is the size of the decision variable. Avoiding the inverse of the Hessian also makes our algorithms applicable to non-convex optimization problems. We refer to these algorithms as $O(n)$-algorithms. These $O(n)$-algorithms are designed to solve the problem for different scenarios based on the available temporal information about the cost. We illustrate our results through various examples, including the solution of a model predictive control problem framed as a convex optimization problem with a streaming time-varying cost function.